Answer:
A mere 15 years back, navigators would have scoffed at the idea of Paperless Navigation on big ocean going ships. After all, since centuries, navigational paper charts had been the heart and soul of ship navigation. Imagining that a day would come where we’d no longer have them onboard was nothing short of blasphemy.
Step-by-step explanation:
The advantages of technology versus old-school methods for determining the position at sea include ease of navigation and safety.
What is the ECDIS?The ECDIS is the abbreviated form Electronic Chart Display and Information System. It is a modern technology used for navigation through waters.
The advantages and disadvantages of technology versus old-school methods for determining the position at sea are as follows:With ECDIS as the dominant source of sailing, the Navigating Officer can plan and summarise the transition much more speedily than on Paper Charts.
This is the background that will sound an alarm if the ship is inside the limit stated.
This scene displays the non-traversable field and marks the confine save that the container can harmlessly cross.
Therefore, we have found that the advantages of technology versus old-school methods for determining the position at sea include ease of navigation and safety.
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Evaluate the log without a calculator ( Show your work )
Look at image. That is the problem.
Answer:
8
Step-by-step explanation:
Given in the question a logarithm expression
[tex]125^(log_{5}2)[/tex]
We will use Exponent of Log Rule
[tex]b^(log_{b}k) = k[/tex]
here b = 5
k = 2
Suppose
[tex]125^(log_{5}2) = x[/tex]
take cube root on both sides of this equation
[tex]\sqrt[ 3]{(125^(log_{5}2)}=\sqrt[3]{x}[/tex]
[tex]\sqrt[3]{(125)} ^(log_{5}2)=\sqrt[3]{x}[/tex]
[tex]5^(log_{5}2)}=\sqrt[3]{x}[/tex]
Now according to the rule
2 = ∛x
to remove cube root take cube on both side
x = 8
so [tex]125^(log_{5}2 )[/tex] = 8
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HERE'S HOW TO DO IT :)
A composite figure is made up of several simple geometric figures such as triangles, rectangles, squares, circles, and semicircles.
To find the area of a composite figure, separate the figure into simpler shapes whose area can be found. Then add the areas together.
(SEE EXAMPLE ATTACHED)
HERES WHAT WE KNOW ABOUT COMPOSITE FIGURES:
Composite Figures. A figure (or shape) that can be divided into more than one of the basic figures is said to be a composite figure (or shape). For example, figure ABCD is a composite figure as it consists of two basic figures
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See the attached picture for the answers:
London owns a hybrid SUV that can travel 400 miles on a 15-gallon tank of gas. Determine how many miles he can travel on 6 gallons and number 16.
Answer:
Step-by-step explanation:
Please help me out.......... :)
Answer:
y = 16Step-by-step explanation:
In a parallelogram opposite angles are congruent. Therefore we have the equation:
10y - 29 = 7y +19 add 29 to both sides
10y = 7y + 48 subtract 7y from both sides
3y = 48 divide both sides by 3
y = 16
Which two values of x are roots of the polynomial below? x^2-11x+15
Answer: The correct options are
(B) [tex]x=\dfrac{11+\sqrt{61}}{2}.[/tex]
(D) [tex]x=\dfrac{11-\sqrt{61}}{2}.[/tex]
Step-by-step explanation: We are given to select the values of x that are the roots of the following polynomial :
[tex]x^2-11x+15.[/tex]
The quadratic equation formed by the given polynomial will be
[tex]x^2-11x+15=0~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
we know that
the solution set of a quadratic equation [tex]ax^2+bx+c=0,~~a\neq 0[/tex] is given by
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}.[/tex]
From equation (i), we have
a = 1, b = -11 and c = 15.
Therefore, the roots of equation (i) will be given by
[tex]x=\dfrac{-(-11)\pm\sqrt{(-11)^2-4\times1\times15}}{2\times1}\\\\\\\Rightarrow x=\dfrac{11\pm\sqrt{121-60}}{2}\\\\\\\Rightarrow x=\dfrac{11\pm\sqrt{61}}{2}.[/tex]
Thus, the roots of the given polynomial are
[tex]x=\dfrac{11+\sqrt{61}}{2},~~~~~x=\dfrac{11-\sqrt{61}}{2}.[/tex]
Options (B) and (D) are CORRECT.
Answer:
b and d
Step-by-step explanation:
(Q10) Compute the exact value of the function for the given x-value without using a calculator.
ANSWER
a. 216
EXPLANATION
The given function is;
[tex]f(x) = {6}^{x} [/tex]
We want to find the value of this function when x=3.
We substitute this value into the function to obtain,
[tex]f(3) = {6}^{3} [/tex]
[tex]f(3) = 6 \times 6 \times 6[/tex]
[tex]f(3) = 216[/tex]
Answer:
The correct answer is option a. 216
Step-by-step explanation:
It is given that,
f(x) = 6ˣ for x = 3
To find the value of f(x)
f(x) = 6ˣ
when x = 3 we can write,
f(3) = 6³ = 6 * 6 * 6 = 216
Therefore the value of f(x) when x = 3 is 216
The correct answer is option a. 216
Write an algebraic expression for "12 less than the quotient of 12 and a number z."
Answer:
Expression is 12 - [tex]\frac{12}{z}[/tex].
Step-by-step explanation:
Given : "12 less than the quotient of 12 and a number z."
To find : Write an algebraic expression .
Solution : We have given 12 less than the quotient of 12 and a number z."
According to question :
Let the quotient = Q
quotient of 12 and a number z.
quotient = [tex]\frac{12}{z}[/tex].
12 less than the quotient of 12 and a number z.
12 - [tex]\frac{12}{z}[/tex].
Therefore, Expression is 12 - [tex]\frac{12}{z}[/tex].
Determine the eccentricity, the type of conic, and the directrix for
r=6/1+2cos theta
Answer:
Choice C is correct
Step-by-step explanation:
The polar equation of the conic section is in standard form. The eccentricity is simply the coefficient of cos theta; thus e = 2
The eccentricity being more than 1 implies the conic section is a hyperbola.
To determine the directrix, divide 6 by 2 to obtain 3. The conic section opens to the left thus;
directrix; x = 3
Answer:
Choice C is correct
Which type of function correctly describes the exponential function
g(x)=3(4)^x-5
Answer:
See below.
Step-by-step explanation:
This function g(x) = 3(4^x) - 5 is an exponential function since it has a variable as an exponent. It has a initial value of 3 and a multiplicative rate of change of 4. The function itself when x = 0 is y = -2.
One letter is selected from the words "conditional probability." What is the probability that an "t" or "a" is chosen?
Answer:
4 out of 22 = 4/22
Step-by-step explanation:
Kelly paid $54.60 for a bike helmet that was 20% off the original price. What was the original price
The original price of the bike helmet was $68.25, calculated by understanding that the $54.60 Kelly paid represented 80% of the original price after a 20% discount.
Explanation:Kelly paid $54.60 for a bike helmet that was 20% off the original price. To find the original price of the helmet, we need to understand that the price Kelly paid is 80% of the original price, after the discount was applied. Therefore, the equation to find the original price (OP) is:
54.60 = 0.80 × OP
To solve for OP, we divide both sides of the equation by 0.80:
OP = 54.60 / 0.80
OP = $68.25
Thus, the original price of the bike helmet was $68.25.
By accident, 8 burned out bulbs have additionally been mixed in with 30 good ones. Ken is replacing old bulbs in his house. If he selects two bulbs at random from the box of 38, what is the probability they both work?
P(Both Work) =
435 / 703
P(Both Work) =
28 / 703
P(Both Work) =
16 / 361
P(Both Work) =
169 / 256
Answer:
The correct answer option is P(Both Work) = 435 / 703
Step-by-step explanation:
We are given that in a box of total 38 bulbs, 8 are the defective ones while the rest are good.
If Ken selects two bulbs at random from the box, we are to find the probability that they both work.
1st bulb: P (bulb works) = [tex]\frac{30}{38} [/tex]
2nd bulb: P (bulb works) = [tex]\frac{29}{37} [/tex]
P (Both Work) = [tex]\frac{30}{38} \times \frac{29}{37}[/tex] = 435 / 703
Answer:
The correct answer is first option. P(Both Work) = 435/703
Step-by-step explanation:
It is given that,
There are 8 burned bulbs and 30 good bulbs.
Therefore total number of bulbs = 8 + 30 = 38
To find the probability
We have to take two working bulbs from total bulbs.
Total bulbs = 38
The probability of taking two working bulbs = P(Both Work)
P(Both Work) = 30C₂/38C₂
= (30 * 29)/(38 * 37) = 435/703
Therefore the correct answer is first option
M=−8r ^2 +11r−6 T=−7r ^2−9r+14 M+T=
Answer is: −15r ^2 +2r+8
Answer:
[tex]\large\boxed{M+T=-15r^2+2r+8}[/tex]
Step-by-step explanation:
[tex]M=-8r^2+11r-6\\T=-7r^2-9r+14\\\\M+T=?\\\\\text{Substitute:}\\\\M+T=(-8r^2+11r-6)+(-7r^2-9r+14)\\\\M+T=-8r^2+11r-6-7r^2-9r+14\qquad\text{combine like terms}\\\\M+T=(-8r^2-7r^2)+(11r-9r)+(-6+14)\\\\M+T=-15r^2+2r+8[/tex]
The expression that represents M + T is -15r^2 + 2r + 8
The equations for M and T are given as:
[tex]M=-8r^2 +11r -6[/tex]
[tex]T=-7r^2-9r+14[/tex]
The sum of M and T is represented as: M + T
This is then calculated as:
[tex]M+T=-8r^2 +11r -6-7r^2-9r+14[/tex]
Collect like terms
[tex]M+T=-8r^2 -7r^2+11r -9r-6+14[/tex]
Evaluate the like terms
[tex]M + T = -15r^2 + 2r + 8[/tex]
Hence, the expression that represents M + T is -15r^2 + 2r + 8
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(Q1) Which of the following is true about the function y = 3 • 2x?
Answer: Third option
Step-by-step explanation:
You have the function:
[tex]y=3*2^x[/tex]
Then, if the value of x increases by 1, you obtain:
-Rewrite the function:
[tex]y=3*2^{(x+1)}[/tex]
-Substitute values for x into the function and observe what happen to y. Then:
x=1
[tex]y=3*2^{(1+1)}=12[/tex]
x=2
[tex]y=3*2^{(2+1)}=24[/tex]
x=3
[tex]y=3*2^{(3+1)}=48[/tex]
The value of y is doubled.
Answer:
C=the value of x increases by 1, the value of y will double.
Step-by-step explanation:
What is the volume of this right rectangular prism. 7 feet length 2 feet width and 3.5 feet Height
i think the answer to this problem is49
Answer:
The volume of this right rectangular prism is 49 Cubic feet.
Step-by-step explanation:
Here, the data is given
Lenght (l) = 7 feet
Widht (b) = 2 feet
Height (h) = 3.5 feet
Now, The Volume of rectangular prism
= l × b × h
= 7 × 2 × 3.5 feet
= 7 × 7 feet
= 49 cubic feet
Thus, The volume of this right rectangular prism is 49 Cubic feet.
-TheUnknownScientist
1 liter equals approximately 1.05 quarts. Which BEST approximates the number of liters in 3 quarts?
A) 3 liters
B) 6 liters
C) 9 liters
D) 12 liters
Answer:should be A
Step-by-step explanation:
I dunno
Answer:
it is A i just did it and i got it right so please trust me it is A
Step-by-step explanation:
Consider the population of all 1-gal cans of dusty rose paint manufactured by a particular paint company. Suppose that a normal distribution with mean μ = 5 ml and standard deviation σ = 0.2 ml is a reasonable model for the distribution of the variable x = amount of red dye in the paint mixture. Use the normal distribution model to calculate the probabilities below. (Round all answers to four decimal places.)
(a) P(x > 5) =
(b) P(x < 5.4)=
(c) P(x lteq.gif 5.4) =
(d) P(4.6 < x < 5.2) =
(e) P(x > 4.5) =
(f) P(x > 4) =
Answer:
A) 0.5000; B) 0.9772; C) 0.9772; D) 0.8185; E) 0.9932; F) 1.0000
Step-by-step explanation:
For each of these, we will use a z score. The formula for a z score is:
[tex]x=\frac{X-\mu}{\sigma}[/tex]
A) Our X is 5, our mean is 5 and our standard deviation is 0.2:
z = (5-5)/(0.2) = 0/0.2 = 0
Using a z table, the value to the left of this, less than, is 0.5000; this means the area to the right of this, greater than, is 1-0.5000 = 0.5000.
B) Our X is 5.4, the mean is 5 and the standard deviation is 0.2:
z = (5.4-5)/0.2 = 0.4/0.2 = 2
Using a z table, the value to the left of this, less than, is 0.9772.
C) The probability for this will be the same as for B; there is no distinction between "less than" and "less than or equal to" in z tables.
D) We find the z score for each of the endpoints of this interval, find the probabilities and subtract them:
z = (4.6-5)/0.2 = -0.4/0.2 = -2; the probability is 0.0228.
z = (5.2-5)/0.2 = 0.2/0.2 = 1; the probability is 0.8413.
The area between them is 0.8413-0.0228 = 0.8185.
E) X is 4.5, the mean is 5 and the standard deviation is 0.2:
z = (4.5-5)/0.2 = -0.5/0.2 = -2.5; the probability less than this is 0.0062. This means the probability greater than this is 1-0.0062 = 0.9938.
F) X is 4, the mean is 5 and the standard deviation is 0.2:
z = (4-5)/0.2 = -1/0.2 = -5. Everything in the z table is larger than this, so the probability is 1.000.
Identify the equation of the translated graph in general form x^2-y^2=8 for T(4,3)
Answer:
B
Step-by-step explanation:
A transformation of T(a,b) in the equation would give this form:
[tex](x-a)^2+(y-b)^2=8[/tex]
So, T(4,3) means translation of 4 units in x and 3 units in y. Thus, we can write:
[tex](x-4)^2+(y-3)^2=8[/tex]
Expanding and rearranging, we get:
[tex](x-4)^2-(y-3)^2-8=0\\x^2-8y+16-y^2+6y-9-8=0\\x^2-y^2-8x+6y-1=0[/tex]
Answer choice B is right.
Answer:
B
x^2-y^2-8x+6y-1=0
The first train leaves the station at 6:15 a m. The second train leaves at 6:55 am. How much does the sec ond train leave the station
Answer: 40
Step-by-step explanation:
second train leaves 40 minutes after
What fraction will each person get if 8 friends share 5 apples equally? Enter your answer in the boxes.
Answer:
5/8
Step-by-step explanation:
5/8 is equal to 5 divided by 8 and your dividing 5 so all the friends can have a equal amount. every friend would also get 5/8 of a apple
Every friend would get 5/8 parts of the total apple.
What is fraction?A fraction is a part of a whole number, and a way to split up a number into equal parts.
Given that, 8 friends want to share 5 apples equally. We need to find that what fraction will each person get,
Since, we have 5 apples, which is to be distributed to 8 persons,
To find the same, we will have to, divide 5 apples equally among 8 persons,
Therefore,
If we divide 5 by 8 then the faction of 5/8 of the whole is the part that each of the 8 friends going to have,
Hence, each friend would get 5/8 parts of the total apple.
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El área de una propiedad en metros cuadrados, mide 704/5. Se construye una casa que ocupa 5/6 del área total. La mitad del área restante se utiliza para construir una terraza, cuanta área falta por construir?
Answer:
The area left to build is [tex]\frac{704}{60}\ m^{2}[/tex]
Step-by-step explanation:
The question in English is
The area of a property in square meters, measures 704/5. A house is built that occupies 5/6 of the total area. Half of the remaining area is used to build a terrace, how much area is left to build?
we know that
The total area represent the fraction 6/6
A house represent the fraction 5/6 of the total area
The remaining area represent the fraction (6/6)-(5/6)=1/6 of the total area
If half of the remaining area is used to build a terrace
then
the area of the terrace represent the fraction (1/6)/2=1/12 of the total area
therefore
The area left to build represent the fraction 1/12 of the total area
so
[tex](\frac{1}{12})\frac{704}{5} =\frac{704}{60}\ m^{2}[/tex]
Identify the graph of 9X^2+4xy+5y^2-40=0 and find theta to the nearest degree.
Answer:
The answer is ellipse; 23° to the nearest degree ⇒ answer (d)
Step-by-step explanation:
* At first lets talk about the general form of the conic equation
- Ax² + Bxy + Cy² + Dx + Ey + F = 0
∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.
∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.
∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.
* Now we will study our equation:
- 9x² + 4xy + 5y² - 40 = 0
∵ A = 9 , B = 4 , 5 = 5
∴ B² - 4 AC = (4)² - 4(9)(5) = -164 < 0
∴ B² - 4AC < 0
∴ If a conic exists, it will be either a circle or an ellipse.
* To find the type of the graph lets check;
- If A and C are nonzero, have the same sign, and are not
equal to each other, then the graph is an ellipse.
- If A and C are equal and nonzero and have the same
sign, then the graph is a circle.
∵ A and C have same signs and are not equal
∴ The graph is an ellipse
* If we have term xy ⇒ B ≠ 0
∴ The graph is rotate by angle Ф
* To find the angle of rotation use the rule:
- cot(2Ф) = (A - C)/B
∵ A = 9 , B = 4 , C = 5
∴ cot(2Ф) = (9 - 5)/4 = 4/4 = 1
∴ tan(2Ф) = 1
∴ 2Ф = 45°
∴ Ф = 22.5° ≅ 23° to the nearest degree
* The answer is ellipse; with angle of rotation = 23°
If price was $2.00 per gallon and decreased to $1.40 per gallon, how does quantity of gasoline demanded change?
The price and demand are inversely proportional to each other, When the price is less, the demand is higher. When the price is high, the demand is low.
So , as given, the gasoline prices has been decreased from $2.00 per gallon to $1.40 per gallon, so now the demand will increase. The quantity of gasoline that will be in demand will increase.
Answer:
The quantity of gasoline demanded will increase.
Step-by-step explanation:
We are asked to find the change in demand of gasoline, when price of gasoline decreased from $2 per gallon to $1.40.
We know that quantity of a product demanded is inversely proportional to supply of the product.
This means that an increase in price will decrease the quantity demanded, while a decrease in price will increase the demand.
Since the price of gasoline is decreased by $0.60 per gallon, therefore, the quantity of gasoline demanded will increase.
One of Alberto's zebra danios is 4/3 the lenght of one of his fancy guppies. Which fish is longer?
Answer:
The Zebra Danios!
Step-by-step explanation:
The zebra danios
4/3 is greater than 1, making it an improper fraction. Suppose that fancy guppy's length is x, the danios' length would be 4/3 x, which, since it is an improper fraction, is greater than x.
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Find the measure of arc KL.
Answer:
The measure of arc KL is [tex]145\°[/tex]
Step-by-step explanation:
we know that
[tex]arc\ JK=arc\ KL=x\°[/tex]
so
[tex]2x+70\°=360\°[/tex] -----> complete circle
solve for x
[tex]2x=360\°-70\°[/tex]
[tex]2x=290\°[/tex]
[tex]x=145\°[/tex]
Liam is a tyre fitter it takes him 56 minutes to fit 4 tyres to a van how long would it take to fit 12 tyres to 3 vans
Answer:
168 minutes, or 2 hours, 48 minutes
Step-by-step explanation:
Set up a proportion and solve.
56 minutes is to 4 tires as 'x' minutes are to 12 tires
becomes
56/4 = x/12 solve for x...
[56(12)]/4 = x (multiply both sides by 12 to get rid of the fraction)
672/4 = x (simplify 52(12) = 672)
168 = x (simplify 672/4 = 168)
The imaginary number i is equal to
−1
, which expression is equivalent to −(4 + 3i) + (2 + 2i)?
A) 2 + 2i
B) 2 − i
C) −2 + i
D) −2 − i
Answer:
D
Step-by-step explanation:
An equivalent expression is an expression which is equal to −(4 + 3i) + (2 + 2i). You can expand or simplify an expression to make an equivalent expression. Combine like terms - constants with constants and imaginary with imaginary - to simplify.
−(4 + 3i) + (2 + 2i) = -4 + 2 -3i + 2i = -2 - i
Simplify 27 2
the 2 is tiny so I think it's 27 to the power of 2
A rectangle whose area is 180 square feet has a width that is 3 feet less than the length. Find the dimensions of the rectangle.
Answer:
The length is [tex]15\ ft[/tex]
The width is [tex]12\ ft[/tex]
Step-by-step explanation:
we know that
The area of rectangle is equal to
[tex]A=LW[/tex]
we have
[tex]A=180\ ft^{2}[/tex]
so
[tex]180=LW[/tex] -----> equation A
[tex]W=L-3[/tex] ------> equation B
substitute equation B in equation A and solve for L
[tex]180=L(L-3)[/tex]
[tex]180=L^{2}-3L[/tex]
[tex]L^{2}-3L-180=0[/tex]
using a graphing tool------> solve the quadratic equation
The solution is [tex]L=15\ ft[/tex]
see the attached figure
Find the value of W
[tex]W=15-3=12\ ft[/tex]
To find the dimensions of the rectangle given its area, we set up an equation using the length and width of the rectangle. Solving the equation will give us the dimensions. In this case, the length of the rectangle is 15 feet and the width is 12 feet.
Explanation:To find the dimensions of the rectangle, let's assume the length of the rectangle is L feet. According to the problem, the width is 3 feet less than the length, so the width would be L - 3 feet. The area of the rectangle is given as 180 square feet, so we can set up the equation: L * (L - 3) = 180. Solving this equation will give us the dimensions of the rectangle.
Multiplying the binomials, we get L^2 - 3L = 180. Rearranging the equation, we have L^2 - 3L - 180 = 0. This is a quadratic equation that can be factored. Factoring, we have (L - 15)(L + 12) = 0. We can now solve for L by setting each factor equal to zero: L - 15 = 0 or L + 12 = 0. This gives us two possible solutions for L: L = 15 or L = -12.
Since we cannot have negative dimensions for a rectangle, we discard the negative solution. Therefore, the length of the rectangle is 15 feet. The width can be found by substituting this value back into the equation: Width = 15 - 3 = 12 feet. So, the dimensions of the rectangle are 15 feet by 12 feet.
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If you have 3 4/6. Cups of sugar then divided it by 2 cups then added 4.9 cups how many eould you have
Answer:
11/6 or decimal 1.8333... + 4.9 = 6.733333....
Step-by-step explanation:
Simplify the following:
(3 + 2/3)/2
Express 4/6 in its lowest form by cancelling out gcd(4, 6) = 2 from the numerator and denominator. 4/6 = (2×2)/(2×3) = 2/3:
(2/3 + 3)/2
Put 3 + 2/3 over the common denominator 3. 3 + 2/3 = (3×3)/3 + 2/3:
((3×3)/3 + 2/3)/2
3×3 = 9:
(9/3 + 2/3)/2
9/3 + 2/3 = (9 + 2)/3:
((9 + 2)/3)/2
9 + 2 = 11:
(11/3)/2
11/3×1/2 = 11/(3×2):
11/(3×2)
3×2 = 6:
Answer: 11/6 or decimal 1.8333... + 4.9 = 6.733333....