The distance between city A and city B is approximately 442.3 km.
What is the law of cosine?
The Law of Cosines, also known as the Cosine Rule, is a mathematical formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. Specifically, it states that:
c² = a² + b² - 2ab cos(C).
We can use the Law of Cosines to find the distance between City A and City B. Let's call this distance d.
From the information given, we know that:
The distance between the satellite and city A is 450 km.
The distance between the satellite and city B is 340 km.
The angle between city A, the satellite, and city B is 1.5 degrees.
Using the Law of Cosines, we have:
d² = 450² + 340² - 2(450)(340)cos(1.5)
d² = 202500 + 115600 - 2(450)(340)cos(1.5)
d² = 318100 - 122328.8
d² = 195771.2
d = √195771.2
d ≈ 442.3
Therefore, the distance between city A and city B is approximately 442.3 km (rounded to the nearest tenth).
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ILL GIVE BRAINLIEST!!!!
Answer:
1 = yes
2 = no
3 = no
4 = yes
5 = yes
6 = no
7 = no
8 = no
Big Ben is a famous clock tower in London. The circumstance around the clock is 72.22. How long is the hour on the clock if it is the radius of the circle
The hour hand is 9 feet (2.7 m) long and the minute hand is 14 feet (4.3 m) long.
One serving of a certain brand of yogurt contains 11 g of fat. The low-fat version contains 36.75% less fat per serving. How many grams of fat does one serving the low-fat yogurt contain?
The amount of fat that the low-fat yogurt contains is 6.9575 g.
It is given in the question that:-
Amount of fat in a certain brand of yogurt = 11g
Percentage of fat less in the low-fat yogurt version = 36.75 %
We have to find the amount of fat in the low-fat yogurt.
We know that,
The amount of fat in the low-fat yogurt = Amount of fat in a certain brand of yogurt - Percentage of fat less in the low-fat yogurt version
Now,
36.75 % of 11g = 4.0425 g
Hence, we can write,
The amount of fat in the low-fat yogurt = 11g - 4.0425g = 6.9575 g
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Eliana treated her sister to lunch while visiting her in Seaside. Their lunch cost $100, and the
sales tax in Seaside is 8%. If Eliana left a 20% tip on the $100, how much in total did she
pay?
Answer:
multiply the numbers
128
Step-by-step explanation:
Answer:
128 is the answer
Step-by-step explanation:
your welcome!
in the illustration below ,The two lights are designed tc pperate at 6 volts, 5 amps each,
5
f the power source is12 volts, what will be the value of the Resistor?
Round to the tenth position. (0.00)
The value of the resistor needed in this scenario is approximately 1.2 ohms.
To find the value of the resistor in the given scenario, we can apply Ohm's Law, which states that the current (I) flowing through a resistor is directly proportional to the voltage (V) across it, and inversely proportional to the resistance (R) of the resistor.
Using Ohm's Law, we have the formula:
V = I * R
Where:
V is the voltage across the resistor (12 volts in this case),
I is the current flowing through the resistor (5 amps for each light, so a total of 10 amps),
R is the resistance of the resistor (which we need to find).
Rearranging the formula, we have:
R = V / I
Plugging in the values:
R = 12 volts / 10 amps
R = 1.2 ohms
Therefore, the value of the resistor needed in this scenario is approximately 1.2 ohms.
It's worth noting that this calculation assumes the lights are connected in parallel, as the current remains the same for each light. If the lights were connected in series, the total resistance would be the sum of the individual resistances, and the calculation would be different.
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Solve for x: -7 < X - 1 < 8
Answer:
4th option
Step-by-step explanation:
-7 < X - 1 < 8
Add +1 on all side
-7+1<x-1+1<8+1
-6<x<9
Answer:
D
Step-by-step explanation:
-7<x-1 and - 1<8
-7<x-1 : x>-6
x-1<8 : x<9
combine x>-6 and x<9
= -6 < x < 9
6.1 Define the term inflation.
Answer:
the action of inflating something or the condition of being inflated.
"the inflation of a balloon"
ASTRONOMY
(in some theories of cosmology) a very brief exponential expansion of the universe postulated to have interrupted the standard linear expansion shortly after the Big Bang.
2.
ECONOMICS
a general increase in prices and fall in the purchasing value of money.
"policies aimed at controlling inflation"
Find a third degree polynomial with rational coefficients that has the given numbers as given roots
4 and 3 - \(\sqrt{2}\)
Answer:
\(x^3-10x^2+31x-28\)
Step-by-step explanation:
Since we are looking for a polynomial with RATIONAL coefficients, then we know that if \(3-\sqrt{2}\) is a root, then its conjugate \(3+\sqrt{2}\) must also be a root
Therefore, we build the polynomial using binomial factors with the given roots as shown below:
\((x-4)*(x-3+\sqrt{2} )*(x-3-\sqrt{2} )= (x-4)((x-3)^2-2)=\\=(x-4)*(x^2-6x+9-2) =(x-4)*(x^2-6x+7)=\\=x^3-10x^2+31x-28\)
Suppose that, starting at a certain time, batteries coming off an assembly line are examined one by one to see whether they are defective (let D = defective and N = not defective). The chance experiment terminates as soon as a nondefective bettery is obtained.a. Give five possible outcomes for this chance experiment.b. What can be said about the number of outcomes in the sample space?c. What outcomes are in the event E, that the number of battery examined is an number?
Answer:
a. Possible outcomes for this chance experiment are:
NDNDDNDDDNDDDDN(Here, D means a defective battery, and N means a nondefective battery.)
b. The number of outcomes in the sample space is infinite, as the experiment could potentially continue indefinitely. However, in practice, we can define a maximum number of batteries that could be examined before the experiment is stopped.
c. The event E, that the number of batteries examined is a number, would include outcomes where the experiment stopped at a particular number of batteries. For example, if the experiment stopped after examining three batteries (i.e., the fourth battery was nondefective), then the outcome would be DDDN, and it would be included in event E. However, outcomes where the experiment continued indefinitely (e.g., DDDDD...) would not be included in event E.
(t+5)(t+2),make t the subject of the formula
Answer:
t= 2p+5/p-1
Step-by-step explanation:
The question is not well writen
Assume p = t+5/t-2
We are to make t the subject of the formula
Cross multiply
p(t-2) = t+5
pt - 2p = t+5
pt - t = 2p+5
t(p-1) = 2p+5
t= 2p+5/p-1
Hence the value of t is 2p+5/p-1
HELP!!!
I WILL MARK BRAINLEST!!!
Rhonda started a business. Her business made $30,000 in profits the first year. Her annual have increased by 5% each year since then.
A) write and explicit equation to model the sequence formed by the profits of Rhonda’s business each year
B) use the rule ti determine what the annual profits of Rhonda’s business can be predicted in 15 years from the start of her business. Round your answer to the nearest dollar. Do not round until the end. Show your work.
Answer:
(a) $ 30000 + 1500 t
(b) $ 52500
Step-by-step explanation:
Initial profit = # 30,000
Profit increases every year by 5 %.
(a) Let the profit after t year is
P = $ 30,000 + 5% of 30,000 t = $ 30000 + $ 1500 t
(b) t = 15 years
P = $ 30000 + $ 1500 x 15 = $ 52500
How is the graph of the parent function, y=√x transformed to produce the graph of y=√-2x?
It is translated horizontally by 2 units and reflected over the x-axis.
It is translated horizontally by 2 units and reflected over the y-axis.
It is horizontally compressed by a factor of 2 and reflected over the x-axis.
It is horizontally compressed by a factor of 2 and reflected over the y-axis.
The graph of the parent function, y=√x transformed to produce the graph of y=√-2x as D. It is horizontally compressed by a factor of 2 and reflected over the y-axis.
How to explain the graphThe graph of y=√-2x is obtained from the graph of y=√x by applying two transformations: a horizontal compression by a factor of 2 and a reflection over the y-axis.
To see this, we can use the following steps:
Start with the graph of y=√x, which is a curve that passes through the origin and increases without bound as x increases.
To compress the graph horizontally by a factor of 2, we replace x with x/2 in the function. This gives us y=√(x/2), which is equivalent to y=(1/√2)√x. This transformation squeezes the graph horizontally by a factor of 2, making it steeper and narrower.
To reflect the compressed graph over the y-axis, we replace x with -x in the function. This gives us y=(1/√2)√-x, which is equivalent to y=(1/√2)i√x, where i is the imaginary unit. This transformation flips the graph horizontally, reflecting it over the y-axis.
Therefore, the correct answer is that the graph of y=√-2x is horizontally compressed by a factor of 2 and reflected over the y-axis.
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In a roll of 50 pennies, there are 12 dated 1977. If a penny is drawn at random, what is the probability that it is dated 1977?
Thus, probability that the one drawn penny is from 1977 dated pennies is 6/25.
Define about the probability:The probability about an occurrence in an experiment is the likelihood that the event will occur. Any event's probability is a number between (including all) "0" and "1".
If an event's probability is represented by P(E), then we get
If and only if the condition E is an impossibility, P(E) = 0.If and just if E is a specific event, then P(E) = 1.Given data:
Total pennies = 50
number of 1977 dated pennies = 12
probability = favourable outcome / total outcome
probability(1977 dated pennies) = number of 1977 dated pennies/ Total pennies
probability(1977 dated pennies) = 12/50
Divide numerator and denominator by 2.
probability(1977 dated pennies) = 6/25
Thus, probability that the one drawn penny is from 1977 dated pennies is 6/25.
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Which of the following is INCORRECT
Answer:
A
Step-by-step explanation:
I need some help with this math problem.
This kinda functions are called signum functions.
Looking at the question
Put n=2(even)
\(\\ \sf\longmapsto \dfrac{n}{2}=\dfrac{2}{2}=1\)
Put n=3(odd)
\(\\ \sf\longmapsto 3(3)+1=9+1=10\)
Hence done .
You can take any input for your answer.
Alice and Bob each have a certain amount of money. If Alice receives n dollars from Bob, then she will have 7 times as much money as Bob. If, on the other hand, she gives n dollars to Bob, then she will have 2 times as much money as Bob. If neither gives the other any money, what is the ratio of the amount of money Alice has to the amount Bob has?
The ratio of the amount of money Alice has to the amount Bob has is approximately 3.36 : 1.
How to find the ratio of money ?According to the problem, two equations can be set up:
If Alice receives n dollars from Bob, then she will have 7 times as much money as Bob. This gives us the equation:
A + n = 7(B - n)
If Alice gives n dollars to Bob, then she will have 2 times as much money as Bob. This gives us the second equation:
A - n = 2(B + n)
We can rearrange these equations to make them easier to solve:
8n = 7B - A
3n = A - 2B
Setting these equal to each other, since they are both equal to 24n, gives:
21B - 3A = 8A - 16B
37B = 11A
A / B = 37 / 11
= 3. 36
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24 divided by [(6 divided by 2) - (4 divided by 2)
Answer:
Im pretty sure the answer is 6
Step-by-step explanation:
Leave the 24 aside for a sec. Focus on the 6÷2 and 4÷2. 6 divided by 2 is 3. And 4 divided by 2 is 2. So now its 24÷3= 8
8-2=6
let $c$ be a complex number. suppose there exist distinct complex numbers $r$, $s$, and $t$ such that for every complex number $z$, we have \[ (z - r)(z - s)(z - t)
There are four possible values of C if there exist distinct complex numbers.
A complex number is an element of a number system that extends the real numbers with a specific element denoted i is called the imaginary unit . the equation every complex number can be expressed as,
a + bi
where a and b are real numbers.
Let p(z) denote the cubic on the left-hand side; the right-hand side is then c3p(z/c). Write p(z)=z3+Az2+Bz+C so
z3 + Az2 + Bz + C ≡ z3+ cAz2 + c2Bz + c3C
⟹ (c−1)A = (c2−1)B = (c3−1)C = 0.
Solving this we can find the possible values of C.
A real number can be said as a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature. continuous means that values can have arbitrarily small variations. Every real number can be almost uniquely represented by an infinite decimal expansion.
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Question is incomplete. The complete question is:
Let c be a complex number. Suppose there exist distinct complex numbers r, s, and t such that for every complex number z, we have
(z−r) (z−s) (z−t) = (z−c r) (z−c s) (z−c t).
Compute the number of distinct possible values of c.
What is the answer of
2+4
5+1
1+1
0+0
Answer:
14
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
2+4
5+1
1+1
0+0
19. What is the total amount to be repaid on a 1-year term
loan of $800 with an interest rate of 14%?
A. $892
B. $902
C. $912
D. $922
Answer: the answer is C $912.
Step-by-step explanation: The interest on the loan is calculated as follows:
Interest = Principal x Rate x Time
where Principal is the amount borrowed, Rate is the interest rate as a decimal, and Time is the length of the loan in years. Substituting the given values, we get:
Interest = $800 x 0.14 x 1
Interest = $112
Therefore, the total amount to be repaid is the sum of the principal and the interest, which is:
Total amount = Principal + Interest
Total amount = $800 + $112
Total amount = $912
What is the total surface area of the triangle prism shown
Answer:
Total surface area = 468 in.²
Step-by-step explanation:
Total surface area of triangular prism = 2BA + PH
Base area (BA) = ½*bh
b = 9 in.
h = 12 in.
2BA = 2(½*9*12) = 108 in.²
Perimeter of base (P) = 9 + 12 + 15 = 36 in.
Height of prism (H) = 10 in.
Plug in the values
Total Surface area of triangular prism = 108 + 36*10 = 468 in.²
MARKING AS BRAINLIST PLS HELP!! 15 points ASAP
Answer:
Set your calculator to Degree mode.
55^2 = 90^2 + 50^2 - 2(90)(50)cos(C)
3,025 = 10,600 - 9,000cos(C)
-7,575 = -9,000cos(C)
cos(C) = 101/120
C = cos^-1 (101/120) = 32.7°
Higher Order Thinking Morgan read
a thermometer at 7:00 P.M. The
temperature was 16°C. This temperature
was 9°C less than the temperature at
2:00 P.M. The temperature at 2:00 P.M.
was 10°C higher than the temperature at
8:00 A.M. What was the temperature at
8:00 A.M.?
The temperature at 8:00 A.M. was 15°C.
Using the given information:
1. At 7:00 P.M., the temperature was 16°C.
2. This temperature was 9°C less than the temperature at 2:00 P.M.
We can use this information to find the temperature at 2:00 P.M.:
Temperature at 2:00 P.M. = 16°C (temperature at 7:00 P.M.) + 9°C
Temperature at 2:00 P.M. = 25°C
3. The temperature at 2:00 P.M. was 10°C higher than the temperature at 8:00 A.M.
Now, we can find the temperature at 8:00 A.M.:
Temperature at 8:00 A.M. = 25°C (temperature at 2:00 P.M.) - 10°C
Temperature at 8:00 A.M. = 15°C
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I will give brainiest to whoever answers correctly !!
Answer:
a. Amount paid for the use of the money is $105
b. Amount paid to the bank is $3,105
Step-by-step explanation:
The amount borrowed = $3000
Simple interest = 3 1/2%=0.035
a.
Amount paid for the use of the money = 3 1/2% of $3000
=0.035*$3000
=$105
PLEASE MARK ME AS BRAINLIEST
b.
Amount paid to the bank= Amount borrowed +simple interest
=$3000+$105
=$3105
What is the area of this figure?
2m
4m
8m
9m
5m
10m
Answer:
98
Step-by-step explanation:
The diagram shows the height of a cone that holds ice cream. The cone has a volume of 4.5 π cubic inches. Which measurement is closest to the radius of the cone in inches?
On solving the query we can say that The slant height, along with the function cone's height and radius, makes a right triangle as it measures from the apex to a certain point on the circular base.
what is function?Mathematics is concerned with numbers and their variations, equations and related structures, shapes and their places, and possible placements for them. The relationship between a collection of inputs, each of which has an associated output, is referred to as a "function". An relationship between inputs and outputs, where each input yields a single, distinct output, is called a function. Each function has a domain and a codomain, often known as a scope. The letter f is frequently used to represent functions (x). X is the input. The four main types of functions that are offered are on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
You are informed that the cone in this scenario has a volume of 4.5 cubic inches. Using the aforementioned calculation, you can determine the radius if you know the cone's height.
Alternately, you may use the Pythagorean theorem to calculate for the radius if you know the cone's slant height. The slant height, along with the cone's height and radius, makes a right triangle as it measures from the apex to a certain point on the circular base.
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Find the y-intercept of the line on the graph
Since no equation of the line, or graph is provided in the question statement, considering the line to be [3x +4y = 12], the y-intercept of the line is 3.
As per question statement, we are supposed to determine the y-intercept of the line on the graph, but no equation of the line, or graph is provided. Hence, we considered the equation of a random line, say,
[3x +4y = 12] and then, determine it's y-intercept.
To solve this question, we can use two methods:
One method is by converting the given equation into the format of the standard equation of a line, and then comparing it to the standard equation to determine the y-intercept, i.e.,
The standard equation of line is (y = mx + c), where, "m" is the slope of the line, and "c" is the y-intercept. Converting [3x +4y = 12] to the form of the standard equation, we get,
\(3x+4y=12\\or,4y=-3x+12\\or,y=\frac{-3x+12}{4}\\ or,[y=(\frac{-3}{4})x+3]...(i)\)
Now comparing (i) to the standard equation of line, we can identify that
(c = 3), i.e., y-intercept of the line [3x +4y = 12] is 3.
Another way we can determine the y-intercept of a line is by, substituting (x = 0) and then solving the equation for "y".
Y-Intercept: The y-intercept is the point on a cartesian plane, where a graph crosses the y-axis, i.e., the value of y when (x = 0).To learn more about Y-Intercepts, click on the link below.
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Write the equation of the line that passes through the points (0, 4) and (- 4, - 5) . Put your answer in fully reduced slope intercept form , unless it is a vertical or horizontal line
Answer:
y=9/4x+4
Step-by-step explanation:
Start by finding the slope
m=(-5-4)/(-4-0)
m=-9/-4 = 9/4
next plug the slope and the point (-4,-5) into point slope formula
y-y1=m(x-x1)
y1=-5
x1= -4
m=9/4
y- -5 = 9/4(x - -4)
y+5=9/4(x+4)
Distribute 9/4 first
y+5=9/4x + 9
subtract 5 on both sides
y=9/4x+4
Select all irrational numbers.
Answer:
B C F
Step-by-step explanation:
If you reduce those answer and try to find the square roots, the decimals are terminating and never ending, while the others are perfect squares.
The is 3/8 as a decimal?