The distance of the boat is 191.2 miles, 12.8° and N12.8E from the original location.
Using Trignometry to find the boat's distance:To calculate the distance, direction angle, and bearing of the boat from its original location, we will need to use trigonometry to determine the final position of the boat.
a) The distance traveled in the eastward direction is 130 miles. Then, using the bearing of N38E, we can calculate the northward and eastward distances traveled in the second leg of the journey. The bearing of N38E can be thought of as an angle of 38 degrees measured clockwise from due east.
Using trigonometry to calculate the northward distance traveled, we have,
(72 miles) * (sin 38°)
= 36 miles
And the eastward distance traveled is (72 miles) * (cos 38°)
= 59.04 miles.
The final position of the boat is at a distance can be calculated by:
130 miles east + 59.04 miles east
= 189.04 miles east and 36 miles north from the original location.
b) To find the distance from the original location, we use the Pythagorean theorem,
d = [tex]\sqrt{189.04^{2} +36^{2} }[/tex]
d = 191.2 miles
To find the direction angle, we use arctan(north/east) = arctan(36/189.04) = 12.8°
Bearing is the direction angle measured clockwise from north. So, bearing = 12.8°
Hence, the final position of the boat is 191.2 miles, 12.8°, and N12.8E from the original location.
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X + 15 _> 64.5 in inequality from
Answer:
X ≥ 49.5
Step-by-step explanation:
X + 15 ≥ 64.5
Subtract 15 from both sides
X ≥ 49.5
So, the answer is X ≥ 49.5
  PLS PLS HELP ASAP!!! ILL GIVE BRAINIEST AND 50 POINTS!!!
Identify or mark the missing side or angle that would make triangle ABC congruent to triangle PDF by AAS. Explain why it’s the missing side or angle.
Answer:
Mark angles C and F as congruent.
Step-by-step explanation:
Angle-Angle-Side (AAS) Congruence Theorem
If any two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
The given triangles have one corresponding angle and one corresponding side marked as congruent.
To satisfy AAS congruency, another pair of corresponding angles need to be marked as congruent.
As an included side is the side between two angles, we cannot mark angles A and P as congruent, as this would not satisfy AAS congruency since sides AB and PD would be the included sides.
Therefore, to make triangle ABC congruent to triangle PDF by AAS, mark angles C and F as congruent.
The bill is 42 dollars, taxes is 9%, and the tip given is 18%. What's the Total?
The total cost of the bill that sells for $42 is $54.0204
How to determine the total cost of the bill?From the question, we have the following parameters that can be used in our computation:
Cost of the bill = $42
Sales tax = 9%
Tip = 18%
The total cost of the bill that sells for $42 is then calculated as
Total cost = Selling price * (1 + Sales tax) * (1 + tip)
Substitute the known values in the above equation, so, we have the following representation
Total cost = 42 * (1 + 9%) * (1 + 18%)
Evaluate
Total cost = $54.0204
Hence, the total cost is $54.0204
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Which statement best describes the function?
A. The function is negative when x<0
B.the function is negative when x<0 and when x>0
C. The function is never negative
D. The function is negative when x>0
Therefore ,Because the function lies above the x-axis for values of x > 0, it is positive. So, choice D is the right one.
What is function?Each x value in the domain has one but only one y value
range, according to the rule of a function. Definition. If there is only one and only one value of x such that f(x) = y, then the function is one-to-one.
Here,
It is discovered that the right answer is provided by: D using function ideas. If x is zero, the function is negative.
The graph is positive if it is located above the x-axis.
A negative graph is one that is located below the x-axis.
The graph of the function in this issue is shown by the red line, and:
The function is negative for x values less than 0 since it is below the x-axis.
Therefore ,Because the function lies above the x-axis for values of x > 0, it is positive. So, choice D is the right one.
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I don’t know I just need the answer
Emily's least favorite weekly chore is mowing the lawn, even though it only takes her about 30 minutes. Her family's lawn is 1,000 square yards, but her parents are thinking about moving to the country, where they would have 5 acres of land. If the time it takes Emily to mow a lawn is proportional to its area, how many hours would it take her to mow 5 acres?
It will take Emily 12.1 hours to mow 5 acres
How determine how many hours it will take to mow 5 acres?
Variation is the relation between a set of values of one variable and a set of values of other variables
Let T and A represent the time and area respectively
Since the time it takes Emily to mow a lawn is proportional to its area. We can write:
T α A
T = kA (where k is constant of proportionality)
It takes her about 30 minutes to mow 1,000 square yards. That is:
T = 30 and A = 1,000
T = kA
30 = 1000k
k = 30/1000
k = 0.03
Time for 5 acres:
5 acres = 5 × 4840 = 24200 square yards (1 acre = 4840 square yards)
T = kA
T = 0.03 × 24200
T = 726 minutes (divide by 60 to get time in hours)
T = 12.1 hours
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Rebecca carries a balance on her credit card each month. Today is the first day of the new, 28-day billing cycle. The current balance is x and the APR is 24%. Rebecca is buying a friend an expensive gift that cost $1,400 that she plans to put on her credit card. this will be her only purchase this month, and she will be making this purchase on the last day of the month
Part A
If her Finance charge will be $51, write and solve an equation to determine her current balance on her credit card. Show work
Part B
How much in finance charges can she save by making the purchase on the last day of the billing cycle versus the first day of the billing cycle? Explain how you determined your answer
Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the laset day of the billing cycle instead of on the first day.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The billing cycle for the month = 28 days
Current beginning balance = x
Annual percentage rate (APR) = 24%
Monthly percentage rate (MPR) = 2% (24% ÷ 12)
Purchase on the last day = $1,400
Total finance charge for the month = $51
Finance charge for the last-day purchase = $1 ($1,400 x 2% x 1/28)
Finance charge for the beginning balance = $50 ($51 - $1)
The current beginning balance, x = $2,500 ($50 ÷ 2%)
Equation for current beginning balance, x = 51 - 1 ÷ 0.02
Total finance charge for the last-day purchase = $28 ($1,400 x 2%)
Savings in finance charge by purchasing on the last day = $27 ($28 - $1)
Hence, Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the laset day of the billing cycle instead of on the first day.
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As drug A gets absorbed into the body, less and less of it remains. A scatterplot of data showed a curved relationship between hours since drug A was administered (x) and the number of milligrams of drug A remaining in the body (y). Taking the logarithm of the milligrams of drug A remaining obtains a linear pattern on a scatterplot, and creates the following printout from a statistical software package:
Predictor Coef SE Coef t-ratio P
Constant 3. 00 0. 401 7. 481 0. 000
Time -0. 0737 0. 005 -14. 74 0. 000
s= 0. 014 R-sq= 98. 5% R-Sq(Adj)= 99. 0%
Required:
Write down the correct equation that follows from this output?
The equation is
log ( milligrams of drug A ) =3 - 0.0737 ( Time)
As per the details stated above,
Curved relationship between the number of milligrams of drug A is (x) still in the body and the number of hours since drug A was delivered (y)
The co-efficient of the constant is 3.00
the co-efficient of the time is -0.0737
the SE co-efficient of the constant is 0.4017
the SE co-efficient of the time is 0.005
the t-ratio of the constant is 7.481
the t-ratio of the time is -14.74
now the equation formed is
logarithm of drug A in milligrams is (The co-efficient of the constant - the co-efficient of the time )
that is log ( milligrams of drug A ) =3 - 0.0737 ( Time).
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A student-athlete can run 10 yards in 6 seconds. Which equation shows the number of yards that can be run in s seconds
The equation for the maximum number of yards per second that can be run is y = 5/3 s.
Define the term Direct Variation?Two quantities are said to be fluctuating directly if they are coupled in a way that an increase for one quantity suggests an increase in the other and a drop in one implies a decrease in the other. The direct variation equation, which connects the two values y and x, looks like this: y=kx, where k is the variational constant.A direct variation measurement between distance covered and time taken can be composed as:
y=kx,
where,
y stands for the number of yards, s stands for the number of seconds, and k is really the constant of variation.This is because the athlete's distance travelled directly varies with the amount of time it takes.
Find k using the given values:
y=kx,
10 = k(6)
k = 10/6
k = 5/3
As a result, the equation for the maximum number of yards per second is y = 5/3 s.
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How to do log2 in Excel?
The syntax for using BASE in Excel is "=LN(number,base)" where "number" is the number for which you want to calculate the logarithm and "base" is the base to which the logarithm should be calculated.
For example, if you want to calculate the logarithm of 10 to the base 2, you would use the formula "=LN(10,2)".
The idea is to express the given integer (20) in terms of either the base or the values given (3 and 5).
Next, since we have the multiplication sign, we use the addition law:
The power of the number becomes the product of the log, so we have:
When you have the same base and number, the result is always 1.
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What is the name of σ?
In mathematics, the symbol " σ" is "σ" (sigma) which is commonly used to represent the sum of a set of values.
It is used to indicate that a series of values are to be added together. For example, the notation "Σx" is read as "the sum of x" and it means to add all values of x together. It is often used in mathematical analysis, statistics, and physics.
For instance, in statistics, the symbol "σ" is used to represent population standard deviation, which is a measure of the dispersion of a set of data points from the mean.
In probability theory, the symbol "σ" is also used to represent the standard deviation of a random variable.
In general, the specific meaning of the symbol "σ" depends on the context in which it is used.
It is also known as Summation notation.
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A farmer sells eggs at a market. She offers three different sizes.
For any size, the weight of each egg can vary up to 8%.
Calculate the missing values in the table.
Is it possible for an egg to be both large and extra large?
Yes
The missing values in the table can be calculated by multiplying the given weights by 0.92 and 0.88 to get the maximum and minimum weights for each size.
Small egg:
Minimum weight = 1.2 * 0.92 = 1.104 ounces;
Maximum weight = 1.2 * 1.08 = 1.296 ounces
Medium egg:
Minimum weight = 1.6 * 0.92 = 1.472 ounces;
Maximum weight = 1.6 * 1.08 = 1.728 ounces
Large egg: Minimum weight = 2 * 0.92 = 1.84 ounces; Maximum weight = 2 * 1.08 = 2.16 ounces
Extra Large egg: Minimum weight = 2.4 * 0.92 = 2.208 ounces; Maximum weight = 2.4 * 1.08 = 2.592 ounces
Yes, it is possible for an egg to be both large and extra large, as long as the weight of the egg is between 1.84 and 2.592 ounces.
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This is mad confusing
Answer: 112 degrees
Explanation:
By the alternate interior angles theorem, m<CAD=40 and m<ACD=28. The quadrilateral is divided into two triangles. The sum of the angles of a triangle is equal to 180 degrees. Now that you know the measurements of two out of the three angles, you can add them up and subtract them from 180.
180-(40+29)=112
Solve −1/5x=6 (probably very easy but I zoned out and missed a lot)
Answer:
-30
Step-by-step explanation:
-1x/5 = 6
-x/5 = 6
-x = 30
x = -30
Park rangers plan to expand the area of a park to 506 square miles. Currently, the length of the park is 18 miles and the width is 17 miles. They want to extend the length and the width by the same number of miles. If they are successful, what will the new dimensions of the park be? Explain and I need this before tomorrow
As 200 is not a perfect square it is not possible to increase the dimensions of the park by the same number of miles.
What are the area and perimeter of a rectangle?The area of a rectangle is the product of its length and width.
The perimeter of a rectangle is the sum of the lengths of all the sides.
We know the area of a rectangle is (length×width).
Given, Park rangers plan to expand the area of the park to 506 square miles.
Currently, the park has an area of (18×17) = 306 square miles.
Therefore, The amount of square miles they need to increase is (506 - 306)
= 200 miles.
Now, They also want to increase the length and the width by the same amount but 200 is not a perfect square so it is not possible to increase the dimensions by the same amount.
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-2(4 - 3x) - 6x = 10
Answer:
this is a problem with no solution look it up if you dont beleve me
Step-by-step explanation:
Explain how the quotient was determined.
please help solve this its for geometry
Answer:
Step-by-step explanation:
1.RS+ST=RT. so 9y+2+2y+7=15y-11
2.11y+9=15y-11
3.15y-11y=11+9
4.4y=20
finally we find the answer is y=5
Someone please help! Picture attached
Answer:
third side = 3
Step-by-step explanation:
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
let the third side be x , then
x² + 4² = 5²
x² + 16 = 25 ( subtract 16 from both sides )
x² = 9 ( take square root of both sides )
x = [tex]\sqrt{9}[/tex] = 3
Which shape has atleast one pair of perpenicular sides
The fourth shape which is a square has at least one pair of perpendicular sides.
What is a quadrilateral?A quadrilateral is a closed object in geometry that is created by connecting four points, any three of which are not collinear. There are 4 sides, 4 angles, and 4 vertices in a quadrilateral.
In the third figure, it is a parallelogram,
In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.
The sum of adjacent angles is 180° but individuals are not right angles.
The fourth figure is a square and by the properties of a square, all the interior angles are right angles.
Therefore, It has two pairs of perpendicular sides.
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A manufacturer tests 1200 computers and finds that 9 of them have defects. Find the probability that a computer chosen at random has a defect. Round your answer to the nearest hundredth.
Probability that computer chosen at random has defect is 0.0075.When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes.
What is probability?It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability. For instance, the theoretical chance of getting a head when tossing a coin is 12.
Total number of computers=1200
Total number of damage computers=9
Probability that question chosen at random has defect = 9/1200=0.0075
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PLEASE HELP I WILL GAVE A BRAINLY Will you guys show me how to make a graph that shows the relationship between height and years. All the other info is filled out so please use that. Thank you for helping!!!
Answer:
Conclusion: Straight line upwards from point (0,3) to (3, 5.25)
Step-by-step explanation:
Your part (a) answer is absolutely correct.
Equation is y = 3/4x + 3
For part (b), you are correct to say that the y-intercept of the graph is 3. The implication is that the initial height of the tree is 3 feet tall. (When the tree just starts to grow at time = 0 years)
Your part (c) answer is absolutely correct as well.
For the graph part,
x = years (independent variable)
y = height (dependent variable)
From the equation you have constructed in part (a), the y-intercept of the graph is 3. Hence, a point (0, 3) can be first plotted in the graph.
Secondly, for part (c), you have also obtained the answer (3, 5.25). Plot that point on the graph as well.
Next, we can see that the graph in (a) is a linear graph in the form y = mx + c, where m is the gradient and c is the y-intercept.
Hence, you can easily draw a straight line upwards from (0,3) to (3,5.25) . It is expected as the gradient of the graph is 3/4, which is a positive number.
the american veterinary association claims.. what is the probabilty that your anual cost will ve within 5 of the mean
The probability that the annual cost will be 5 of the mean is 0.0912.
How does probability analysis work?A method used by risk managers to predict upcoming events, like accidental and commercial losses. In order to determine a probability distribution that can be applied to forecast future losses, this procedure involves reviewing historical loss data.
X = Annual cost of medical care for dogs.
X~ Normal (μ = 200, σ = 60)
Sample size n = 16
We know that the sample mean Xbar has a normal distribution with mean = μ and sd = σ/√n
Xbar ~ Normal (μ’ = 200, σ’ = 60/√16 = 15)
Required probability -
P[Average cost of medical care for 16 sampled dogs is > 220]
= P[Xbar > 220]
= P[(Xbar-μ’)/σ’ > (220-200)/15]
= P[Z > 1.3333], Z is a standard normal variable.
= 1 - P[Z < 1.3333]
= 1 - 0.9087, from standard normal table.
= 0.0912
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The complete question is:
A veterinary association claims that the annual cost of medical care for dogs averages $200 with a standard deviation of $60, and for cats averages $240 with a standard deviation of $70. Assume the costs follow a normal distribution. What is the probability the average annual cost of medical care for 16 randomly chosen dogs is greater than $220.
An auditorium has 30 seats in the first row, 38 seats in the second row, 46 seats in the third row, and so on. how many seats are in the 10th row?
a. 60
b. 93
c. 102
d. 110
Answer:
Step-by-step explanation:Its actually 102, not 110
RIGHT ANSWER WILL GET BRAINLEIST
A circular table has a diameter of 3 feet. Kristin is taping a piece of border around the edge of the table. Exactly how much border does Kristin need?
Exact length of border required by Kristin is calculated to be 9.42 ft.
This question can be solved using the concept of circumference of a circle.
The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were expanded out and straightened out to a line segment, the circumference would be the length of the arc. The curve/arc length around any closed figure is more often referred to as the perimeter. The term "circumference" can also refer to the circle's actual location, which corresponds to a disk's edge. A sphere's circumference is equal to the length of any one of its great circles.
Circumference of a circle is given by 2πr.(r is the radius of the circle)
In the given question,
diameter= 3ft
radius= half times of diameter
radius= 1.5 ft.
Circumference= 2πr
= 2×3.14×1.5
=9.42 ft
Kristin will require 9.42 ft of border around the edge of the table.
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43 inches tall. Each book 1/2 - inch thick
Answer:
If you're asking how many books there are its 86.
Step-by-step explanation:
If each book is 1/2 thick that means there are 2 books per inch.
Because there are 43 inches you're going to multiply by 2.
43(2)= 86.
Hope that helped, have a good day!
PLEASE HELP ME ASAP!!!!!!!
At a carnival, Diana sees a balloon shooter game. The ticket cost is $3. The rule is that the first person to shoot 10 balloons from a total 30 balloons wins $10. What is the expected payoff for the winner?
Answer:
$13
Step-by-step explanation:
The expected payoff for the winner would be the ticket cost, $3, plus the prize money, $10, which totals $13. This is the expected value of playing the game. However, it's important to note that this does not guarantee that the winner will receive exactly $13, as the outcome of the game is dependent on chance and the player's skill. There is always a chance that the player could win more or less than the expected value.
A karaoke machine regularly costs $146 and is on sale for 35% off. What is the discount?
Answer:51.1
Step-by-step explanation:
In right triangle abc, altitude cd with length h is drawn to its hypotenuse. we also know ad = 12 and db = 3.
The value of h is 6.
Now, According to the question:
In right triangle, ABC
Given data:
AD = 12 and DB = 3
The equivalent ratio of the triangles is:
h : 12 = 3 : h
Express as fractions
[tex]\frac{h}{12} =\frac{3}{h}[/tex]
Cross Multiply:
[tex]h^2[/tex] = 36
Take positive square roots of both sides
h = 6
Hence, the value of h is 6.
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Maria believes that she will get a 1 hit in 10% of her softball games, 2 hits in 30% of her games, 3 hits in 55% of her games, and 4 hits in 5% of her games. About how many hits can Maria expect to have each game
According to the probability or likelihood , Maria can expect 2 hits in the game.
What person founded probability?Blaise Pascal and Pierre de Fermat are recognized as the fathers of probability because they laid the foundation for the field by thinking through a gambling issue posed by Chevalier de Mere in 1654.
[tex]E(X)=x.P(X=x)[/tex]
Given,
[tex]P(X=1)=0.20\\P(X=2)=0.25\\P(X=3)=0.50\\P(X=4)=0.05\\[/tex]
putting in formula,
[tex]E(X) = (1*0.20)+(2*0.25)+(3*0.50)+(4*0.05)=2.4[/tex]
As the number can not be fraction, hence number of hit will be 2.
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