By applying the law of cosine, the smallest angle which the swimmers must turn between the buoys is 41.4°.
How to determine the smallest angle?In order to determine the smallest angle which the swimmers must turn between the buoys, we would apply the law of cosine.
Given the following data:
Side AB = c = 400 meters.Side BC = a = 500 meters.Side CA = b = 600 meters.
Form the law of cosine, we have:
[tex]CosC =\frac{a^2 + b^2 - c^2}{2ab} \\\\CosC =\frac{500^2 + 600^2 - 400^2}{2 \times 500 \times 600}\\\\CosC =\frac{450000}{600000}\\\\C = cos^{-1} 0.75\\\\[/tex]
C = 41.4°.
For angle B, we have:
[tex]CosB =\frac{a^2 + c^2 - b^2}{2ac} \\\\CosB =\frac{500^2 + 400^2 - 600^2}{2 \times 500 \times 400}\\\\CosB =\frac{1}{8}\\\\B = cos^{-1} 0.125\\\\[/tex]
B = 82.8°.
For angle A, we have:
[tex]CosA =\frac{b^2 + c^2 - a^2}{2bc} \\\\CosA =\frac{600^2 + 400^2 - 500^2}{2 \times 600 \times 400}\\\\CosA =\frac{9}{16}\\\\A = cos^{-1} 0.5625\\\\[/tex]
A = 55.8°.
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The Breaker's Manufacturing Company makes 80% of a particular sensor, the Cartin Company makes 15% of them, and the Flutes Company makes the other 5%. The sensors made by Breaker's have a 4% defect rate, the Cartin sensors have a 6% defect rate, and the Flutes sensors have a 9% defect rate. If a sensor is randomly selected from the general population of all sensors, what is the probability that it is defective, given that it was made by Breaker’s?
Answer:
0.04
Step-by-step explanation:
The sensors made by Breaker's have a 4% defect rate
What's the mean, median, mode, and range of 8, 10, 8, 14, 8 and 15
Answer: Mean: 10.5, Median: 9 Mode: 8 Range: 7
Step-by-step explanation
mean put the numbers in order, so 8,8,8,10,14,15 the mean is adding all numbers together and dividing by the number so 8 + 8 + 8 + 10 + 14 + 15 divided by 6 is 10.5,
median is middle so 9 since theres two middle numbers u add them both and then divide by 2
mode is the most so its 8 since 8 is there 3 times
range is the highest number and lowest number and u subtract them so 15 - 8 = 7
sorry if this is long but the answers are at the top
Answer:
Below in bold.
Step-by-step explanation:
Mean = ( 8 + 10 + 8 + 14 + 8 + 15) / 6
= 10.5.
Arrange in ascending order to find the median:
8 8 8 10 14 15
Median = mean of the middle 2 numbers
= (8 + 10)/2
= 9.
Mode = most occurring number = 8.
Range = greatest - least = 15 - 8 = 7.
Mary bought an aquarium that is cuboid in shape. The bottom is a rectangle with sides of 50 cm and 70 cm. The height of the aquarium is 4 dm. Find how many gallons of water this aquarium can hold. How much a square decimeter of glass was used to make the aquarium when it was open at the top and the bottom was plastic?
Answer:
Area of the paper required =7000 cm²
Step-by-step explanation:
Dimensions of an Aquarium:
Length (l) = 80 cm,
Breadth (b) = 30 cm,
Height (h) = 40 cm
/* According to the problem given,
Area of the paper required =
Area of the base + 2×Area of two side faces + Area of the back side
(Front side should be visible,So, it is not covered )
= lb+2×bh+lh
= 80×30+2×(30×40)+80×40
= 2400+2×1200+3200
= 2400+2400+3200
= 7000 cm²
Therefore,
Area of the paper required =7000 cm²
Step-by-step explanation:
Find the area of the figure. A. 24.3 ft2 B. 38.1 ft2 C. 48.6 ft2 D. 35.7 ft2
The area of the figure is the amount of space on it, and the calculated area is 48.6 square feet
How to determine the area?The figure is a triangle with the following parameters:
Base = 20
Height = 4.86
The area of a triangle is:
Area = 0.5 * Base * Height
So, we have:
Area = 0.5 * 20 * 4.86
Evaluate
Area = 48.6
Hence, the calculated area is 48.6 square feet
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Which Angle measure must equal 52•
Answer:
c
Step-by-step explanation:
vertically opposite angles are always equal
here, the angle with the measure 52 degree and angle c are vertically opposite angles
so angle with the measure 52 degree = angle c
angle c equals to 52 degree
PLEASE HELP THIS IS DUE AFTER 20 MINS!! I’LL GIVE BRAINLIEST!
Answer:
lol
Step-by-step explanation:
lol
Surface Area
For the two figures below, the base area and the heights have been provided.
Figure A
Figure B
4 cm
5 cm
25 cm?
20 cm
what the volume for both figures?
Answer:
V of both A and B is 100 cm³
Step-by-step explanation:
the volume (V) of a prism is calculated as
V = Ah ( A is the area of the base and h the height )
A
A = 20 and h = 5 , then
V = 20 × 5 = 100 cm³
B
A = 25 and h = 4 , then
V = 25 × 4 = 100 cm³
diring the repair the mechanics will need to connect a cable between chairs b and j, and then continue that cable to chair g. what is the anhle formed by the cable
The angle that will be formed by the cable based on the information given will be 15°.
How to calculate the angle?From the complete information, it's important to divide the total angle by 12. This will be:
= 360°/12 = 30°
Then, the relations that will be used will be:
= 1/2(60° - 30°)
= 1/2 × 30°
= 15°
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Given that l is the centroid of triangle CDE, find CH.
A. 3
B. 4
C. 8
D. 12
Answer:
D. 12.
Step-by-step explanation:
As I is the centroid G is the midpoint of CE, so
2x + 5 = 5x - 4
5+4 = 5x - 2x
3x = 9
x = 3.
x + 5 = 2/3 * CH (Properties of the centroid of a triangle).
So as x = 3
2/3 CH = 3 + 5
CH = 8 * 3/2
CH = 12.
Given: f(x) = -2x² +x+6
5.1 Calculate the coordinates of the turning point of f.
Answer:
[tex]\left(\dfrac{1}{4},\dfrac{49}{8}\right)[/tex]
Step-by-step explanation:
Turning points (stationary points) occur when the gradient of a graph is zero.
To find when the gradient of the graph is zero, differentiate the function, set it zero, then solve for x.
Given function:
[tex]f(x)=-2x^2+x+6[/tex]
Differentiate:
[tex]\implies f'(x)=(2)(-2)x^{2-1}+(1)x^{1-1}+6(0)[/tex]
[tex]\implies f'(x)=-4x+1[/tex]
Set the differentiated function to zero and solve for x:
[tex]\implies f'(x)=0[/tex]
[tex]\implies -4x+1=0[/tex]
[tex]\implies 4x=1[/tex]
[tex]\implies x=\dfrac{1}{4}[/tex]
To find the y-coordinate, input the found value of y into the given function:
[tex]\implies f\left(\dfrac{1}{4}\right)=-2\left(\dfrac{1}{4}\right)^2+\left(\dfrac{1}{4}\right)+6[/tex]
[tex]\implies f\left(\dfrac{1}{4}\right)=\dfrac{49}{8}[/tex]
Therefore, the turning point of the function is:
[tex]\left(\dfrac{1}{4},\dfrac{49}{8}\right)[/tex]
answers
f=1/4=49/8
Step-by-step explanation:
identify the coefficients
a=-2, b=1
substitute the coefficient into the expression
x= -1/((2x(-2))
then solve it out the equation
x=1/4
evaluate the function x =1/4
f(x) =-2x²+x+6(1/4)
f=1/4=49/8
Please help! Asap!!!
Step-by-step explanation:
mean value : the sum of the measurements of all 10 plants divided by 10 (the number of measurements).
A)
since the 2 measurement errors are compensating each other in the sum of measurements (-5 cm vs. +5 cm), the sum stays the same, the number of measurements stays the same (10), so the mean value stays the same (72 cm).
B)
the mean absolute deviation was the mean value of the absolute values of the differences of each measurement to the plant measurements.
since the mean value stayed the same, so did the difference of the 8 originally correct measurements to that mean value.
the only change is with the 2 corrected measurements.
the original (but wrong) measurement of 65 had a difference of 7 (to 72).
and now it is only 2 (70 to 72).
and the other one had a difference of 6 (72 to 78).
and now it is only 1 (73 to 72).
so, the sum of all the differences decreased by (7-2) + (6-1) = 5 + 5 = 10.
we had originally a mean absolute deviation of 8.5. the sum of all 10 original differences was therefore 8.5×10 = 85.
now this sum went down to 85-10 = 75.
and the new mean absolute deviation is 75/10 = 7.5.
buffy's beverages has increasing profits each week during the hot summer months. Buffy finds that each week his profits increase by 20% over what they were the previous week. In his first week of business his profits were $200
The exponential function that gives the profit after x weeks is given by:
[tex]P(x) = 200(1.2)^x[/tex].
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem:
Buffy finds that each week his profits increase by 20% over what they were the previous week, hence r = 0.2.In his first week of business his profits were $200, hence A(0) = 200.Thus, the equation is given by:
[tex]A(x) = 200(1 + 0.2)^x[/tex]
[tex]A(x) = 200(1.2)^x[/tex]
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i need help with v-math
Answer:
Y=p/9
Step-by-step explanation:
Can u see p = 9y?
But there is no option of p = 9y
So try to work a bit on the formula to y = p/9
Round the following numbers
to the nearest len
1)7
2)23
3)1.562
1) 7 = 7.0
2) 23 = 23.0
3) 1.562 = 1.6
Answer:
1) round off 7 to the nearest 10 is 10
2) round off 23 to the nearest 10 is 20
3)round off 1.562 to the nearest 10 is1.6
step by step explanation :
any whole number that is 5 and more can be rounded off to 10 e.g 5, 6 ,7 but numbers that are less than 5 can't be rounded off to 10 so it's becomes 0 e.g 4,2,3
example : round off 12 to the nearest ten
the answer is 10
A bag contains 9 marbles: 2 are green, 3 are red, and 4 are blue. Raina chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that both marbles she chooses are red? Write your answel as a fraction in simplest form.
=========================================================
Explanation:
There are 3 red out of 9 total
The probability of picking red at random is 3/9 = 1/3
If the first marble is not put back, then the chances of picking red again are now 2/8 = 1/4
Notice how I subtracted 1 from the numerator and denominator of 3/9 to get to 2/8. This is because the red count and the total count both go down by 1 each.
Now multiply the fractions mentioned:
(3/9)*(2/8) = (1/3)*(1/4) = (1*1)/(3*4) = 1/12
If you did this trial 12 times, then you should expect to get two reds about once. That's one way to interpret the probability of 1/12.
Side note: 1/12 = 0.0833 = 8.33% approximately
#11 can someone help with this and also explain how they found the answer so ik how to do it
Answer:
24 units
Step-by-step explanation:
I really don't understand this, except for the fact that i found a workbook that has an answer with no work
hope this helps?:)
3
x + 2
3
3
12
32
12
Solve for x.
Answer:
6
explanation
[tex]since \: they \: are \: similar \\ \frac{x + 2}{32} = \frac{3}{12} \\ crossmultiplying \\ 32 \times 3 = 12(x + 2) \\ 96= 12x + 24 \\ 12x = 96 - 24 \\ 12x = 72 \\ dividing \: bothsides \: y \: 12 \\ x = \frac{72}{12} \\ x = 6[/tex]
It’s confusing on how they worded it to me
You're looking for the equation of the line through the two yellow points, whose coordinates are (4, 0) and (8, 9).
Compute the slope:
(9 - 0) / (8 - 4) = 9/4
Using the point-slope formula, the equation of the line is
y - 0 = 9/4 (x - 4)
or
y = 9x/4 - 9
Valentina has a tray where she keeps all of her important papers. the tray is in the shape of a rectangular prism with no top. a rectangular prism with a length of 12 inches, width of 10 inches, and height of 2.5 inches. what is the volume of papers that the tray can hold? 160 inches cubed 180 inches cubed 280 inches cubed 300 inches cubed
The volume of a rectangular prism with a length of 12 inches, width of 10 inches, and height of 2.5 inches is 300 cubic inches
Volume of a rectangular prismLength= 12 inchesWidth = 10 inchesHeight = 2.5 inchesVolume of a rectangular prism = length × width × height
= (12 × 10 × 2.5) inches
= 300 inches
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answer with procedure
Answer:
2
Step-by-step explanation:
there needs to be qtr with 88 by 779900
What is the probability of pulling a card from a deck of 52 cards and getting a king and a queen?
Answer:
4/52 or 1/13
Step-by-step explanation:
In a standard deck of 52 cards, there are 4 suits and each suit has 13 cards.
There are 4 kings, 4 queens, 4 aces, and 4 jacks.
So the probability of drawing a king would be:
4/52 = 1/13
Answer:
The probability of drawing a King is 4/52 or about . 0769, which is also the probability of drawing a Queen. The probability that a card drawn from the deck will be both a King and a Queen is zero. The probability that a card will be either a King or a Queen is 8/52.
Step-by-step explanation:
52 cards in a deck 4 queens and 4 kings
I need help with this equation. Please solve for k
Hey there!
18 = -k + 3
-k + 3 = 18
-1k + 3 = 18
SUBTRACT 3 to BOTH SIDES
-1k + 3 - 3 = 18 - 3
SIMPLIFY IT!
-1k = 18 - 3
-1k = 15
DIVIDE -1 to BOTH SIDES
-1k/-1 = 15/-1
SIMPLIFY IT!
k = 15/-1
k = -15
Therefore, the answer is: k = -15
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
3) If 5 pencils costs $0.75, 7 pencils will cost
Your answer
dollars. *
Answer:
$1.05
Step-by-step explanation:
Find the unit price by dividing $0.75 by 5.
$0.75/5 = $0.15
Now find the price of 7 pencils by multiplying 7 and the unit price of $0.15.
$0.15 x 7 = $1.05
What additional information do you need to prove the triangles are congruent by SAS
Answer:
Step-by-step explanation:
Please awnser the question does anyone want to help me with my math assignments
The two angles are supplementary angles and form a straight line which equals 180 degrees
x = 180 - 125
X = 55 degrees
Answer:
hope this will help you
Step-by-step explanation:
x+125=180
x=180-125
x=55°
PLEASE HELP WILL GIVE BRAINLIEST!!!
Answer:
▪︎ Domain: all real numbers (x can be any number)
▪︎ Range: y <= 0 (y can never become greater than 0 bc the vertex of this function (highest point) is (0,0))
What is the answer please?
Answer: D (bottom option)
Not Congruent
Step-by-step explanation:
Assuming the trapezoids are to scale, they are not the same shape. This means that they could not be congruent even if they were centered on top of each other.
Point B is between A and C. If AB = 3x, BC = 4x-2, and AC = 12, find the length of BC
Answer:
BC = 6 units
Step-by-step explanation:
given that B is between A and C , then
AB + BC = AC ( substitute values )
3x + 4x - 2 = 12
7x - 2 = 12 ( add 2 to both sides )
7x = 14 ( divide both sides by 7 )
x = 2
Then
BC = 4x - 2 = 4(2) - 2 = 8 - 2 = 6
Answer:
6
Step-by-step explanation:
from the question, since point B is between Ac
AC = AB + BC
12 = 3X+4X -2
3X+4X-2 = 12
7X = 12+2
7X = 14
dividing bothsides by 7
7X/7 = 14/7
X = 2
the length BC = 4X-2 = 4(2)-2 = 8-2= 6
length of BC = 6
PLEASE HELP, I NEED THE ANSWER BEFORE 3 HOURS 1. In the fraction the 11 represents the? a. Dividend b. Divisor c. Denominator 2. In the decimal number 125.795 the 9 represents the d. Quotient e. Both B & C place.
Answer:
e. Both B & ChundredthsStep-by-step explanation:
Q1
In the fraction 5/11, 11 represents the divisor and the denominator.The correct option is eQ2
In the number 125.795, the 9 represents the hundredths placeAnswer:mbvcdhfguh
Step-by-step explanation:kvghjve5yr
Write the repeating decimal as a fraction.
1.4979
Answer:
1 4979/9999
Step-by-step explanation:
1.497949794979....
= 1 4979/9999