This question is not complete
Complete Question
A boat sails 4km on a bearing of 038 degree and then 5km on a bearing of 067 degree.(a)how far is the boat from its starting point.(b) calculate the bearing of the boat from its starting point
Answer:
a)8.717km
b) 54.146°
Step-by-step explanation:
(a)how far is the boat from its starting point.
We solve this question using resultant vectors
= (Rcos θ, Rsinθ + Rcos θ, Rsinθ)
Where
Rcos θ = x
Rsinθ = y
= (4cos38,4sin38) + (5cos67,5sin67)
= (3.152, 2.4626) + (1.9536, 4.6025)
= (5.1056, 7.065)
x = 5.1056
y = 7.065
Distance = √x² + y²
= √(5.1056²+ 7.065²)
= √75.98137636
= √8.7167296826
Approximately = 8.717 km
Therefore, the boat is 8.717km its starting point.
(b)calculate the bearing of the boat from its starting point.
The bearing of the boat is calculated using
tan θ = y/x
tan θ = 7.065/5.1056
θ = arc tan (7.065/5.1056)
= 54.145828196°
θ ≈ 54.146°
The cost of renting a car is $75/wk plus $0.25/mi traveled during that week. An equation to represent the cost would be y = 75 + 0.25x, where x is the number of miles traveled. If your cost was $96.25, how many miles were you charged for traveling?
Answer:
We know we have to pay $75 per weel plus $0.25 for each mile we traveled, from that, if we call x the miles we have travelled, the total cost would be:
[tex]C = 75 + 0.25x[/tex]
As each mile we travel costs $0.25. Now that we have that expression, they ask us how many miles did we travel if we had to pay $96.25.
The only thing we have to do is replacing the C (our total cost) per $96.25 and solve the equation we get:
[tex]96.25=75+0.25x[/tex]
[tex]96.25-75=0.25x[/tex]
[tex]21.25=0.25x[/tex]
[tex]\frac{21.25}{0.25} = x[/tex]
[tex]85 = x[/tex]
We hve traveled 85 miles.
Mark is a nurse anesthetist. He administers medication that puts people to sleep for surgeries and other invasive medical procedures. For healthy adults, the manufacturer recommends using a dose of 0.6mcg/kg, which means that Mark must give his patients 0.6mcg of medication for each kg they weight. If Mark's patient weights 60kg, how much medication should he administer?
Answer:
Quantity of medicine provide to patient = 36 mcg
Step-by-step explanation:
Given:
Quantity recommend = 0.6 mcg / kg
Weight of patient = 60 kg
Find:
Quantity of medicine provide to patient
Computation:
Quantity of medicine provide to patient = Weight of patient × Quantity recommend
Quantity of medicine provide to patient = 60 × 0.6
Quantity of medicine provide to patient = 36 mcg
Refer to the figure below. (Remember: The sum of the thre
Find a if A = 75°.
Answer:
15°
Step-by-step explanation:
The sum of three interior angles in a triangle is 180.
180-90-75=15°
PLS HELP FOR BRAINLIEST ANSWER
Answer:
Point C which is 1.
Step-by-step explanation:
A = -6
E = 8
M = (A + E)/2
M = (-6 + 8)/2 = 2/2 = 1
The midpoint is 1 which is point C.
1/2(30)-(40) this is on integers math maze freebie to search up
Answer:
hey thanks for ur points too
Step-by-step explanation:
midpoint (-4.-27), endpoint (-5, -19)
Answer:
(-3,-35), and the slope is -8/1
Step-by-step explanation:
If you're trying to find the other endpoint, that's it, and the slope is -8/1
Which expressions are equal to 0 when x = –1? Check all that apply.
Answer: ACE
Step-by-step explanation:
The expression first, third, and fourth becomes zero when plugging x = -1 in the equation.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
First,
[tex]=\rm \dfrac{4\left(x+1\right)}{4x+5}[/tex]
Plug x = -1
The expression value becomes zero.
Second,
[tex]= \rm \dfrac{4\left(x-1\right)}{5-4x}[/tex]
Plug x = -1
= -8/9
Third,
[tex]\rm \dfrac{4\left(x-\left(-1\right)\right)}{4x+5}[/tex]
Plug x = -1
The expression value becomes zero.
Fourth,
[tex]\rm \dfrac{4\left(x+\left(-1\right)\right)}{4x+5}[/tex]
Plug x = -1
The expression value does not become zero.
Fifth,
[tex]\rm \dfrac{4\left(x+1\right)}{5-4x}[/tex]
Plug x = -1
The expression value becomes zero.
Thus, the expression first, third, and fourth becomes zero when plugging x = -1 in the equation.
Learn more about the expression here:
brainly.com/question/14083225
#SPJ2
Hi, what is the answer to 4 • 7 – 62 ÷ 3
Answer:
22/3
Step-by-step explanation:
[tex]4\times\:7-\frac{62}{3}\\\\\mathrm{Multiply\:the\:numbers:}\:4\times\:7=28\\=28-\frac{62}{3}\\\\\mathrm{Convert\:element\:to\:fraction}:\quad \:28=\frac{28\times\:3}{3}\\=\frac{28\times\:3}{3}-\frac{62}{3}\\\\=\frac{28\times\:3-62}{3}\\\\28\times\:3-62=22\\\\=\frac{22}{3}[/tex]
A car is traveling at the speed of 50 meters per second. What is the cars speed in kilometers per hour? How many kilometers will the car travel in 2 hours? Do not round your answers.
the midpoint of the coordinates (13,15) and (12,8) is ________
Answer:
[tex] \boxed{ \bold{ \huge{\boxed{ \sf{(12.5 \: , \: 11.5)}}}}}[/tex]
Step-by-step explanation:
Let the points be A and B
Let A ( 13 , 15 ) be x₁ , y₁ and B ( 12 ,8 ) be x₂ , y₂
Finding the midpoint
[tex] \bold{ \boxed{ \sf{midpoint \: = (\: \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2}) }}}[/tex]
[tex]\dashrightarrow{ \sf{ (\frac{13 + 12}{2} , \: \frac{15 + 8}{2} )}}[/tex]
[tex] \dashrightarrow {\sf {(\frac{25}{2} \: , \: \frac{23}{2} )}}[/tex]
[tex] \dashrightarrow{ \sf{(12.5 \: , \: 11.5)}}[/tex]
Hope I helped!
Best regards! :D
0.28
x 0.86
it’s no answer choices ;((
Answer:
Hey there!
0.28 times 0.86 is equal to 0.2408
Let me know if this helps :)
The lunch special at Karen’s restaurant is a sandwich, a drink and a dessert. THERE ARE 2 sandwiches, 4 drinks, and 1 dessert to choose from. How many lunch specials are possible?
Answer:
There are 8 possible combinations.
Look at this example:
2 sandwiches: PB&J, turkey sandwich
4 drinks: soda, water, lemonade, tea
1 dessert: cake
all 8 combos:
PB&J, soda, cakePB&J, water, cakePB&J, lemonade, cakePB&J, tea, caketurkey sandwich, soda, caketurkey sandwich, water, caketurkey sandwich, lemonade, caketurkey sandwich, tea, cakehope this helps
red and blue ceramic tiles are laid according to a pattern such that every 21 red tiles used, 4 blue tiles are used. if a total of 425 tiles are used, how many of them are blue? setup a proportion for this scenario( use x for your unknown number of blue tiles).
Answer:
X= blue tiles
Y = red tiles
X/y = 4/21
X+y= 425
Y= 357 tiles
X= 68 tiles
Step-by-step explanation:
red and blue ceramic tiles are laid according to a pattern.
The pattern= every 21 red tiles used, 4 blue tiles are used
Total number of tiles used = 425 tiles
X= blue tiles
Y = red tiles
X/y = 4/21
X+y= 425
21x= 4y
X= 4y/21
X+y= 425
4y/21 + y = 425
25y= 425(21)
Y=( 425*21)/25
Y= 357 tiles
X= 4y/21
X= (4*357)/21
X= 1428/21
X= 68 tiles
Using proportions, it is found that there are 68 blue tiles.
This question is solved by proportions, using a rule of three.For every 21 red tiles used, 4 blue tiles are used, hence, out of every 25 tiles, 4 are blue. How many blue tiles are there out of 425?The rule of three is:
4 blue - 25 total
x blue - 425 total
Applying cross multiplication:
[tex]25x = 4(425)[/tex]
[tex]x = \frac{4(425)}{25}[/tex]
[tex]x = 68[/tex]
There are 68 blue tiles.
To learn more about proportions, you can check https://brainly.com/question/24372153
Lynne was making cookies and she
wanted to double the recipe. If the
recipe requires 2 cups of flour, how
much flour will Lynne need?
Answer:
4 cups of flour
Step-by-step explanation:
We just need to double 2. The phrase "double" means to multiply by 2 so the answer is 2 * 2 = 4 cups of flour.
8y=(5y+24) find the value of y
[tex]8y=5y+24[/tex] collect like-terms
[tex]8y-5y=24[/tex] subtract
[tex]3y=24[/tex] now divide
[tex]y = \frac{24}{3}\\[/tex]
[tex]y=8[/tex]
plug in the value of [tex]y[/tex] to check if the answer is correct:
[tex]8y=5y+24\\8(8)=5(8)+24\\64=40+24\\64=64[/tex]
ergo, [tex]y = 8[/tex]
Describe a pattern in the sequence of numbers. Predict the next number.
1. 256, 64, 16, 4, ...
2. 2, 6, 18, 54, ...
Answer:
Pattern = Start at 256 and divide by 4 each time. Next number = 1.Pattern = Start at 2 multiply by 3 each time. Next number = 162In the first sequence, the next term here is 1. In the second sequence; the next term is 162.
What is arithmetic sequence?An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
In the first sequence, 256, 64, 16, 4, ...
Consider ratio of the next term with its preceding term, so we will get the common ratio;
4/ 16 = 1/4
So, we can see that the next term of the sequence is 1/4 times the previous term.
Hence, the unknown term will be; 1/4 times of previous term.
That is , 1/4 × 4 = 1
Therefore, the next term here is 1
In the second sequence; 2, 6, 18, 54, ...
Do the same procedure as above, we will get the common ratio as :
54 / 18 = 3
Thus, the next term is 3 times the preceding term, that is :
3 × 54 = 162
Hence, the next term is 162
Learn more about arithmetic sequence here:
https://brainly.com/question/3702506
#SPJ2
PLEASE HELP ILL PICK YOUR ANSWER AS THE BRAINLIEST FOR POINTS! Jaime flipped a coin 20 times, and it landed on heads 15 out of the 20 times. Which would be the BEST way for Jaime to change his experiment so that his experimental probability of the coin landing on heads is closer to the theoretical probability? * 1 point He could use 20 different coins and flip each coin once. He could use 10 different coins and flip each coin twice. He could flip the coin only 2 times. He could flip the coin 100 times.
Answer:
the first one im pretty sure
Step-by-step explanation:
Answer:
The First one is correct im pretty sure.
A library has 167 trees on their property, but they are having trouble growing grass so they need to pay to have trees cut down each year until the property has less than 50 trees. If they can pay to have only four trees cut down this year, but eight trees cut down every year after that, in how many years will they have less than 50 trees on their property?
Answer:
15 years
Step-by-step explanation:
Given:
Number of trees = 167This year limit = 4 treesYearly limit following years = 6 trees per yearTarget number of trees = 50Building inequality:
167 - 4 - 8x < 508x > 113x > 113/8x > 14.125Adding current year to 14 we get 15 years as answer
Express the following expression in the form of a + bi: (39 + 34i) + (76 + 89i) - (47 +26i).
Answer:
68+97i
Step-by-step explanation:
work shown and pictured
Answer:
68+97i
Step-by-step explanation:
(39 + 34i) + (76 + 89i) - (47 +26i).
Distribute the minus sign
(39 + 34i) + (76 + 89i) + (-47 -26i)
Combine like terms
(39+76-47)+(34i+89i-26i)
68+97i
3
En el numeral 341, 427,538 ¿Cuál dígito está
en el lugar de la centena de
millón? *
(1 Punto)
O A. 2
B. 7
O
C, 4
O
D. 3
Answer:
The answer is D. 3
Step-by-step explanation:
A number refers to the expression of a quantity or a magnitude. In mathematics, a number represents a fixed quantity of something or generally of a number system.
The numbers have a fixed order that determines their value.
The numbers are in order of:
Unit = 8
Ten = 3
Hundred = 5
Unit of thousand = 7
Ten thousand = 2
Hundred thousand = 4
Million unit = 1
10 million = 4
And a hundred million represented by = 3.
Use set notation to list all the elements of the set. The natural number less than 37 that are divisible by 5.
Answer:
{5, 10, 15, 20, 25, 30, 35}
Step-by-step explanation:
The set can be listed (rostered). When it is, it will be ...
{5, 10, 15, 20, 25, 30, 35}
__
Set notation can also be used to describe the set as being a natural number less than 37 and divisible by 5:
[tex]\{n\in\mathbb{N}:(n<37)\land(n\mod{5}=0)\}[/tex]
Among all pairs of numbers with a sum of 149149, find the pair whose product is maximum. Write your answers as fractions reduced to lowest terms.
Correct question is;
Among all pairs of numbers with a sum of 149, find the pair whose product is maximum. Write your answers as fractions reduced to lowest terms
Answer:
The pair whose product is maximum is 149/2 and 149/2
Step-by-step explanation:
We are told that pair of number with sum as 149 and to find the product that is maximum.
Now,let x and y be the numbers. Thus;
x + y = 149 and xy is maximum.
So, y = 149 - x
Thus, plugging 149 - x for y into the product equation gives; x(149 - x). This can be expanded to be -x² + 149x.
Using method of completing the square, we will arrive at;
-(x² - 149x) = -(x² -149x + (149/2)²) + (149/2)² = (149/2)² - (x - (149/2))²
Now, the expression gotten will have a maximum of (149/2)² when (x - (149/2))² has its minimum value of zero. This means that when x = 149/2, as x moves away from 149/2, (149/2)² would be reduced by the square of the difference between the value of x and 149/2, and the square would always be positive.
Thus, the maximum product in it's simplest form is x = y = 149/2
6. Four more than two-thirds of a number is twenty-two. Find the number.
Answer:
27
Step-by-step explanation:
Let x be the number
2/3 x+4 = 22
Subtract 4 from each side
2/3x +4-4 = 22-4
2/3 x = 18
Multiply each side by 3/2
3/2 ( 2/3x) = 18 * 3/2
x = 27
Answer:
[tex]\Huge \boxed{27}[/tex]
Step-by-step explanation:
Let the number be x.
[tex]\frac{2}{3} x+4=22[/tex]
Solve for x.
Subtract 4 from both sides.
[tex]\frac{2}{3} x+4-4=22-4[/tex]
[tex]\frac{2}{3} x=18[/tex]
Multiply both sides by [tex]\frac{3}{2}[/tex].
[tex]\frac{2}{3} x \cdot \frac{3}{2} =18 \cdot \frac{3}{2}[/tex]
[tex]x=27[/tex]
The number is 27.
if a family has 7 children, what is the interval within which the "number of children they have really falls"
Answer:
Step-by-step explanation:
If a family has 7 children, what is the interval within which "the number of children they have" really falls.
Now, number of children is a discrete variable, not a continuous one.
You are sure that the family has 7 children because the question states that.
The true interval within which the number of children they have falls is (0 - 8)
PLEASE HELPPPPP ASAPPPPPP
Answer:
2208
Step-by-step explanation:
So first we can write this as 4(500+50+2)
Then we distribute it 4*500+4*50+4*2
Multiply to get 2000+200+8
So the answer is 2208
4. Write a verbal expression for 6g^2/5
Answer:
the product of 6 and a squared number divided by 5Step-by-step explanation:
The mean of a set of data is 4.68 and its standard deviation is 2.83. Find the z score for a value of 9.38. a.1.83 b.1.49 c.1.66 d.1.96
Answer:
[tex]z = 1.66[/tex]
Step-by-step explanation:
Given
Mean = 4.68
Standard Deviation (SD) = 2.83
Value, x = 9.38
Required
Determine the z score
z score is calculated using the following formula;
[tex]z = \frac{x - Mean}{SD}[/tex]
Substitute 9.38 for x; 2.83 for SD and 4.68 for Mean
[tex]z = \frac{9.38 - 4.68}{2.83}[/tex]
[tex]z = \frac{4.7}{2.83}[/tex]
[tex]z = 1.66[/tex] (Approximated)
Hence, the z score is 1.66
HELP!!! MATH!!! PLEASE HELP PLEASE!!! Determine the answer to 3 + (−5) and explain the steps using a number line. (5 points)
Answer:
3+(-5) = -2
Step-by-step explanation:
If you were at 3 in the number line then went back 5 spaces (which represents -5) it would be -2
Can somebody help me with the first set please you have to match it
Answer:
they are in the link. i answered each on in the same order they are in the picture soooo here u are.
Find the length of segment AB. (Find the distance between the two points). A(-3,5) B(0,1)
Answer:
5
Step-by-step explanation:
The formula is [tex]\sqrt{(x_{1}-x_{2})^{2} +(y_{1}-y_{2}})^{2} }[/tex]
[tex]x_{1}[/tex]=-3 [tex]x_{2}[/tex]=0
[tex]y_{1}[/tex]=5 [tex]y_{2}[/tex]=1
[tex]x_{1}- x_{2}[/tex]=-3
[tex]y_{1}- y_{2}=4[/tex]
Therefore: [tex]\sqrt{(-3)^{2}+4^{2} } =\sqrt{9+16} =\sqrt{25}=5[/tex]