The equation which is required to solve how many of each board John needs is x + x - 7 = 23.
The number of 20-foot boards is 15.
The number of 16-foot boards is 8.
As per the given data, John needs 23 boards to build rafters for his house.
He can use 16-foot or 20-foot length boards.
He needs seven fewer 16-foot boards than 20-foot boards.
Here we have to determine how many of each board John needs.
Let the number of 20-foot boards be x.
Then the number of 16-foot boards be x - 7.
Total number of boards are 23.
Equation to determine how many of each board John needs:
x + x - 7 = 23
2x - 7 = 23
2x = 23 + 7
2x = 30
x = 15
The number of 20-foot boards are 15.
The number of 16-foot boards are x - 7
= 15 - 7
= 8
The number of 16-foot boards are 8.
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michael has a drawer with 8 pairs of black socks and 12 pairs of white socks. without looking he takes a white pair of socks out of the drawer. what is the probability that the next pair he takes out is white?
The Probability that the next pair Michael takes out is black = 8 / 19
What is Probability?
Probability is deals with "occurrence of Random event. The value is expressed from 0 to 1".
According to the question,
Total number of pairs of socks = 8 + 12 =20
Probability of taking pairs of black socks, P(B )= 8 / 20
Probability of taking pairs of white socks, P(W) = 12 / 20
But after taking Black pair socks the total number socks = 19.
Hence, the Probability of taking Black pair socks from drawer is 8 / 19 .
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If a figure is a quadrilateral, then it has four sides.
A triangle does not have four sides.
A closed quadrilateral is a kind of polygon having 4 sides, 4 vertices, and 4 angles. A triangle doesn't have four sides because if it did, it wouldn't be a triangle. It would be a quadrilateral, the term used to describe geometric objects with four sides.
Three line segments combine to form a triangle, which is a straightforward closed curve or polygon. In Euclidean geometry, any three points, notably non-collinear ones, independently create a singular triangle and a singular plane.
In Euclidean geometry, any three points, notably non-collinear ones, independently create a singular triangle and a singular plane. polygon with 4 sides that is a quadrilateral.
One fascinating feature of a quadrilateral is that its opposite parallel sides are possible. Four non-collinear points are joined to create it. Since a triangle would not have four sides
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take away 7 from 4 times x
Answer:
4x-7
thats your answer
Step-by-step explanation:
:))))
So I’ve answered everything but perimeter can someone please figure that out for me?
The area of rectangle WXYZ is 115. 5 in. ² what is the perimeter of triangle XYZ

The perimeter of triangle XYZ is 38.95 inches
Consider the following figure.
The area of rectangle WXYZ is 115. 5 in.²
From given figure we can observe that PQ = 4 in.
So, XW = YZ = 2 × PQ
XW = YZ = 2 × 4
XW = YZ = 8 inches
This means, the width of rectangle WXYZ is 8 inches
We know that the area of the reactngle is given by the formula,
A = length × width
here, A = 115.5 in.² and width = 8 in.
115.5 = length × 8
length = 115.5 / 8
length = 14.44 in.
So, XY = WZ = 14.44 in.
For right triangle XYZ using Pythagoras theorem,
XZ² = XY² + YZ²
XZ² = 14.44² + 8²
XZ² = XY² + YZ²
XZ² = 272.51
XZ = 16.51 in.
So, the perimeter of triangle XYZ would be,
P = XY + YZ + XZ
P = 14.44 + 8 + 16.51
P = 38.95 inches
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A blender has blades as shown.
A rotation of the 270º will map the blade formed by triangle CBD onto the blade formed by triangle EDF.
How to obtain the counter clockwise rotation?The rotations are defined as clockwise or counterclockwise as follows:
Clockwise: from right to left.Counterclockwise: from left to right.The entire circumference formed by the image has an angle measure given as follows:
360º.
Triangle EDF is 3/4 of the circumference away from triangle CBD, hence the angle measure of the counterclockwise rotation is given as follows:
3/4 x 360º = 0.75 x 360º = 270º.
Which is the angle measure used to complete the blank in this problem.
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if it takes 8 seconds for a ball to roll 24 meters downhill, what is the average speed of the ball?
The average speed of the ball which travelled 24 meters in 8 seconds is 3m/s.
What is the average speed of the ball?Speed is simply referred to as distance traveled per unit time.
Mathematically, Speed = Distance ÷ time.
Given the data in the question;
Distance travelled by the ball = 24 metersElapsed time = 8 secondsSpeed of the ball = ?To determine the average speed of the ball, plug the given values into the above equation and simplify.
Speed = Distance / time
Speed = 24 meters / 8 seconds
Speed = 3m/s
Therefore, the speed is 3 meters per seconds.
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Determine the values of m in the equation m2 = 36.
m = 18
m = 6
m = ±18
m = ±6
the values of m in the equation m^2 = 36 , is m= ±6.
What is Square root?A square root of a number is a value that, when multiplied by itself, gives the number. In mathematics, a square root of a number x is a number y such that y² = x; in other words, a number y whose square is x.
here, we have,
given that,
the equation m^2 = 36.
taking root on both side, we get,
m= ±6.
Hence, the values of m in the equation m^2 = 36 , is m= ±6.
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Please help me ASAP please please please
The two column proof to show that ABCD is a parallelogram is as shown below
How to complete two column proof?A two-column proof is defined as a geometric proof that consists of a list of statements, and the reasons that we know those statements are true.
Statement 1; BD bisects AC
Reason 1; Given
Statement 2; ∠BAC ≅ ∠DCA
Reason 2; Given
Statement 3; AB║ CD
Reason 3; Properties of parallelogram
Statement 4; ∠BEA ≅ ∠CED
Reason 4; Alternate Interior angles
Statement 5: AE ≅ EC
Reason 5: Diagonals of a parallelogram bisect each other
Statement 6: ΔABE ≅ ΔCDE
Reason 6: SAS Congruency postulate
Statement 7: BA ≅ DC
Reason 7: Properties of parallelogram
Statement 8: ABCD is a parallelogram
Reason 8: Corresponding parts of congruent triangles are congruent
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The amount a tree grows in one month is directly proportional to the amount of water it is given When the tree is given 23 gallons of water, it grows 4 cm that month. What is the constant of proportionality for this variation? Round your answer to the nearest thousandth
The constant of proportionality for this variation is 0.174cm/gallon .
Every relationship that always maintains the same ratio is referred to be proportionality. For instance, the average amount of apples per tree determines the proportionality between both the quantity of apples in a crop and the number of trees in the orchard.
Let the amount a tree grows in one month be - x
The amount of water given be - y
If the amount a tree grows in one month is directly proportional to the amount of water given, then
x ∝ y
x = ky
k is defined as the constant of proportionality
k = [tex]\frac{x}{y}[/tex]
Given
x = 4cm
y = 23 gallons
k = [tex]\frac{4}{23}[/tex]
k = 0.174cm/gallon
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8. A cylindrical basket has a volume of 15 cubic feet. If the height of the basket is 1.5 feet, what is the area of the base of the basket?
The Area of the base of the basket is 10 ft².
What is volume and area of the cylinder? Volume and area are two different measures of a cylinder. Volume measures the amount of space an object occupies, while area measures the two-dimensional surface of an object. The volume of a cylinder is equal to the area of its base multiplied by its height. The area of a cylinder is equal to the circumference of its base multiplied by its height.To find the volume of a cylinder, multiply the area of its base by its height. The area of the base can be calculated by multiplying pi (3.14) by the radius of the base squared. The circumference of the base can be calculated by multiplying pi (3.14) by the diameter of the base. The height of the cylinder is simply the distance between the two bases. Once the area of the base and the height of the cylinder are known, the volume of the cylinder can be calculated by multiplying the area of the base by the height.The area of the cylinder can be calculated by multiplying the circumference of the base by the height.Given,
Volume of basket = 15 cubic feet
h = 1.5 ft
V = πr²h
15 = πr² (1.5)
πr² = 15/1.5
πr² = 10 ft²
Area of base of the basket = 10 ft²
(or)
15 = πr² (1.5)
r = √15/π(1.5)
Simplifying the values, we can get radius of basket = 1.78
Then, area of base of basket = πr²
Substituting the values of π = 3.14 and r = 1.78 in above formula, we get,
Area of base of the basket ≈ 9.95 ft²
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A cylinder can be measured in two separate ways: volume and area. As area gauges an object's two-dimensional surface, volume gauges how much space an object takes up.
What area of the base of the basket?If the cylinder's height and base area are known, the cylinder's volume may be determined by multiplying the base area by the cylinder's height. By dividing the base's circumference by its height, one may get the cylinder's area.
Given,
Volume of basket = 15 cubic feet
h = 1.5 ft
V = πr²h
15 = πr² (1.5)
πr² = 15/1.5
πr² = 10 ft²
Area of base of the basket = 10 ft²
(or)
15 = πr² (1.5)
r = √15/π(1.5)
We may obtain radius of basket = 1.78 by simplifying the numbers.
Then, area of base of basket = πr²
By replacing the values of 3.14 and 1.78 in the formula above, we obtain,
Area of base of the basket ≈ 9.95 ft²
Therefore, The Area of the base of the basket is 10 ft².
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What is 2/3 x 9/16?
Answer:
.375 as a decimal
Step-by-step explanation:
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 9 above 80 to 89, at 9 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Flower Town.
When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
IQR, because Desert Landing is skewed
IQR, because Desert Landing is symmetric
Range, because Flower Town is skewed
Range, because Flower Town is symmetric
Range provides a precise measurement of variability for both sets of data because it compares the greatest and lowest values in a dataset.
It is a helpful measure of variability for comparing the constancy of temperature between Desert Landing and Flower Town because it is unaffected by skewness or symmetry.
The histogram is what?A histogram is a graph that shows how a dataset is distributed. In a dataset, it is a way to show the frequency of various values or ranges of values.
In a histogram, the y-axis normally indicates the frequency or count of the values, and the x-axis typically shows the values or ranges of values.
Each bin in the data is represented by a bar whose height is equal to the number of observations in that bin. The data is divided into bins. The distribution of data is visualized using histograms, which are also used to spot anomalies and spot patterns or trends in the data.
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assume we are playing a game. you will roll an unfair dice with the following probability p = {1 : 0.1, 2 : 0.3, 3 : 0.1, 4 : 0.2, 5 : 0.1, 6 : 0.2}. (i.e. p(x = 2) = 0.3). the reward depends on whether the rolled dice shows an even number or an odd number. if you roll an even number you will win 100$ and if you roll an odd number you will lose 200$ (i.e. you win -200$). what is the expected reward amount (the expected value may be negative)?
The expected reward amount is -10$.
Expected Reward Amount
The product of the likelihood of each occurrence and the related reward results in the anticipated reward amount, which is equal to the expected reward value.
According to the question
We must multiply the odds of rolling an even number by the payout for rolling an even number, the odds of rolling an odd number by the payout for rolling an odd number, and then sum the results to determine the expected payoff.
P(odd) = P(1) + P(3) + P(5) = 0.1 + 0.1 + 0.1 = 0.3
P(Even) = P(2) + P(4) + P(6) = 0.3 + 0.2 + 0.2
The expected reward is calculated as follows:
(p(even) * 100 + (p(odd) * 200)) = (0.7 * 100 + (0.3 * 200)) = 70 - 60 = -10
As a result, the predicted reward is -10$.
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Neely has $1. 73 in coins. He gives his friend 1 quarter and 3 nickel
What is the value of the coins he has left?
If Neely has $1.73 in coins and he gives his friend 1 quarter and 3 nickel , then the value of coins he has left is $1.65 .
the value of number of coins Neely has is = $1.73 ;
he gives his friend "1 quarter" , and the value of 1 quarter in dollar is = $0.25
the amount left with Neely is = $1.73 - $0.25 = $1.48 ;
next he gave his friend "3 nickels" , and value of 3 nickels in dollars in $0.15 ;
So , the amount left with Neely is - $1.48 - $0.15 = $1.65 .
Therefore , the Neely is left with $1.65 value of coins .
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Logan spent $275 for a tree for the front yard. He was charges 7% sales tax. How much money did he spend on the sales tax? How much did he spend in total?
Answer:294,25$
Step-by-step explanation:
you make 7% of 100 multiply by $275 and the price that gives you you make more $275 and that gives you your results
The table represents a proportional relationship. Write an equation to represent the relationship.
For the table of values gives, the equation of line is obtained as y = 1/3x.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The coordinate points for cups of flour, x and loaves of bread y is given in the table.
The slope-intercept form of an equation is - y = mx + b
To find the slope m use the formula -
(y2 - y1)/(x2 - x1)
Substituting the values in the equation -
(3 - 2)/(9 - 6)
1/3
So, the slope point is obtained as m = 1/3.
The equation becomes - y =1/3 x + b
To find the value of b substitute the values of x and y in the equation -
2 = 1/3(6) + b
2 = 2 + b
b = 2 - 2
b = 0
So, the value for b is 0.
Now, the equation becomes -
y = 1/3x + 0
y = 1/3x
The graph is plotted for the equation.
Therefore, the equation is y = 1/3x.
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Drag each object to show whether cost is proportional to area in the situation represented.
The image has been dragged to show where cost is proportional to area and attached
When is a linear function proportional?Equation y = kx can be used to define proportional functions, which are linear functions that include the origin.
While all proportional functions are linear, not all linear functions are proportional functions.
From the table the equation s calculated to be y = kx
where k = 1.25
for x = 400, y = 1.25 * 400 = 500
for x = 500, y = 1.25 * 500 = 750 and so on
this is a proportional function
For asphalt sealant the labor fee added made the function not to be a proportional function
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a fair six-sided die is tossed 300 times. find the expected value of the sample mean of the values obtained in these 300 tosses (write it up to first decimal place).
The expected value of the sample mean of the values obtained in these 300 tosses is 3.5
300 fair throws of a six-sided die are made.
The expected value of the sample mean of the results acquired from these 300 tosses must be determined.
Six sides make up a dice:
Every side of a fair dice has an equal chance of happening.
Now, each side's likelihood of being present is 1/6.
Now, the sample mean of the values collected in these 300 tosses is predicted to be equal to:
E(x) = Σx P(x =x)
= 1*1/6 + 2*1/6 + 3*1/6 + 4*1/6 + 5*1/6 + 6*1/6
= 1/6 + 2/6 + 3/6 + 4/6 + 5/6 + 6/6
= 1/6 (1+2+3+4+5+6)
= 1/6 (21)
= 21/6
E(x) = 3.5
Hence, the expected value of the sample mean of the values obtained in these 300 tosses is 3.5
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Dean's savings account started with $100. After one year, it had $110. The
second year, it had $121. The third year it had $133.10.
Is a single linear model a reasonable option for this data? Yes or No?
The statement that answers the linear model possibility is NO
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
Initial = 100
Year 1 = 110
year 2 = 121
year 3 = 133.10
The savings account balance is increasing at an inconsistently increasing rate, which is not linear.
The savings account starts with $100, and increases by $10 in the first year, by $11 in the second year, and by $12.10 in the third year.
This is an example of exponential growth, which cannot be modeled by a single linear equation.
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Explain whether there is enough information given in each figure to prove that the triangles are congruent using SSS or SAS. Fill in the table.
The triangles in this problem are similar using the SSS theorem.
What are similar triangles?Similar triangles are triangles that share these following two features:
Congruent angle measures.Proportional side lengths.For this problem, we have that the two triangles share two common angle measures.
A triangle is composed by three angles, and the sum of their measures is of 180º, hence the third angle measure will be equal for both triangles.
As the angle measures are equal, the side lengths are going to be proportional, thus the triangles are similar by the SSS theorem.
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Three lots with parallel side boundaries extend from the avenue to the boulevard find to the nearest tenth of a meter the fronteages of the lots
Three lots with parallel side boundaries extend from the avenue to the boulevard.
x + y + z = 140 meters
According to the proportion theorem,
Solving for x, using cross multiplication:
Similarly,
x/40 = z/35
solving for z by cross multiplication,
z = 35x/40
z = 7x/8
Now, the third proportions,
y/30 = z/35
Solving for y,
y = 30z/35
y = 6z/7
x + y + z = 140
4y/3 + 6z/7 + 7x/8 = 140
(224y + 144z + 147x)/168 = 140
224y + 144z + 147x = 23520
Substituting z = 7x/8,
224y + (144 × 7x/8) + 147x = 23520
224y + 126x + 147x = 23520
224y + 273x = 23520
Now,
Substitute y = 3x/4
(224×3x/4) + 273x = 23520
168x + 273x = 23520
441x = 23520
x = 53.33
Now,
We know that
y = 3x/4
so,
y = 40
And,
z = 7x/8
Z = 46.66
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Brianna has a points card for a movie theater.
She receives 55 rewards points just for signing up.
She earns 14. 5 points for each visit to the movie theater.
She needs at least 235 points for a free movie ticket.
Which inequality can be used to determine v, the minimum number of visits Brianna needs to earn her first free movie ticket?
The inequality 14.5v ≥ 235 can be used to determine the minimum number of visits Brianna needs to earn her first free movie ticket.
The inequality 14.5v ≥ 235 can be used to determine the minimum number of visits Brianna needs to earn her first free movie ticket.14.5v ≥ 235
To figure out how many visits Brianna needs to earn her first free movie ticket, we can set up an inequality. We'll set the left side of the equation equal to the total points needed for a free movie ticket (235 points). We'll set the right side of the equation equal to the points earned per visit (14.5 points) multiplied by the number of visits (v).
14.5v ≥ 235
The inequality 14.5v ≥ 235 can be used to determine the minimum number of visits Brianna needs to earn her first free movie ticket.
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How do you solve this problem?
Answer:
x = -1
Step-by-step explanation:
Since a triangle's angles all add up to 180 based on this formula: 180(n-2) (n being the # of sides of the shape you're solving for, and the total being the interior), we can set up this equation:
46 + (x+62) + 73 = 180
Now, we can solve for x:
x = 180-73-62-46
x = -1
a personal trainer analyzes the progress of her clients. so she calculates the body mass index (bmi) for each. the bmis for all of her current clients are summarized in the histogram below. histogram with 5 bars of heights 1, 3, 5, 2, 1 and bar edges of 18.1, 20.7, 23.3, 25.9, 28.5, and 31.1. the horizontal axis is labeled bmi and the vertical axis is labeled clients. she would like to offer a discount to her clients that have a current bmi of at least 25.9 in order to encourage them to keep working with her. the discount is for $50 off of their next month's training. if she were to offer these, how much total money would she give in discounts next month?
The total number of clients with a BMI of 25.9 or higher is therefore equal to 1 * 2.6 + 3 * 2
The total amount of money she would need to give in discounts next month can be found by calculating the total number of clients with a BMI of 25.9 or higher. To calculate this, the frequencies of each BMI range need to be multiplied by the width of the corresponding bar. The total amount of money she would need to give in discounts is then equal to the total number of clients with a BMI of 25.9 or higher multiplied by $50.
Using the histogram, the number of clients in each BMI range are: 18.1-20.7 (1), 20.7-23.3 (3), 23.3-25.9 (5), 25.9-28.5 (2), 28.5-31.1 (1).
The width of each bar is: 18.1-20.7 (2.6), 20.7-23.3 (2.6), 23.3-25.9 (2.6), 25.9-28.5 (2.6), 28.5-31.1 (2.6).
The total number of clients with a BMI of 25.9 or higher is therefore equal to 1 * 2.6 + 3 * 2
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15% of the contents of a 454 gram can of dog food is protein. How many grams of protein are in the can?
Answer:
68.1 grams
Step-by-step explanation:
454 × .15 = 68.1
A large district employs 3,461 teacher. If there are 28 students per teacher, how many students are there?
Answer:
If there are 3,461 teachers and 28 students per teacher, to find the total number of students, you can multiply the number of teachers by the number of students per teacher:
3,461 teachers * 28 students/teacher = 97,268 students
So there are 97,268 students in the district.
A cone has a diameter of
36 meters and a slant height of
24 meters. What is the height of the cone to the nearest tenth?
The height of the cone is about 15.9 meters.
The hypotenuse of the right triangle, which also contains the cone height as one of its legs, is formed by the radius (18 m) and slant height. You may find out the height (h) using the Pythagorean theorem.
The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the squares on the legs.
So,
18² + h² = 24²
h = √(576 -324) = √252
h ≈ 15.9 . . . . . meters
The height of the cone is about 15.9 meters.
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Noah and Lin are making paper cones to hold popcorn to hand out at a parent math night. They want the cones to hold 9π cubic inches of popcorn. What are two different possible values for height h and radius r for the cones?
The two different possible values for height h and radius r for the cones are height = 3 inches when radius = 3 inches and height = 4.5 inches when radius = 2 inches.
The volume of a cone is given by the formula [tex]V = (1/3)\pi r^2 h[/tex].
We can use this formula to find the values of h and r that will give us a cone with a volume of 9π cubic inches.
We have a volume of the cone -
(1/3)π[tex]r^2[/tex]h = 9π
solving for h, we get,
h = (3/[tex]r^2[/tex]) * 9
Now we have a formula for h in terms of r. We can substitute different values for r and see what values of h we get. Let's consider two possibilities:
case 1: r = 3 inches:h = (3/[tex]3^2[/tex]) * 9 = 3 inches
case 2: r = 2 inches:h = (3/[tex]2^2[/tex]) * 9 = 4.5 inches
So, one possible cone has a height of 3 inches and a radius of 3 inches, and another possible cone has a height of 4.5 inches and a radius of 2 inches.
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a ship at position (1, 0) on a nautical chart (with north in the positive y direction) sights a rock at position (4, 5). what is the vector joining the ship to the rock?
The vector joining the ship to the rock is t= 5i+5 j
A vector is a quantity or phenomenon that has two independent properties: magnitude and direction, a quantity that has both magnitude and direction but not position.
The direction is 0.9505 radians east of north.
The position vector of the ship: r= 1i+0j
The position vector of the ship: s= 4i+5j
The vector joining the ship to the rock is: t=r+s
t=(1 i + 0 j) + (4i + 5 j)
t=5i+5j
Θ=π/2-arctan(5/7)
Θ=0.9505 radians
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Please help im on a time limit and i need to turn this in asap!!
Questuon:Susan works for the school newspaper and wants to conduct a survey to ask students whom they will vote for in the upcoming School elections which sample should she choose to best represent the entire population ?
They will vote for in the upcoming School actions maybe they have to choose example should to best represent the entire population is they have to ask to every tenth student in the cafeteria.
Every Nth name from the list of target population members is chosen in systematic sampling. For instance, every tenth member on the list will be included in the sample. Thus, the 10th, 20th, 30th, and so forth will be chosen to make up the sample group.
According to this, they must consult a student in the tenth grade because he is the most knowledgeable about school and has the most experience of anybody.
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