The magnitude of the total velocity of the boat is 38 knots, and the direction is 32°, so the correct option is d.
How to get the velocity of the boat?
First, we need to write need to find the component of the two given velocities.
For the boat, the magnitude is 28 knots and the angle is 36°, then the components are:
x-component = (28 knots)*cos(36°) = 22.65 knotsy-component = (28 knots)*sin(36°) = 16.46 knotsFor the wind, the components are:
x-component = (10 knots)*cos(22°) = 9.27 knotsy-component = (10 knots)*sin(22°) = 3.75 knotsAdding these, the total components of the boat's velocity are:
x-comp = 22.65 knots+ 9.27 knots = 31.92 knotsy-comp = 16.46 knots + 3.75 knots = 20.21 knotsThen the magnitude of the velocity is:
|V| = √( (31.92 knots)^2 + (20.21 knots)^2) =37.78 knots
That can be rounded to 38 knots
To get the angle, we take the arctangent of the quotient between the y-component and the x-component:
a = Atan(20.21 knots/31.92 knots) = 32.34°
Then the correct option is d) 38 knots and 32°
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Answer:
It is 38 knots; 32 degrees
Step-by-step explanation:
The answer below is right
I took the test
Find the volume of this triangular prism.
Step-by-step explanation:
To find volume of triangular prism the formula is : 1/2 base× height × length
so,1/2 × 7cm × 6cm × 10cm
420cm³/2
= 210cm³
can someone help me with this queston
Step-by-step explanation:
1) option A OR B AS THEY ARE THE SAME
2) option a
Answer: question 1 is b
Question 2 is a
Step-by-step explanation: hope it helps
in question 1 a and b are the same so choose this or this
25/22 as a decimal rounded to the nearest hundreth
Answer:
1.14
Step-by-step explanation:
Long division! Image attached below!
The width of a rectangular garden is 9 feet, and its length is 12 feet. Three of these expressions equal the perimeter of the garden, in feet. Which expression does NOT?
Answer:
breadth does it 9 feet
12 feet
Abebi surveyed how many miles the students in her Algebra 1 class travel to get to school, and ended up with the following set of data: 4.75, 2.25, 3, 3.5, 1.75, 2.25, 1.5, 5, 4.5, 2.25, 2, 3, 2.65, 4.8, 3.5\
Match the measures of central tendency to the correct values.
Hint:
MEAN = Sum of the data/# of data values
MEDIAN = middle data value when values are listed least to greatest
MODE = value appearing the most times
RANGE = difference between the largest and smallest values
Answer:
Mean: 3.1
Median: 3
Mode: 2.25 appears 3 times
Range: 5 - 1.5 = 3.5
Mean = (4.75+2.25+3+3.5+1.75+2.25+1.5+5+4.5+2.25+2+3+2.65+4.8+3.5)/16
= 3.56625
Median = 3.50
Mode = 2.25
Range = 9.10
What type of triangle is defined by the following set of side lengths
12, 8, 16
Question 3 options
Acute
Obtuse
Right
Not a triangle
The type of triangle defined by the following set of side lengths is an obtuse triangle
Properties of a triangle.Triangles are 2-dimensional shapes with 3 sides and angles.
The triangle with the sides 12, 8 and 16 is considered a triangle since the sum of two of its sides is greater than the third.
The triangle is not right angle since the sum of its longest side is not equal to the sum of the square of other two sides.
This shows that the triaangle can either be acute or obtuse. Since one of the sides differes from the other by 8 units, hence one of its angles will be greater than 90 degrees.
This shows that the type of triangle defined by the following set of side lengths is an obtuse triangle
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HELP PLEASE I HAVE A TIME LIMIT
the net for a pentagonal prism has 7 regions and 10 vertices. use Euler's formula to find the number of segments
Using the Euler's formula, the number of segments in the pentagonal prism is: 15.
What is the Euler's Formula?The Euler's formula is given as, F + V = E + 2, where:
F = number of faces (number of regions)V = verticesE = number of edges (number of segments).Given that the pentagonal prism has the following dimensions:
F = 7V = 10E = number of segments = ?Plug in the values into the Euler's formula, F + V = E + 2:
7 + 10 = E + 2
17 - 2 = E
E = 15
Therefore, using the Euler's formula, the number of segments in the pentagonal prism is: 15.
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using the similar triangles below, solve for x !
Answer:
Step-by-step explanation:
Remarks.
This can be solved as a proportion. A proportion is 2 ratios making a total of 4 parts. If we know 3 of the parts, we can solve for the 4th.
63/(8x - 2) = 49 /42
Notice that the given parts of the top triangle are the numerators of the ratios. The 2 parts of the bottom triangle are the denominators of the proportions
Proportion
63/(8x - 2) = 49 /42
Solution
63/(8x - 2) = 49 /42 Cross Multiply
(8x - 2)*49 = 63 * 42 Combine the right.
(8x - 2)*49 = 2646 Divide by 49
8x - 2 = 54 Add 2 to both sides
8x -2+2=54+2 Combine
8x = 56 Divide by 8
8x/8 = 56/8
Answer: x = 7
What is the difference between the two fractions explain in full detail. Type out answer
Answer:
Step-by-step explanation:
There is no difference between the two fractions. I can show you this in the following way, assuming you understand the distributive property. We can write the fraction -7/2 in the following way:
[tex]-\frac{7}{2} =-1(7*2^-^1)[/tex]
Hopefully you agree with me that we can bring the 2 into the numerator if we switch the signs of the exponent. And hopefully you agree that a negative sign is equivalent to multiplying by -1. Therefore, this negative 1 can distribute to the 7 or the 2. It really does not matter. To sum this up:
[tex]-\frac{7}{2} =\frac{-7}{2} =\frac{7}{-2}[/tex]
For each number set in this assignment, give the mean, median, mode, and range. If one of these quantities does not exist in the set, then put "0". 47, 31, 84, 50, 68, 85, 67, 56
Answer:
Mean: 54
Median: 61.5
Mode: 0
Range: 54
Step-by-step explanation:
Mean: Add everything up and divide by the amount of numbers
(47 + 31 + 84 + 50 + 68 + 85 + 67 + 56 = 488/8 = 54)
Median: Put all numbers in order from smallest to largest, the middle number is the median. Since we have 2 middle numbers, we add both 67 and 67 together, then divide them by 2.
31, 47, 50, 56, 67, 68, 84, 85
(56 + 67 = 123/2 = 61.5
Mode: The mode is the number that appears most often in the set of given numbers.
(There are no numbers that appear more than once so the mode is 0)
Range: The range is the largest number subtracted by the smallest number.
(85 - 31 = 54)
When ranking candidates running for office, describe how it would or would not be possible for a voter to give two people the same rank.
It would be possible to give two people the same rank, as it is always possible to have a tie-breaker vote if two candidates are ranked the same by all voters.
It would be possible to give two people the same rank, as there are so many votes generated during the election that one vote giving two people the same rank would not make a difference.
It would not be possible to give two people the same rank, as ranking candidates means that one and only one candidate is given a specific rank.
It would not be possible to give two people the same rank, as the reason candidates are ranked is to make sure there are no ties.
Answer:
I believe it is Option C.
Step-by-step explanation:
There has only been one single tie since the passing of the 12th Amendment. It is a very low chance for a possible tie to take place, so they would have no reason to ensure it doesn't happen as it's already unlikely, ruling out option D. Giving two people the same rank would definitely make a difference as you are basically adding not 1, but two votes. Though it would even the count out, each person would gain 1 point, so it would make a difference. Option B is ruled out. This also potentially explains debunking A as there's no possible way to plan a tie to that extent. Again. ties happen very rarely, so it would be unlikely that voting for both candidates would impact the choice at all.
Carl is the owner of a shoe store and notices that his electricity bill has increased by 3%. Which of the expressions below represent a 3% increase?
1. a + 0.03a
2. a + 0.3a
3. 1.03a
4. 1.3a
expression 1 only
expression 2 only
expressions 1 and 3
expressions 2 and 4
Answer:
1 and 3
Step-by-step explanation:
please find the area of the shaded region. EFGH is a square
Which number line shows the solution set for Ip-31-97
-129
3
6 9 12
-12 -9
-6
-3
0
3
6
9 12
.
+
-12 -9
-6 3 0
+
9
12
o
3
-12 g 6
-3
0
12
Graph the solution to this inequality on the number line.
12x−3<−138
Answer:
Step-by-step explanation:
1. Solve
12x-3+3<-138+3 <=== Add three to both sides to simplify the inequality
12x÷12<-135÷12 <=== divide by 12 on both sides so we can find what x is so that we can graph the inequality
x<-11.25 <=== negative divided by positive is always negative
2. Graph
1) you find -11.25 on the number line
2) you put an ray with an empty/hollow circle facing towards the negative side
plsss need help nowwww
Answer:
49/12
Step-by-step explanation:
1 ⅓ can be written as 1 + 1/3
1 ⅓
= 1 + 1/3
LCM = 3
= 3/3 + 1/3
= ( 3 + 1 )/3
= 4/3
2 ¾
= 2 + 3/4
LCM = 4
= 8/4 + 3/4
= ( 8 + 3 )/4
= 11/4
1 ⅓ + 2 ¾
= 4/3 + 11/4
LCM = 3 x 4 = 12
4/3 x 4/4
= ( 4 x 4 )/( 3 x 4 )
= 16/12
11/4
= 11/4 x 3/3
= ( 11 x 3 )/( 4 x 3 )
= 33/12
16/12 + 33/12
= ( 16 + 33 )/12
= 49/12
Answer:
I don’t know if it correct, but when I solved it I got 4 1/12
Step-by-step explanation:
(1+2) (1/3 + 3/4)
3 + 13/12
3 + 1 1/12
3 + 1 + 1/12
4 + 1 /12
4 1/12
Three times a number increased by two
times another number equals 28. Two
times the first number increased by
three times the second number equals
27. Find the two numbers.
Answer:
r={21}
Step by Step Explanation:
PREMISES
Two times three plus a number, say, r=27
ASSUMPTIONS
Let r=the number
CALCULATIONS
The numerical expression “two times three plus a number r=27” can be denoted as:
(2×3)+r=27
6+r=27
6–6+r=27–6
0+r=27–6
r=21
PROOF
If r=21, then the equations
(2×3)+r=27
6+21=27 and
27=27 prove the root (zero) r=21 of the statement (2×3)+r=27
PREMISES
Two times three plus a number, say, r=27
ASSUMPTIONS
Let r=the number
CALCULATIONS
The numerical expression “two times three plus a number r=27” can be denoted as:
(2×3)+r=27
6+r=27
6–6+r=27–6
0+r=27–6
r=21
PROOF
If r=21, then the equations
(2×3)+r=27
6+21=27 and
27=27 prove the root (zero) r=21 of the statement (2×3)+r=27
Answer:
5 and 6
Step-by-step explanation:
let the 2 numbers be x and y , then
3x + 2y = 28 → (1)
2x + 3y = 27 → (2)
multiplying (1) by 2 and (2) by - 3 and adding will eliminate x
6x + 4y = 56 → (3)
- 6x - 9y = - 81 → (4)
add (3) and (4) term by term to eliminate x
0 - 5y = - 25
- 5y = - 25 ( divide both sides by - 5 )
y = 5
substitute y = 5 into either of the 2 equations and solve for x
substituting into (1)
3x + 2(5) = 28
3x + 10 = 28 ( subtract 10 from both sides )
3x = 18 ( divide both sides by 3 )
x = 6
The 2 numbers are 6 and 5
answer needed please
Answer:
the top answer should be stretched
How do you write 950% as a fraction, mixed number, or whole number?
what is 1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30*0.0
Answer:
435
Step-by-step explanation:
1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30*0.0= 435
Answer:
the answer is: 435
Step-by-step explanation:
1. Look at the sequence in this table.
n
1
2
3
4
On
5
an
а.
-1
1
3
5
7
Which function represents the sequence?
+ 1
A. a = 8,-1
B. a = 8,-1
+1
1+2
+ 2
n
a
c. a, = 2a,-1-1
a
D. a = 2a-,-3
-1
n
,
n
n1
option (C) is correct
Step-by-step explanation:[tex]a_1=-1-\infty[/tex]
[tex]a_2=1-2[/tex]
[tex]a_3=3[/tex]
[tex]a_4=5[/tex]
[tex]from \ (1)\ and\ (2)[/tex]
[tex]a_2=2(-1)-1=-1[/tex]
[tex]ie.,\ a_2=2(a_1)-1[/tex]
[tex]so,\ a_n=2a_n_-_1-1[/tex]
[tex]Answer:option\ (C)\ is\ Correct[/tex]
I hope this helps you
:)
Solve for xx. Round to the nearest tenth, if necessary.
sin U= |TS| / |US|
-> |US| = |TS| / sinU
-> x= 0.6 / sin 37°
-> x≈1,0
Edwin sells jars of jam for $1.20 each. Determine how many jars of jam Edwin needs to sell to break even if the variable cost per jar is $0.80 and fixed expenses are $42,500.00 per year. (2 points)
17,000
21,250
98,170
106,250
2.
(05.01 MC)
Haven Baskets manufactures 61,755 woven baskets each year. Determine the minimum sales price Haven Baskets must sell each basket for to break even, if the total annual fixed costs are $562,795.00 and the variable cost per basket is $15.25. (2 points)
$22.90
$24.36
$29.97
$33.25
3.
(05.01 LC)
Jaslyn makes 443 wooden frames per month. Calculate her monthly profit if she sells each frame for $28.99, has fixed monthly expenses of $3,692.00, and has variable expenses of $9.15 per frame. (2 points)
$4,876.50
$5,097.12
$5,124.56
$5,190.87
4.
(05.01 MC)
Luca owns a pool cleaning business. Luca wants to have a monthly profit of $6,135.00 with 45 customers, fixed monthly expenses of $2,345.00, and variable expenses of $16.90 per pool. Determine how much Luca needs to charge per customer to reach his profit goal. (2 points)
$154.32
$175.89
$199.87
$205.34
5.
(05.01 LC)
Rafi Smiles produces custom greeting cards. The company has fixed monthly expenses of $5,750.00 and variable expenses of $0.80 for each card they make. Determine the company's ROI if they are able to make 4,175 cards per month and charge $4.50 per card. Round the final answer to the nearest hundredth. (2 points)
94.00%
94.01%
106.36%
106.68%
The number of jars of jam that has to be sold in order to break even is 106,250.
The minimum sales price is $24.36.
The monthly profit is $5,097.12.
The price per customer is $205.34.
The ROI is 106.68%.
What is the breakeven point?
Breakeven quantity = fixed cost / price – variable cost per unit
$42500 / (1.2 - 0.8) = 106,250
What is the minimum sales price?
Minimum price = (fixed cost / breakeven sales) + variable cost
($562,795.00 / 61,755) + $15.25 = $24.36
What is the profit?
Profit = revenue - total cost
Revenue = 443 x 28.99 = $12,842.57
Total cost = $3692 + (9.15 x 443) = $7,745.45
Profit = $12,842.57 - $7,745.45 = $5097.12
What is the price?
Price = (profit + total cost) / number of customers
Total cost = $2,345 + (16.90 x 45) = $3,105.50
($6,135.00 - 3105.50) / 45 = $205.34
What is the ROI?
ROI = (profit / cost of the investment) x 100
Cost = fixed cost + variable cost
$5,750 + (0.80 x 4175) = $9090
Profit = total revenue - cost
(4.5 x 4175) - 9090 = $9,697.50
ROI = $9,697.50 / $9090 = 106.68%
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Please help me with this
254.47cm^2
Step-by-step explanation:
A= pi x 3x3
= 9pi
x2 (there is 2 circles)
18pi
C=pi x D
= pi x 6
= 6pi
Width of rectangle wrap perfectly around the circle, so the circumference of 6pi will become the width of the rectangle
Rectangle:
A=lxw
= 10.5 x 6pi
= 63pi
Add up:
63pi + 18pi = 81pi
81pi = 254.469.....
Round to nearest 100th would be 254.47cm^2
(100th is 1/100= 0.01)
Hope this helps!
Find the mean and the median of this data: 9, 6, 5, 3, 28, 6, 4, 7.
Answer: 9 is mean and median is 6
Step-by-step explanation:
what are the answers?
Answer:
Step-by-step explanation:
hello : 12=4x and x-3=0
A study claims that the average home sale price in Kansas is less than the average home sale price in Missouri. The average sales price for 35 home sales in Kansas is $240,993 with a standard deviation of $25,875. The average home sales price for 37 homes in Missouri is $249,237 with a standard deviation of $27,110. At the (alpha) a= 0.10, is there enough evidence to reject the study’s claim?
Complete a full hypothesis test for the following. Include the hypotheses, critical
value(s), test value and graph, your decision to reject or not reject, and a summary of
the information
Since [tex]|z| = 1.301 \leq z_1 = 1.64[/tex] null hypothesis on this data is not rejected.
Null and Alternative HypothesisData;
sample mean x1 = 240993population standard deviation σ1 = 25875sample size n1 = 35sample mean x2 = 249237population standard mean σ2 = 27110sample size n2 = 35significance level α = 0.10H_o = μ1 = μ2
H_o = μ1 ≠ μ2
This is a two-tailed test and population standard deviation will be used.
Test StatisticThe z-stat is
[tex]z = \frac{x_1 - x_2}{\sqrt{\frac{\sigma_1^2}{n_1}+ \frac{\sigma_1 ^2}{n_2} } } \\z=\frac{240993-249237}{\sqrt{\frac{25875^2}{35}+ \frac{27110^2}{35} } } \\z = \frac{-8244}{6334.6388} \\z = -1.301[/tex]
The significance level is α = 0.1 and the critical value for a two-tailed test is
[tex]Z_t = Z_1 - _\alpha _/_2 = 1.64[/tex]
Since [tex]|z| = 1.301 \leq z_1 = 1.64[/tex], we can assume that the null hypothesis is not rejected.
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PLS HELP- WILL GIVE BRAINLIEST!!
Answer:
b = 4 mm
Step-by-step explanation:
[tex]b=\sqrt{5^{2}-3^{2} } =\sqrt{25-9}=\sqrt{16} =4[/tex]
Hope this helps
Answer:
The missing leg measures b = 4 millimeters in length.
Step-by-step explanation:
The Pythagorean theorem should be used to find the missing leg measure.
The formula is a2+b2=c2, where a and b are the leg lengths and c is the hypotenuse length. This is known as the Pythagorean theorem.
Let's use the Pythagorean theorem now that a = 3 and c = 5.
a^2 + b^2 = c^2 - This is the Pythagorean theorem equation.
3^2 + b^2 = 5^2 - Fill in the equation with a=3 and c=5.
9 + b^2 = 25
b^2 = 16 - Take 9 off both sides or subtract.
square root of b^2 = square root of 16 - Take the square root of both sides of the equation.
b = 4 - Simplify
The missing leg measures b = 4 millimeters in length.
If AB is translated right 5 units and down 2 units, what are the coordinates of A', the image of point A?
Answer:
(1,0)
PLEASE mark me brainliest!!
Answer:
1, 0
Step-by-step explanation:
What is 20% of 60?
please and fanks
Answer:
heya! ^^
so the question demands us to calculate what is 20% of 60.
that's quite simple. so let's see how we gótta do this question.
[tex]\\\\ \fbox{20\% \: \: of \: \: 60} \\ \\ \dashrightarrow \: \frac{2\cancel0}{\cancel{100}} \times 6\cancel0 \\ \\ \dashrightarrow \: 2 \times 6 \\ \\ \dashrightarrow \: 12[/tex]
hope helpful :D
Answer:
12
▬▬How to▬▬Convert 20% to fraction.[tex]20[/tex]% ⇒ [tex]\frac{1}{5}[/tex]Flip [tex]\frac{1}{5}[/tex] to [tex]\frac{5}{1}[/tex][tex]\frac{5}{1}[/tex] also equals 5Add 5 and 1[tex]5 + 1 = 6[/tex][tex]6 * 2 = 12[/tex]Hence, the answer is 12