Final answer:
To find the function representing the total number of bacteria Q(t) in the petri dish at any time t, we integrate the growth rate function q(t)=12t and add the initial amount. The resulting function is Q(t) = 6t^2 + 89 million. After 3 hours, there will be 143 million bacteria in the dish.
Explanation:
The student is given the rate of bacterial growth in a petri dish as q(t)=12t, which represents the number of millions of bacteria per hour, and the initial number of bacteria is 89,000,000 (or 89 million). To find the function that gives the total number of bacteria at any time t, we integrate the rate of growth and add the initial amount. Since the rate of growth is linear, the integral of q(t)=12t with respect to t is 6t2, and adding the initial amount we get the total number of bacteria Q(t) = 6t2 + 89 million.
After 3 hours, we substitute t=3 into this function to get the number of bacteria:
Q(3) = 6(3)2 + 89 = 6(9) + 89 = 54 + 89 = 143 million bacteria.
Final answer:
A function q(t) representing the number of bacteria over time can be determined by integrating the growth rate function and adding the initial amount of bacteria. After 3 hours, there will be 89,000,054 million bacteria in the dish.
Explanation:
The question asks us to find a function q(t) that gives the number of bacteria in a petri dish at any time t, given that it starts with 89,000,000 bacteria, and the growth rate is 12t million bacteria per hour. To find q(t), we need to integrate the growth rate function and then add the initial amount:
[tex]q(t) = \int (12t) dt + 89,000,000[/tex]
Upon integrating we get:
[tex]q(t) = 6t^2 + 89,000,000[/tex]
To find the number of bacteria after 3 hours, we plug in t = 3:
[tex]q(3) = 6(3)^2 + 89,000,000[/tex] = [tex]6(9) + 89,000,000[/tex] = [tex]54 + 89,000,000[/tex]
Therefore, the number of bacteria after 3 hours is 89,000,054 million.
A company had 15 employees whose salaries are shown below.
Answer:
14,740
Step-by-step explanation:
The mean of a set of data is another way of saying the average
To find the average you find the sum of all the numbers/amount of numbers
In this case it would be 221,100/15
For some constants a and b let \[f(x) = \left\{ \begin{array}{cl} 9 - 2x & \text{if } x \le 3, \\ ax + b & \text{if } x > 3. \end{array} \right.\]The function f has the property that f(f(x)) = x for all x. What is a + b?
Answer:
The value of a+b is 4.
Step-by-step explanation:
The given function is
[tex]\[f(x) = \left\{ \begin{array}{cl} 9 - 2x & \text{if } x \le 3, \\ ax + b & \text{if } x > 3. \end{array} \right.\][/tex]
It is given that for some constants a and b the function f has the property that f(f(x))=x for all x.
For x≤3,
[tex]f(x)=9-2x[/tex]
For x>3,
[tex]f(x)=ax+b[/tex]
At x=0,
[tex]f(0)=9-2(0)=9[/tex]
[tex]f(f(0))=f(9)\Rightarrow a(9)+b=9a+b[/tex]
Using property f(f(x))=x,
[tex]f(f(0))=0[/tex]
[tex]9a+b=0[/tex] .... (1)
At x=1,
[tex]f(1)=9-2(1)=7[/tex]
[tex]f(f(1))=f(7)\Rightarrow a(7)+b=7a+b[/tex]
Using property f(f(x))=x,
[tex]f(f(1))=1[/tex]
[tex]7a+b=1[/tex] .... (2)
Subtract equation (2) from equation (1).
[tex]9a+b-(7a+b)=0-1[/tex]
[tex]2a=-1[/tex]
Divide both sides by 2.
[tex]a=-\frac{1}{2}[/tex]
Substitute this value in equation (1).
[tex]9(-\frac{1}{2})+b=0[/tex]
[tex]b=\frac{9}{2}[/tex]
The value of a is [tex]-\frac{1}{2}[/tex] and value of b is [tex]\frac{9}{2}[/tex]. The value of a+b is
[tex]a+b=-\frac{1}{2}+\frac{9}{2}[/tex]
[tex]a+b=4[/tex]
Therefore the value of a+b is 4.
There is a 0.9986 probability that a randomly selected 33-year-old male lives through the year. A life insurance company charges $182 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $110 comma 000 as a death benefit. Complete parts (a) through (c) below.
Answer:
Expected Value = -$42 (loss of 42 dollars)
Step-by-step explanation:
Complete Question Below:
"There is a 0.9986 probability that a randomly selected 33-year-old male lives through the year. A life insurance company charges $182 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $110 comma 000 as a death benefit. If a 33-year-old male purchases the policy, what is his expected value?"
We can say P(survival) = 0.9986 and thus P(not survival) = 1 - P(survival) = 1-0.9986 = 0.0014
Also,
In case 33 year old doesn't live, the payment would be 100,000 - 182 = $99,818
And
In case 33 year old lives, the payment is
-$182
We know, the expected value is the sum of the product of each possibility with its probability.
[tex]ExpectedValue=\Sigma x*p(x)=(99818)(0.0014)+(-182)(0.9986)=-42[/tex]
This means a loss of $42 (or -$42)
I am so confused and lost!! Please Help!!!
Answer:
x = 2.4
Step-by-step explanation:
To find the value when f(x) = x, you just have to replace f(x) for x
[tex]f(x) =-\frac{1}{4}x +3 \\x = - \frac{1}{4}x +3 \\x +\frac{1}{4}x=3 \\\frac{5}{4} x= 3 \\ x = 3*\frac{4}{5} \\x = 2.4[/tex]
Wayne is hanging a string of lights 58 feet long around the three sides of his patio, which is adjacent to his house. The length of his patio, the side along the house, is 6 feet longer than twice its width. Find the length and width of the patio.
Answer:
The length of the patio is 32 ft and the width is 13 ft
Step-by-step explanation:
see the attached figure to better understand the problem
Let
L ----> the length of his patio
W ---> the width of his patio
we know that
[tex]L+2W=58[/tex] ----> equation A
[tex]L=2W+6[/tex] ----> equation B
substitute equation B in equation A and solve for W
[tex]2W+6+2W=58[/tex]
[tex]4W+6=58[/tex]
[tex]4W=58-6[/tex]
[tex]4W=52[/tex]
[tex]W=13\ ft[/tex]
Find the value of L
[tex]L=2W+6[/tex] ----> [tex]L=2(13)+6=32\ ft[/tex]
therefore
The length of the patio is 32 ft and the width is 13 ft
The required patio length(L) = 32 and width(w) = 13.
Given that,
Wayne is hanging a string of lights 58 feet long,
And the side along the house, is 6 feet long.
We have to find,
The length and width of the patio.
According to the question,
Let, the length of his patio be L and width w,
Wayne is hanging a string of lights 58 feet long around the three sides of his patio, which is adjacent to his house.
L + 2W = 58
And The length of his patio, the side along the house, is 6 feet longer than twice its width.
L = 2W + 6
Solving the equation putting the of L from equation 2 in equation 1,
= 2W + 6 + 2W = 58
= 4W = 58 - 6
= 4W = 52
= W = [tex]\frac{52}{4}[/tex]
= W = 13
And L = 2(13) + 6 = 32
Patio length(L) = 32 And width(w) = 13.
Hence , The required patio length(L) = 32 And width(w) = 13.
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If you eat one quarter of a pizza and your dog eats one eighth of it, what percent is left over?
Answer:
5/8 after subtraction :)
Step-by-step explanation:
Answer: The answer is: 62.5 % (left over).
______________________________________________
Step-by-step explanation:
______________________________________________
[tex]\frac{1}{4} + \frac{1}{8} = ?[/tex] ;
Change "(1/4)" to: "(?/8)" ;
What is "(?)" ? ;
→ (1/4) = (?/8) ;
notice the denominators;
(1/4) = (?/8) ; In the first fraction, how does the "denominator", "4" ; turn to "8" ? Specifically, since we dealing with "fractions", what number do we multiply "4" by, to get: "8" ??? ;
→ " 4 * ? = 8 " ?? ;
→ " 8 ÷ 4 = ? " ;
= 2 ;
______________________________________________
so " 1/4 = ?/8 " ;
Since we multiply the denominator, "4" ; by "2" , to get:
"8" (the denominator in the other fraction);
we multiply the numerator, "1" ; by "2" ; to get:
"2" (the denominator in the other fraction):
______________________________________________
→ " [tex]\frac{1}{4} = \frac{(1*2)}{(4*2)} = \frac{2}{8}[/tex] ;
______________________________________________
Now, the amount of the pizza that "you" ate is: "(2/8)" ;
The amount of the pizza eaten by "your dog" is: "(1/8)" ;
Let's add up the amount of pizza eaten:
[tex]\frac{2}{8} + \frac{1}{8} = \frac{(2+1)}{8} = \frac{3}{8}[/tex] .
The total amount of the pizza would be: " [tex]\frac{8}{8}[/tex] " .
Note: " [tex]\frac{8}{8}[/tex] = 8 ÷ 8 = 1 whole [pizza].
To find the amount left over, subtract the amount eaten; "(3/8)" ; from the whole pizza; "(8/8)" ; as follows:
______________________________________________
→ [tex]\frac{8}{8} - \frac{3}{8} = \frac{(8-3)}{8} = \frac{5}{8}[/tex] .
______________________________________________
Now, the question asks, what percent is left over? ;
So, we convert "(5/8)" into a percentage;
Change "(5/8)" to: "(?/100)" ;
→ Notice the denominators;
(5/8) = (?/100) ; In the first fraction, how does the "denominator", "8" ; turn to "100" ? Specifically, since we dealing with "fractions", what number do we multiply "8" by, to get: "100" ??? ;
→ " 8 * ? = 100 " ?? ;
→ " 100 ÷ 8 = ? " ;
= 12.5 ;
______________________________________________
so " 5/8 = ?/100 " ;
Since we multiply the denominator, "8" ; by "12.5" , to get:
"100" (the denominator in the other fraction);
we multiply the numerator, "5" ; by "12.5" ; to get:
"2" (the denominator in the other fraction):
______________________________________________
→ " [tex]\frac{5}{8} = \frac{(5*12.5)}{(100*12.5)} = \frac{62.5}{100}[/tex] ;
______________________________________________
→ [tex]\frac{62.5}{100} = 62.5 % .
______________________________________________
Hope this helpful to you!
Wishing you the best!
______________________________________________
Reasoning if you multiply two decimals that are less than 1,can you predict whether the product will be less thanor greater than either of the factors? Explain
Answer:
if both are positive, the result will be smaller than eitherif one is negative, the result is less than the positive number and greater than the negative number.if both are negative, the result is greater than eitherStep-by-step explanation:
The magnitude of a fraction of a fraction (their product) is always smaller than the magnitudes of either fraction. So, if both decimals are positive, the result is less than either factor.
___
Negative numbers are less than 1, so there can be several cases of interest when one or both numbers are negative.
Both numbers negative
The product will be positive, so will be greater than either negative factor.
__
One number negative, the other number positive
The product will be negative, so will be less than the positive factor and greater than the negative factor. (Multiplying a negative number by a positive fraction moves it closer to zero on the number line, hence to a value that is greater than the negative factor.)
Simplify. Assume all variables are non-zero. HELP ASAP!
Answer:
D
Step-by-step explanation:
((p^4*q)/p^8)^2.
p^4/p^8=p^(4-8)=p^-4=1/p^4
(q/p^4)^2=(q^2/p^8)
To simplify an algebraic expression, eliminate denominators, distribute factors, rearrange and combine like terms, and isolate the variable. Checking the reasonableness of the answer is also important after simplification.
Explanation:To simplify an algebraic expression or equation involving variables, you should first look at what needs to be solved for and then work the problem out using only variables. This helps in minimizing calculation time and reducing the chance of errors. Here are some steps to simplify algebraic expressions:
Eliminate denominators by multiplying through by the Least Common Denominator.Remove parentheses by distributing any factors outside the parentheses through the terms inside.Get all variable terms on one side of the equation by adding or subtracting them.Combine like terms or factor out the variable if it appears in more than one term to simplify further.Isolate the variable (solve for the variable) using multiplication or division as needed.Additionally, by variable rescaling and setting some limits for the error margin, you can further simplify the algebra by eliminating as many parameters as possible. Always check your final answer to ensure it's reasonable.
Anyone know the answer to this geometry problem?
Answer:
540°
Step-by-step explanation:
The sum of the interior angles of a polygon is:
(n-2)*180
where n = number of sides
Here you have :
(5 - 2)*180 = 540°
Estimate the value of:
square root of 34
Answer:
d. √34 ≈ 5.82
Step-by-step explanation:
Both of choices B and D are valid calculations and should have resulted in the same estimate. Choice B, however, is incorrectly rounded, leaving choice D as the better answer.
___
The other answer choices do not result in a number between 5 and 6, so are clearly incorrect.
Express the confidence interval 0.333 < p < 0.777 in the form p +/- E.
Answer:
p= 0.555 ; E= 0.222; then we have 0.555 +/- 0.222
Step-by-step explanation:
The confidence interval goes from 0.333 to 0.777.
To find the p, we need to locate the median of that series of numbers.
The median is 0.555 as is the middle value of that interval.
Now the E corresponds to the deviation or the Error that we can measure.
And since we know that our variance ranges between 0.333 and 0.777, we can sustract 0.333 to p and we can get 0.222. We can also check if we add 0.222 to p, and we can get 0.777.
Two boats leave port at the same time. One goes west and the other south. The speed of the southbound boat is 5 mph more than the westbound boat. After 3 hours the boats are 27 miles apart. Find the speed of the southbound boat. Round to the nearest tenth of a mile per hour.
Westbound boats speed = X
Southbound boats speed = X + 5
In 3 hours they are 27 miles apart:
3X + 3(x+5) = 27
Simplify:
3x + 3x +15 = 27
Combine like terms:
6x + 15 = 27
Subtract 15 from both sides:
6x = 12
Divide both sides by 6:
x = 12/6
x = 2
Westbound was 2 miles per hour
Southbound was 2 +5 = 7 miles per hour
Check:
2 miles per hour x 3 hours = 6 miles
7 miles per hour x 3 hours = 21 miles
21 + 6 = 27 miles
Selena is driving to visit her grandmother who lives 325 miles away from Selena home. she travels an average of 60 miles per hour. Determine the independent and dependent quantities in each scenario. Be sure to include the appropriate units of measure for each quantity
Answer:
Step-by-step explanation:
independent quantity=60 m/h
dependent =time taken=t
60 t=325
t=325/60=65/12=5 5/12 hours
Consider this bag of marbles.
Answer:
p(green) = 0.5odds in favor of green: 1 : 1Step-by-step explanation:
There are 5 green marbles among the 10 in the bag, so the probability of drawing one at random is 5/10 = 0.50.
The odds in favor of drawing a green marble will be the ratio of the number of green marbles to the number that are not green: 5 : 5. Usually, the odds are expressed using integers with no common factors, so they would be written as 1 : 1.
The population of ages at inauguration of all U.S. Presidents who had professions in the military is 62, 46, 68, 64, 57. Why does it not make sense to construct a histogram for this data set?
Answer: You only have 5 samples, always when you want to do statistics, you need a large sample size.
let's suppose you throw a dice 5 times, the results that it shows are 1,4,2,1,4. If you make statistics whit that numbers, you will think that the 1 and 4 have a bigger possibility than the other numbers, but that can't be, if you throw the dice enough times you will se that all numbers have the same possibility.
I don’t get this question, please help.
Answer:
A = 7
B = 2
Step-by-step explanation:
The question is asking for the simplified form of √(-98). You are expected to know that √-1 = i, and you are expected to be able to factor the number 98.
[tex]\sqrt{-98}=\sqrt{(-1)(7^2)(2)}=7i\sqrt{2}[/tex]
Matching parts of the simplified expression to the form you are given, you see that ...
A = 7
B = 2
For a certain commodity the supply equation is given by S = 2p + 5 At a price of $1, there is a demand for 19 units of the commodity. If the demand equation is linear and the market price is $3, find the demand equation.
Answer:
The demand equation is: D=-4p+23
Step-by-step explanation:
To get started, we should keep in mind that the market price (p=3) occurs when supply equals demand ,therefore when p=3
S=2(3)+5=11
Thus, when p=3 D=11 and, according to the problem when p=1 D=19.
We already know two points on the demand curve. Great!
The demand equation is linear, so it has form D=bp+c.
The variable b is the slope of the demand linear equation . It can be computed through the formula
[tex]b=\frac{y2-y1}{x2-x1}[/tex]. equation 1
Substituting the two points (3,11) and (1,19) on equation 1.
[tex]b=\frac{19-11}{1-3} =\frac{8}{-2}[/tex]
b=-4
Now we can find the value of intercept of the demand equation c trough point-slope form y-y1=b(x-x1).
We can use any of the points. Let's take (3,11) and write in point-slope :
y-11=-4(x-3)
y=-4x+11+12
y=-4x+23
Rewrite the linear equation according our variables D and p
D=-4P+23
Finally we found the demand equation !
Find the domain and range, graph
Answer:
Step-by-step explanation:
An way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.
f(x) = x(2x/2)/x(x+5)(x+6)^2
Find the vertical asymptotes?
Answer:
x = -5, x = -6
Step-by-step explanation:
After canceling common terms from numerator and denominator, there are two factors remaining in the denominator that can become zero. The vertical asymptotes are at those values of x.
[tex]\displaystyle F(x)=\frac{x\frac{2x}{2}}{x(x+5)(x+6)}=\frac{x}{(x+5)(x+6)}[/tex]
The denominator will be zero when ...
x + 5 = 0 . . . . at x = -5
x + 6 = 0 . . . . at x = -6
Kenya plans to make a down payment plus monthly payments in order to buy a motorcycle. At one dealer she would pay $2,350 down and $175 each month. At another dealer, she would pay $2,850 down and $150 each month. After how many months would the total amount paid be the same for both dealers? What would that amount be?
Answer:
20 months
Step-by-step explanation:
Let x be the number of months. The cost equation for each dealer is the total of the down payment and the total monthly contribution. Thus,
Deal 1 cost = $2,350 + $175x
Dealer 2 cost =$2,850 + $150x
The number of months after which the costs from both dealers are equal is calculated by equating the costs for both dealers. Therefore,
$2,350 + $175x = $2,850 + $150x
$175x -$150x =$2,850 -$2,350
$25x =$500
x= $500/$25
x = 20 months
Rewrite the expression 225 divided by 5/8 as 225 x 8/5. So, the quotient says a sloth may move 360 feet in 1 hour. Rewrite 90 minutes as 1 1/2 hour. Multiply by 1 1/2 to get feet in 90 minutes.
Answer:
540 feet
Step-by-step explanation:
225x(8/5)
360 feet in 1 hour
6 feet in 1 minute
540 feet in 90 minutes
The equivalent expressions of the given expressions is 540 feet in 90 minutes.
What are equivalent expressions?Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.
The expression of 225 divided by 5/8 as 225 x 8/5.
225 x (8/5)
So, the quotient says a sloth may move 360 feet in 1 hour.
360 feet in 1 hour
Then, 6 feet in 1 minute
90 minutes as 1 1/2 hour.
Multiply by 1 1/2 to get feet in 90 minutes.
540 feet in 90 minutes
The equivalent expressions of the given expressions is 540 feet in 90 minutes.
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The function f(x) = (x − 4)(x − 2) is shown. On a coordinate plane, a parabola opens up. It goes through (2, 0), has a vertex at (3, negative 1), and goes through (4, 0). What is the range of the function? All real numbers less than or equal to 3 all real numbers less than or equal to −1 all real numbers greater than or equal to 3 all real numbers greater than or equal to −1
Answer: all real numbers greater than it equal to negative one.
Step-by-step explanation: if you graph this equation you see that the vertex is at (3,-1). We know that Range is all possible Y values.so, By looking at their graph we can see that the lowest point it touches is at -1. The rest of the graph goes off into positive and negative infinity.
Range= Y is greater than it equal to -1.
Answer:
All real numbers greater than or equal to −1
Step-by-step explanation:
Here, the given parabola,
[tex]f(x) = (x-4)(x-2)[/tex]
[tex]f(x) = x^2-4x-2x + 8[/tex]
[tex]f(x) = x^2 - 6x+8[/tex]
∵ Leading term = positive
So, the parabola is upward.
We know that an upward parabola is minimum at its vertex
Or it gives minimum output value at its vertex.
for instance, If (h, k) is the vertex of an upward parabola,
then its range = { x : x ≥ k, x ∈ R }
Note : Range = set of all possible output values
We have given,
Vertex = (3, -1)
Hence, Range = all real numbers greater than or equal to −1
LAST option is correct.
find the are of the first one and the circumference of the second one :)
Answer:
area = π/16 in²circumference = (3/4)π inStep-by-step explanation:
The area formula is ...
A = πr²
When r = 1/4 in, the area is ...
A = π(1/4 in)² = π/16 in²
__
The circumference formula is ...
C = πd
When the diameter is 3/4 in, the circumference is ...
C = π(3/4 in) = (3/4)π in
You are given 1000 one dollar bills and 10 envelopes. Put the bills into the envelopes in such a way that someone can ask you for any amount of money from $1 to $1000 (examples - $532, $619, $88, etc.) and you can give it to them through a combination of the envelopes.
Answer:
We can do it with envelopes with amounts $1,$2,$4,$8,$16,$32,$64,$128,$256 and $489
Step-by-step explanation:
Observe that, in binary system, 1023=1111111111. That is, with 10 digits we can express up to number 1023.This give us the idea to put in each envelope an amount of money equal to the positional value of each digit in the representation of 1023. That is, we will put the bills in envelopes with amounts of money equal to $1,$2,$4,$8,$16,$32,$64,$128,$256 and $512.
However, a little modification must be done, since we do not have $1023, only $1,000. To solve this, the last envelope should have $489 instead of 512.
Observe that:
1+2+4+8+16+32+64+128+256+489=1000Since each one of the first 9 envelopes represents a position in a binary system, we can represent every natural number from zero up to 511. If we want to give an amount "x" which is greater than $511, we can use our $489 envelope. Then we would just need to combine the other 9 to obtain x-489 dollars. Since [tex]x-489\leq511[/tex], by 2) we know that this would be possible.Two clocks are turned on at the same time.One clock chimes every 15 minutes.The other clock chimes every 25 minutes.In how many minutes will they chime together
Answer:
The two clock will chime together in 75 minutes
Step-by-step explanation:
- Two clocks are turned on at the same time
- One clock chimes every 15 minutes
- The other clock chimes every 25 minutes
- We need to know in how many minutes they will chime together
- The two clock will chime together in the multiples of 15 and 25
- Lets find the first common multiple of 15 and 25
∵ 15 = 5 × 3
∴ The prime factors of 15 are 3 and 5
∵ 25 = 5 × 5
∴ The prime factor of 25 is 5
∴ The lowest common multiple of 15 and 25 = 5 × 3 × 5 = 75
∴ The two clocks will chime together every 75 minutes
The two clock will chime together in 75 minutes
The exact number of kilometers in m miles is f(m), where f is the function defined by f(m) = 1.609344m. (a) find a formula for f−1(k). (b) what is the meaning of f−1(k)?
Answer:
f⁻¹(k) = k/1.609344f⁻¹(k) is the exact number of miles in k kilometersStep-by-step explanation:
(a) If we let k = f(m), we can solve for m to find f⁻¹(k).
k = 1.609344m
k/1.609344 = m = f⁻¹(k)
__
(b) Since k is the number of kilometers in m miles, m is the number of miles in k kilometers.
__
In summary ...
(a) f⁻¹(k) = k/1.609344
(b) f⁻¹(k) is the exact number of miles in k kilometers
A space plane skims the edge of space at 4000 miles per hour. Neglecting altitude, if the circumference of the planet is approximately 25000 miles, how long will it take for the plane to travel around the planet?
A plane traveling at a speed of 4000 miles per hour would take approximately 6.25 hours to travel around a planet with a circumference of 25,000 miles.
Explanation:To solve this question, we will use the concept of time, speed, and distance. We know that the plane travels at a speed of 4000 miles per hour and the Earth's circumference is 25000 miles. Thus to compute the time it would take for the plane to travel around the planet, we can use the relation 'Time = Distance / Speed'.
The distance in this case is the circumference of the Earth, which is 25000 miles and the speed is the plane's speed, which is 4000 miles/hour. So, we simply divide 25000 miles by 4000 miles/hour:
Time = 25000 / 4000 = 6.25 hours
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Can someone help me with number 10? Thank you.
Answer:
east 95 kmsouth 89 kmStep-by-step explanation:
SOH CAH TOA can remind you of the relationships between triangle measures. The distance east is the side of the right triangle that is opposite the angle, so is related to the hypotenuse (ship's travel distance) by the sine function.
sin(43°) = (travel distance)/(distance east)
So, ...
(distance east) = (travel distance)·sin(43°)
Likewise, the cosine function can be used to find the distance south.
Then we have ...
east = (130 km)sin(43°) ≈ 95 km
south = (130 km)cos(43°) ≈ 89 km
find the value of x, question and choices attached above
Answer:
E. 22Step-by-step explanation:
Look at the picture.
The lines l and m are parallel, therefore alternate interior angles are congruent.
Therefore [tex]\beta=50^o[/tex]
Supplementary angles add up to 180°.
Therefore
[tex](5x-16)+\theta=180[/tex] add 16 to both sides
[tex]5x+\theta=196[/tex] subtract 5x from both sides
[tex]\theta=196-5x[/tex]
We know: the sum of the triangle angle measures is 180°.
Therefore we have the equation:
[tex]50+2x+196-5x=180\\\\-3x+246=180\qquad\text{subtract 246 from both sides}\\\\-3x=-66\qquad\text{divide both sides by (-3)}\\\\x=22[/tex]
(1 pt) A data set consists of the 11 data points shown below, plus one additional data point. When the additional point is included in the data set, the sample standard deviation of the 12 points is computed to be 12.091. If it is known that the additional data point is 25 or less, find the value of the twelfth data point. 25, 41, 49, 25, 30, 13, 31, 34, 27, 54, 38 Value of the additional data point
Answer:
12.83
Step-by-step explanation:
S = 12.091
N = 12
We must find the 12th point, X
The formula of S² (variance) as a function of µ (media) is as follows:
S² = (1/N Ʃ Xi²) - µ²
S² = 146.2
Multiplying both members by N,
N S² = Ʃ Xi² – N µ²
On the other hand,
µ = (25 + 41 + 49 + 25 + 30 + 13 + 31 + 34 + 27 + 54 + 38 + X) / 12
µ = (367 + X) / 12
Replacing,
12 x 146.2 = 13607 + X² – 12 (367 + X)² / 144
1754.4 = 13607 + X² – 0.0833 (134689 + 734 X + X²)
1754.4 = 13607 + X² – 11219.5 – 61.14 X – 0.0833 X²
0.92 X² – 61.14 X + 633.1 = 0
This is solved by finding the two values of X that satisfy the equation.
The solution requires solving the quadratic formula,
X12 = (-b ± √(b² - 4ac)) / 2a
The values are:
X1 = 12.83
X2 = 53.62
Since we know that the value is 25 or less, the answer is 12.83
The twelfth data point in the data set is x = 16.32
How to find the aditional point?
Let x be the value of the twelfth data point. We know that the sample standard deviation of the 12 points is 12.091. We can use the following formula to calculate the sample standard deviation:
s = √((Σ((xₙ - M)²) / (n - 1)))
where:
s is the sample standard deviationxₙ is the value of the n-th data pointM is the sample meann is the number of data pointsWe can plug in the given values to get the following equation:
if x is the missing data point then:
M = (25 + 41 + 49 + 25 + 30 + 13+ 31 + 34 + 27 + 54 + 38 + x)/12
M = 30.6+ x/12
And we know that:
s = 12.091
n = 12
Replacing these values we get:
12.091 = √((Σ((xₙ - 30.6 - x/12)²) / (12 - 1)))
Apply the square in both sides:
146.19 = (Σ((xₙ - 30.6 - x/12)²) / (11)
Multiply both sides by 11:
146.19*11 = Σ((xₙ - 30.6 - x/12)²
1,608.12 = Σ((xₙ - 30.6 - x/12)²
Now we can solve the right side:
1,608.12 = (-5.6 - x/12)² + (10.4 - x/12)² + (18.4- x/12)² + (-5.6 - x/12)² + (-0.6 - x/12)² + (-17.6 - x/12)² + (0.4 - x/12)² + (3.4 - x/12)² + (-3.6 - x/12)² + (23.4 - x/12)² + (7.4 - x/12)² + ( x - x/12)²
Now we can graph this, the positive solution is x = 16.32
Learn more about stardard deviation:
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