The approximation of the integral ∫cos(x² + 5) dx using simple Simpson's rule is approximately -0.65314.
The integral ∫cos(x² + 5) dx using simple Simpson's rule, we need to divide the integration interval into smaller subintervals and apply Simpson's rule to each subinterval.
The formula for simple Simpson's rule is:
I ≈ (h/3) × [f(x₀) + 4f(x₁) + f(x₂)]
where h is the step size and f(xi) represents the function value at each subinterval.
Assuming the lower limit of integration is a and the upper limit is b, and n is the number of subintervals, we can calculate the step size h as (b - a)/n.
In this case, the limits of integration are not provided, so let's assume a = -1 and b = 1 for simplicity.
Using the formula for simple Simpson's rule, the approximation becomes:
I ≈ (h/3) × [f(x₀) + 4f(x₁) + f(x₂)]
For simple Simpson's rule, we have three equally spaced subintervals:
x₀ = -1, x₁ = 0, x₂ = 1
Using these values, the approximation becomes:
I ≈ (h/3) × [f(-1) + 4f(0) + f(1)]
Substituting the function f(x) = cos(x² + 5):
I ≈ (h/3) × [cos((-1)² + 5) + 4cos((0)² + 5) + cos((1)² + 5)]
Simplifying further:
I ≈ (h/3) × [cos(6) + 4cos(5) + cos(6)]
Now, we need to calculate the step size h and substitute it into the above expression to find the approximation. Since we assumed a = -1 and b = 1, the interval width is 2.
h = (b - a)/2 = (1 - (-1))/2 = 2/2 = 1
Substituting h = 1 into the expression:
I ≈ (1/3) × [cos(6) + 4cos(5) + cos(6)]
Evaluating the expression further:
I ≈ (1/3) × [cos(6) + 4cos(5) + cos(6)] ≈ -0.65314
Therefore, the approximation of the integral ∫cos(x² + 5) dx using simple Simpson's rule is approximately -0.65314.
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A student-fare bus pass costs half as much as an adult-fare pass. Together, one student pass and one adult pass cost $129. How much does each pass cost?
Each pass costs $86 and $43 for an adult-fare and student-fare bus pass respectively.
Let the cost of an adult-fare bus pass be A student-fare bus pass costs half as much as an adult-fare pass, hence, the cost of a student pass will be $129 - A.
Mathematically, this is represented as:A = 2($129 - A) $A = $258 - 2A 3A = $258 A = $86Therefore, the cost of an adult-fare bus pass is $86.A student pass costs half as much as an adult-fare pass.
Since the cost of an adult-fare pass is $86, therefore the cost of a student pass will be half of $86. Mathematically, this can be represented as:Cost of student pass = 1/2 x $86 = $43
Therefore, each pass costs $86 and $43 for an adult-fare and student-fare bus pass respectively.
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Is the spinner shown a fair spinner? Explain
why or why not.
A system of equations is created by using the line that is created by the equation 3x-2y=-4 and the line that is created
by the data in the table below.
Х
y
-9
-3
-1
-5
3
3
5
7
What is the y-value of the solution to the system?
Answer:
y=6x-8
Step-by-step explanation:
3x-2y=-4
3x^2-2y^2=-4^2
6x-y=8
y=6x-8
Does anyone know the answer to this and if you do pls give it to me I need it ASAP
Answer:
7,3 if rounded up...
not rounded up..... 7, 3.3????? I think???
Slope-intercept form: y = mx + b
First find the slope : [tex]\frac{rise}{run} = \frac{-1}{3}[/tex]
Slope = -1/3
Now we got y = -1/3x + b
Next find y-intercept. This is where your line crosses the y line (vertical)
Y-intercept = 3
b = 3
Answer: y = -1/3x + 3
r17 is greater than or equal to 545.7
Answer:
r17 is that a mistake or actually the number?
The perimeter of a rectangle is 100 feet, and one side is 6 feet longer than the other side. An equation to find the length x of the shorter side is:
a. x + (x + 6) = 100
b. x + (x - 6) = 100
c. x + (x + 6) = 50
d. x + (x - 6) = 50
So the answer is not among the options provided. To find the equation that represents the relationship between the length of the shorter side (x) and the perimeter of the rectangle,
we can use the given information.
Let's denote the length of the shorter side as x. According to the problem, the other side is 6 feet longer, so the length of the longer side would be x + 6.
The perimeter of a rectangle is given by the sum of all its sides. In this case, the perimeter is 100 feet.
The equation to find the length x of the shorter side can be written as:
2x + 2(x + 6) = 100
Simplifying the equation, we have:
2x + 2x + 12 = 100
4x + 12 = 100
4x = 100 - 12
4x = 88
x = 88/4
x = 22
therefore, the correct equation to find the length x of the shorter side is:
2x + 2(x + 6) = 100
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The equation to find the length x of the shorter side is x + (x - 6) = 50.
Option (d) is the correct answer.
Given that the perimeter of a rectangle is 100 feet, and one side is 6 feet longer than the other side.
Let's suppose that x represents the length of the shorter side of the rectangle.
Therefore, the length of the longer side of the rectangle is (x + 6).
Using the formula of the perimeter of a rectangle, we get:
Perimeter = 2 × (Length + Width)
According to the problem,
Perimeter = 100
Length = (x + 6)
Width = x
Substituting the values,
Perimeter = 2 × (Length + Width)
100 = 2 × [(x + 6) + x]
50= 2x + 6
x = (50 - 6)/2
x = 22
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If arc ED=(9x-3) , arc BF=(15x-39) and angle BCF=(11x-9) find arc ED
Answer:
ED = 105
Step-by-step explanation:
Answer:
ED=105 and x=12
Step-by-step explanation:
The tangent lines of a simple curve have azimuths 300 and bearing N 04° E, respectively. A third tangent line AB intersects the two tangent lines at bearing S 34 E. Stationing of the Pl of the curve is 16 + 464.35 and the distance from point B to the Pl of the curve is 277.6 m (ie BV = 277.6 m). Determine the following: a. Radius of the simple curve that shall be tangent to these three lines. b. Stationing of the PC Stationing of the PT
The radius of the simple curve is not provided and b. The stationing of the PC and PT is not provided.
The given information is insufficient to determine the radius of the simple curve or the stationing of the PC (Point of Curvature) and PT (Point of Tangency).
To determine the radius of the simple curve, additional information is needed, such as the angle between the two tangent lines or the length of the third tangent line AB. Without this information, we cannot calculate the radius.
Similarly, the stationing of the PC and PT requires more details, such as the length of the curve or the degree of curvature. The information provided in the question does not include these parameters, making it impossible to determine the stationing of the PC and PT.
Therefore, based on the given information, we cannot determine the radius of the simple curve or the stationing of the PC and PT.
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d) Vegetable ghee is stored in a rectangular vessel of internal dimensions
60 cm x 10 cm x 45 cm. It is transferred into the identical cubical vessels. If the
internal length of each cubical vessel is 10 cm. how many vessels are required to
empty the rectangular vessel?
27 vessels
Step-by-step explanation:
get the volume of the rectangular vessel 60cm ×10cm ×45cm giving you 27000cm3.Find volume of one of the cube 10cm×10cm×10cm giving 1000cm3.
if 1 cube =1000cm3
? = 27000cm3
27000cm3× 1cube
1000cm3
di
vide then get your answer as 27 vessels
If a and b are the legs of a right triangle, and c is the hypotenuse, what is
the length of b if a = 6 and c = 18.5? (If necessary, round to the nearest
tenth)
what is this answer?
Given 15 patients 5 of them has a particular heath disease, what is the probability of taking 2 out of 4 selected patients has heart disease? 5. A certain clinic in the America is on average has a patient of 3 an hour. Find the probability that the clinic will have 4 patients in the next hour.
The probability of selecting 2 out of 4 patients with heart disease from a group of 15 patients, where 5 of them have the disease, can be calculated using the combination formula. The probability is approximately 0.595.
B. Explanation:
To calculate the probability, we need to use the concept of combinations. The formula for calculating combinations is given by:
C(n, k) = n! / (k!(n-k)!)
Where n is the total number of elements and k is the number of elements we want to choose.
In this case, we have a total of 15 patients, out of which 5 have the heart disease. We want to choose 2 patients with heart disease from a group of 4 patients.
The probability can be calculated as:
P(2 patients with heart disease) = C(5, 2) / C(15, 4)
C(5, 2) represents the number of ways to choose 2 patients with the heart disease from the group of 5 patients, and C(15, 4) represents the total number of ways to choose 4 patients from the group of 15 patients.
Using the combination formula, we can calculate C(5, 2) and C(15, 4) as follows:
C(5, 2) = 5! / (2!(5-2)!) = 10
C(15, 4) = 15! / (4!(15-4)!) = 1365
Substituting these values into the probability formula:
P(2 patients with heart disease) = 10 / 1365 ≈ 0.007
Therefore, the probability of selecting 2 out of 4 patients with the heart disease from the given group is approximately 0.595.
Moving on to the second part of the question, to find the probability that the clinic will have 4 patients in the next hour, we need to determine the average number of patients per hour and use the Poisson distribution.
The average number of patients per hour is given as 3. The Poisson distribution formula is:
P(x; λ) = (e^(-λ) * λ^x) / x!
Where P(x; λ) is the probability of x events occurring in a given interval, λ is the average rate of events, e is the base of the natural logarithm, and x! denotes the factorial of x.
In this case, we want to find P(4; 3), which represents the probability of having 4 patients when the average rate is 3.
Substituting the values into the formula:
P(4; 3) = (e^(-3) * 3^4) / 4!
Calculating the values:
P(4; 3) ≈ 0.168
Therefore, the probability that the clinic will have 4 patients in the next hour is approximately 0.168.
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yo someone help will give brainliest
Answer:
[tex]x=3[/tex]
Step-by-step explanation:
Equation - [tex]5=x+2[/tex]
Solve - subtract 2 from both sides - [tex]3 = x[/tex]
Answer:
X= 3 oz.
Step-by-step explanation:
Count left side. Minus the oz. on the right from that amount. You get 3. Chess piece weighs 3 oz.
Hope I helped.
0548 f(x) = 2100 The mean age of a woman in a certain country when her child is born can be approximated by the function where x = 10 corresponds to the year 2010. Estimate the mean age of the woman at the birth of her first child in the following years, The mean age of a woman at the birth of her first child in 2015 is
(a) Mean age in 2010 ≈ 23.9 years
(b) Mean age in 2013 ≈ 24.4 years
(c) Mean age in 2016 ≈ 24.9 years
To estimate the mean age of a woman at the birth of her first child in the given years, we can substitute the corresponding values of x into the function f(x) = 21 × [tex]x^{0.0521[/tex].
(a) For the year 2010 (x = 10):
f(10) = 21 × [tex](10)^{0.0521[/tex] ≈ 21 × 1.136 ≈ 23.856
The mean age of a woman at the birth of her first child in 2010 is approximately 23.9 years.
(b) For the year 2013 (x = 13):
f(13) = 21 × [tex](13)^{0.0521[/tex] ≈ 21 × 1.161 ≈ 24.381
The mean age of a woman at the birth of her first child in 2013 is approximately 24.4 years.
(c) For the year 2016 (x = 16):
f(16) = 21 × [tex](16)^{0.0521[/tex] ≈ 21 × 1.185 ≈ 24.885
The mean age of a woman at the birth of her first child in 2016 is approximately 24.9 years.
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The question is -
The mean age of a woman in a certain country when her child is born can be approximated by the function
f(x)=21x0.0521,
where
x=10
corresponds to the year 2010. Estimate the mean age of the woman at the birth of her first child in the following years.
(a) 2010
(b) 2013
(c) 2016
(a) The mean age of a woman at the birth of her first child in 2010 is?
(b) The mean age of a woman at the birth of her first child in 2013 is?
(c) The mean age of a woman at the birth of her first child in 2016 is?
(Type an integer or decimal rounded to one decimal place as needed.)
help with segment relationships in circles...picture attatched.
Answer:
x=23
Step-by-step explanation:
Hello There!
The relationship between chords can be found below in the image.
Pretty much the product of the segments in the same chord is equal to the product of the other segments in the other chord if that makes sense
So more specifically for this problem
10 * 18 = 9(x-3)
once we are able to create a formula/equation this problem is a lot easier to understand
Now we use basic algebra to solve for x
10 * 18 = 9(x-3)
step 1 combine like terms
10 * 18 = 180
now we have
180 = 9(x-3)
step 2 distribute the 9 to what's in the parenthesis (x and -3)
9*x=9x
9*-3=-27
now we have
180 = 9x - 27
step 3 add 27 to each side
-27 + 27 cancels out
180 + 27 = 207
now we have
207 = 9x
step 4 divide each side by 9
207/9 = 23
9x/9=x
we're left with x = 23
Now we want to check our answer
is 10 * 18 = 9*(23-3) then our answer is correct
10*18=180
23-3=20
20*9=180
180=180 is true hence the answer is 23
Prince Ivan rides Grey Wolf at a constant speed from King's Castle to the Magic Apple Garden in 5 hours. On their return trip to King's Castle, Grey Wolf runs at that original constant speed for the first 36 km. Then he runs the rest of the way 3 km/h faster. What was Grey Wolf's original speed if the return trip took 15 minutes less than the trip from King's Castle to the Magic Apple Garden?
Answer:
48 and 9
Step-by-step explanation:
36/x + 5x-36/x+3 = 5-0.25
Answer:
9 and 48 km/hr
Step-by-step explanation:
The Formula [tex]S=\frac{D}{T}[/tex] along with its variations are used
Let's say for the initial ride, the speed was x. Because the time was 5 hours, the distance was 5x km. Now for the return. For the first part, the speed remains x but our distance is 36km. So, our time is 36/x hours. For the second part, the speed is x+3 but our distance is 5x-36 (The total minus the distance of the first part.) So, our time is [tex]\frac{5x-36}{x+3}[/tex]. Now we have the equation [tex]\frac{36}{x} + \frac{5x-36}{x+3}=5-\frac{1}{4}[/tex] as our times add up to 5 hours minus 1/4 of and hour. Solving, we get x=9, x=48.
Please help!!! I’ll do anything!!
Answer:
I believe the answer would be m = -28
Step-by-step explanation:
To remove the demoninater, multiple both sides by 7
12*7 = 84 so now you have -3 = 84
Divide 84 by -3, giving you -28
5. Let T1 and T2 be two stop times with respect to the same filtration. Prove that me (T1, T2) and T₁ +T2 are also stopping times.
T1 and T2 are stop times, both of these events belong to Ft, their union also belongs to Ft. Hence, we can conclude that T1 + T2 is also a stop time.
We are given two stop times T1 and T2 with respect to the same filtration.
We are to prove that the maximum and the sum of T1 and T2, i.e., max(T1, T2) and T1 + T2 are also stop times.
Let us consider the stop time T1.
This means that the event {T1 ≤ t} belongs to the sigma-algebra Ft, for all t≥0.
Similarly, let us consider the stop time T2.
This means that the event {T2 ≤ t} belongs to the sigma-algebra Ft, for all t≥0.
We are to prove that max(T1, T2) is also a stop time.
We can do so by considering the following event:{max(T1, T2) ≤ t}.
If T1 ≤ T2, then this event reduces to {T2 ≤ t} which belongs to Ft.
Similarly, if T2 ≤ T1, then this event reduces to {T1 ≤ t} which also belongs to Ft.
Thus, we can conclude that max(T1, T2) is a stop time.
We are to prove that T1 + T2 is also a stop time.
We can do so by considering the following event:{T1 + T2 ≤ t}.
This event can be expressed as:{T1 ≤ t − T2} ∪ {T2 ≤ t − T1}.
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Put the following numbers in order from least to greatest: √42, 7, 6, √38.
Answer:
6, √38, √42, 7
Step-by-step explanation:
The numbers in order from least to greatest is 6,√38,√42,7
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Finding the least common multiples of the denominator expressions can help. Then using the similar method as we use in sum of fractions would give the sum of algebraic fractions.
Given;
√42, 7, 6, √38
√42=6.4
√38=6.1
Therefore, the order of algebra will be 6,√38,√42,7
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please help!
PQRS is a kite. Enter coordinates
for point S.
P(0, b)
S
Q(a, 0)
R(0, -c)
S([ ? ] ,[ ? ])
Answer:
(-a, 0)
Step-by-step explanation:
By telling you that the quadrilaretal is a kite the problem is telling you that SQ is perpendicular to PR, and that PS=PQ (by simmetry, it follows that also RS=RQ). So S has to be the symmetric of Q to the center (intersection of the diagonals), which means that, since Py=0, its coordinates are (-a, 0)
give the slope of the line with equation 17x = -34; then graph the line
Consider this right triangle.
Enter the ratio equivalent to sin (B)
Answer:
[tex]\boxed {\boxed {\sf sin(B)= \frac {21}{29}}}[/tex]
Step-by-step explanation:
Sine is the ratio of the opposite side to the hypotenuse.
[tex]sin \theta= \frac {opposite}{hypotenuse}[/tex]
We want to find the sine of angle B. The side AC, which measures 21, is opposite angle B.
The side AB, which measures 29, is the hypotenuse because it is the longest side and opposite the right angle.
[tex]opposite= 21\\hypotenuse=29[/tex]
Substitute the values into the formula.
[tex]sinB= \frac {21}{29}[/tex]
This ratio cannot be reduced further, so it is the final answer.
The sine of B is 21/29
Im giving brainliest
Answer:
> there you go
Step-by-step explanation:
Answer:
>
Step-by-step explanation:
It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 34 small cars at 65 miles per hour and records the braking distance. The sample average braking distance is computed as 115 feet. Assume that the population standard deviation is 20 feet. Use Table 1.
Use α = 0.01 to determine if the average braking distance differs from 120 feet. The average braking distance is (significantly/not significantly) different from 120 feet.
The average braking distance for small cars traveling at 65 miles per hour significantly differs from the advertised value of 120 feet.
In this case, we want to determine if the average braking distance is significantly different from 120 feet. Since the researcher wants to detect any difference, whether it is shorter or longer than 120 feet, the alternative hypothesis will be two-tailed.
H0: The average braking distance for small cars traveling at 65 miles per hour is 120 feet.
Ha: The average braking distance for small cars traveling at 65 miles per hour is not equal to 120 feet.
To conduct the hypothesis test, we will use the sample data provided by the researcher. The sample size is 34, and the sample average braking distance is 115 feet. The population standard deviation is given as 20 feet.
The formula for the test statistic (z-score) is:
z = (sample average - hypothesized population average) / (population standard deviation / √sample size)
Plugging in the values from the problem:
z = (115 - 120) / (20 / √34)
z = -5 / (20 / √34)
Using Table 1 or a statistical calculator, we can determine the critical z-value corresponding to a significance level of 0.01. Since we have a two-tailed test, we need to split the significance level in half. Each tail will have an alpha of 0.005 (0.01/2).
Looking up the z-value for α/2 = 0.005, we find it to be approximately 2.576.
Now we compare the calculated z-value to the critical z-value:
If the calculated z-value falls outside the range defined by the critical z-values, we reject the null hypothesis. Otherwise, if the calculated z-value falls within the range, we fail to reject the null hypothesis.
In our case, the calculated z-value is -5 / (20 / √34), which we need to compare to -2.576 and +2.576.
If the calculated z-value is less than -2.576 or greater than +2.576, we reject the null hypothesis. Otherwise, if the calculated z-value is between -2.576 and +2.576, we fail to reject the null hypothesis.
By performing the calculation, we find that the calculated z-value falls outside the range defined by -2.576 and +2.576. Therefore, we can reject the null hypothesis.
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what equation matches the graph?
Answer:
b
Step-by-step explanation:
The largest U.S flag in the world is 225 feet by 505 feet.
Is the ratio of the length to the width equivalent to 1:19,
the ratio for official government flags?
Answer:
Step-by-step explanation:
Remark
The ratio should be 10 : 19
Given
Flag Ratio: 225 : 505
Break the dimensions into prime factors.
225: 15 * 15 = 3*5 * 3*5
505: 5 * 101
Conclusion
101 is prime so this dimension cannot be broken down any further
The fives cancel out. The dimensions of this flag are in the ratio of 45/101 which is 0.4455
10/19 = 0.5263
I would say this is reasonably close.
Need help with this
Answer:
search it up
Step-by-step explanation:
please help me out! I don’t understand
Answer:
10/26
Step-by-step explanation:
out of 26 student 10 have a brother 8 people have only a brother and 2 people have both a sister and a brother. so you have 10/26
y = 100(1.25)^t
1. What is your initial value?
Need help with this question
Answer:
Function A rate = 5/1
Function B rate = -4.5
Function A because its rate is positive while Function B's rate is negative