When the sides of the triangle are in the ratio 5:7:8 and the longest side is 36 cm longer than the shortest side, the perimeter is 240cm.
How to calculate the perimeterLet's assume the shortest side of the triangle has a length of x cm. According to the given ratio, the sides of the triangle are in the ratio 5:7:8. Therefore, the lengths of the sides can be expressed as:
Shortest side: 5x
Second side: 7x
Longest side: 8x
We are also given that the longest side is 36 cm longer than the shortest side. So we can set up the following equation:
8x = 5x + 36
Now, let's solve this equation to find the value of x:
8x - 5x = 36
3x = 36
x = 36 / 3
x = 12
Now we can substitute this value back into the expressions for the side lengths to find their actual lengths:
Shortest side: 5x = 5 * 12 = 60 cm
Second side: 7x = 7 * 12 = 84 cm
Longest side: 8x = 8 * 12 = 96 cm
Finally, we can calculate the perimeter of the triangle by adding the lengths of all three sides:
Perimeter = Shortest side + Second side + Longest side
= 60 cm + 84 cm + 96 cm
= 240 cm
Therefore, the perimeter of the triangle is 240 cm.
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Romberg integration for approximating L',f(x) dx gives R21 = 6 and R22 = 6.28 then R11 5.16 4.53 2.15 0.35
The Romberg integration method is used to approximate definite integrals. Given the values R21 = 6 and R22 = 6.28, we can determine the value of R11.
To find R11, we can use the formula:
R11 = (4^1 * R21 - R22) / (4^1 - 1)
Substituting the given values, we have:
R11 = (4 * 6 - 6.28) / (4 - 1)
= (24 - 6.28) / 3
= 17.72 / 3
≈ 5.9067
Therefore, the approximate value of R11 is approximately 5.9067.
Romberg integration is an extrapolation technique that refines the accuracy of numerical integration by successively increasing the order of the underlying Newton-Cotes method. The notation Rnm represents the Romberg approximation with m intervals and n steps. The general formula for calculating Rnm is:
Rnm = (4^n * Rn-1,m-1 - Rn-1,m) / (4^n - 1)
In this case, R21 represents the Romberg approximation with 2 intervals and 1 step, while R22 represents the approximation with 2 intervals and 2 steps. By substituting these values into the formula, we can calculate R11. The numerator is obtained by multiplying R21 by 4 and subtracting R22. The denominator is calculated by subtracting 1 from 4^n. Evaluating this expression yields the approximate value of R11 as 5.9067.
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Consider the seriesn+1
(-1)
(n +1)
7t
ns1
Reviewing the Alternating Series Test to determine which of the following statements is true for the given series. Assume you can only use the Alternate Series Test. Do not go beyond it.
a) The series converges
b) Sincelim anメ0, the series diverges
c) Sincean+i S ancannot be shown to be true for all n, the series diverges
d)Sincean+i S ancannot be shown to be true for all n, the Alternating Series Test cannot be applied
e)Sincelim anメ0, the Alternating Series Test cannot be applied
The correct option is (a). The other options are incorrect because the given series satisfies all the conditions of the alternating series test, and thus, the test is applicable.
The given series is as follows: n+1
(-1)
(n +1)
7t
ns1
An alternating series test is a significant tool for determining whether or not a given series converges. A series is said to be convergent if the sequence of partial sums converges to a finite limit, and divergent otherwise. For the alternating series test to apply to a series, there must be the following three conditions: The series must have alternating terms, meaning that every other term is negative. The sequence of absolute values of the terms of the series must be monotonically decreasing, meaning that the absolute values of each successive term must be smaller than the preceding term's absolute value. The sequence of absolute values must approach zero in the limit. Thus, it can be observed that for the given series, the first two conditions are met. Now, to check the third condition, we must calculate the limit of the terms.
Let us take an=1/(n+1)7tnSince lim an=0, the series passes the third test as well.
Thus, we can apply the alternating series test to the given series. By the alternating series test, we have that the series converges. Thus, the correct option is (a). The other options are incorrect because the given series satisfies all the conditions of the alternating series test, and thus, the test is applicable. Thus, we can safely conclude that option (a) is correct.
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What is the range of the function f : [0,[infinity]) → R, defined by the rule f(t) = e^-2x ? (a) (0,1] (b) R (c) ([0,1] (d) (0,[infinity]).
The range of the function f is (0, [infinity]). The correct option is d.
The range of the function f : [0, [infinity]) → R, defined by the rule f(t) = e^(-2x), can be determined by analyzing the behavior of the exponential function.
As x approaches infinity, e^(-2x) approaches 0, but it never reaches 0. This means that the function f(t) will approach 0 as t approaches infinity, but it will never actually reach 0.
On the other hand, as x approaches negative infinity, e^(-2x) approaches positive infinity. Therefore, the function f(t) will approach positive infinity as t approaches 0.
Based on this analysis, we can conclude that the range of the function f is (0, [infinity]), which means option (d) is the correct answer.
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A booster club sells raffle tickets • Before tickets go on sale to the public, 120 tickets are sold to student athletes. • After tickets go on sale to the public, the tickets sell at a constant rate for a total of 8 hours spread over I days. • At the end of this time, all tickets have been sold. If represents the hours since tickets go on sale to the public and represents the number of raffle tickets sold, which graph best represents the scenario?
Answer:
The top graph.
Step by step:
Before the tickets go on sale, 120 tickets were already sold.
After that, the tickets sell at a constant rate for a total of 8 hours.
At the end of this time, all the tickets were sold (we have 0 tickets left)
If x (horizontal axis) represents the hours since tickets go on sale, and y (vertical axis) represents the number of raffle tickets sold.
Then, at x = 0, we should already see y = 120
Because we start with 120 tickets sold.
Then, as x increases, the number of tickets sold also should increase, until we get x = 8 hours, where y stops increasing because all tickets are already sold.
Then we should have an increasing line that stops increasing at x = 8 hours.
Then the correct option is the above graph, where we have:
An increasing line.
y = 120 in the vertical axis (y = 120 when x = 0)
solve the integral given below for suitable using the Beta function 1 (₁-t²g x dt = ?
The solution to the given integral is: frac{pi}{4}g(x) + frac{1}{2}cdot frac{Gamma(frac{3}{2})Gamma(frac{1}{2})}{Gamma(2)} cdot g(x).
Given integral: int_0^1 (1-t^2)g(x) dt
To solve the given integral, we will make use of Beta function.
The Beta function is defined as follows:
B(p,q) = int_0^1 t^{p-1}(1-t)^{q-1} dt
Using substitution, t = sin theta, we get:
int_0^1 (1-t^2)g(x) dt = int_0^{frac{pi}{2}} (1-sin^2 theta)g(x) cos theta dtheta
= int_0^{frac{\pi}{2}} cos^2 theta g(x) d\theta
= frac{1}{2}\int_0^{\frac{\pi}{2}} (1+\cos 2\theta) g(x) d\theta
= frac{1}{2} \left(\int_0^{\frac{\pi}{2}} g(x) dtheta + int_0^{frac{pi}{2}} g(x) cos 2theta dtheta right)
Using B(p,q)$ for the second integral, we get:
int_0^1 (1-t^2)g(x) dt = frac{1}{2}left(frac{pi}{2}g(x) + frac{1}{2}cdot frac{Gamma(frac{3}{2})Gamma(frac{1}{2})}{Gamma(2)} cdot g(x) right)
= frac{pi}{4}g(x) + frac{1}{2}cdot frac{Gamma(frac{3}{2})Gamma(frac{1}{2})}{Gamma(2)} cdot g(x).
Hence, the value of the given integral int_0^1 (1-t^2)g(x) dt is frac{pi}{4}g(x) + frac{1}{2}cdot frac{Gamma(frac{3}{2})Gamma(frac{1}{2})}{Gamma(2)} cdot g(x).
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Complete the statement. Round to the nearest hundredth if necessary.
6 lb =
oz
Answer: 96 oz
Step-by-step explanation:
The slope of the line containing the points (6, 4) and (-5, 3) is:
1
-1
1/11
Answer:
1/11
Step-by-step explanation:
(6, 4) and (-5, 3)
Slope:
m=(y2-y1)/(x2-x1)
m=(3-4)/(-5-6)
m= (-1)/(-11)
m = 1/11
identify the values of coefficient a,b,and c in the quadrant equation
5x² = 4x + 7
a =
b =
C=
Answer:
a = 5, b = -4, c = - 7-----------------------
Standard form of a quadratic equation:
ax² + bx + c = 0Convert the given into standard form:
5x² = 4x + 7 5x² - 4x - 7 = 0Compare the equations to find coefficients
a = 5, b = -4, c = - 7on the graph of f(x)=sinx and the interval [0,2π), for what value of x does f(x) achieve a maximum? choose all answers that apply.
On the graph of f(x) = sin(x) on the interval [0, 2π), the function achieves a maximum value at x = π/2.
The function f(x) = sin(x) is a periodic function with a period of 2π. Within one period, the function oscillates between the values of -1 and 1. The maximum value of sin(x) is 1, and it occurs when the angle x is π/2.
In the given interval [0, 2π), the function f(x) = sin(x) completes one full period. Starting from x = 0, the function increases and reaches its maximum value of 1 at x = π/2. After that, it starts decreasing and goes through one complete cycle by the time it reaches x = 2π.
Therefore, on the graph of f(x) = sin(x) on the interval [0, 2π), the function achieves a maximum value at x = π/2.
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a single die is rolled one time. Find the probability of rolling a number greater than 4 or less than 3.
A. 37
B. 53
C. 127
D. 217
What’s the answer????
Answer:
I believe its 10 but forgive me if I'm wrong
A cup of milk has 10 grams of protein. How much protein is in 2.5 cups of milk?
Answer:
25 grams of protein
Step-by-step explanation:
10 grams of protein is in 1 cup of milk.
To understand how many grams of protein are in 0.5 cups of milk, I would need to divide 10 by 2, to get 5.
There are 5 grams of protein in 0.5 cups of milk.
Now if I want to see how many grams of protein are in 2 cups of milk, I would multiply 10 by 2, to get 20.
There are 20 grams of protein in 2 cups of milk.
But, the question is asking for how much protein is in 2.5 cups of milk.
Since we know how much is in 2 cups, and 0.5, we can just add them together, because 2+0.5 is 2.5.
20+5 is 25 grams.
There are 25 grams of protein in 2.5 cups of milk.
thanks for the help! i dont really understand numbers with letters easily : )
Answer: x=6
Step-by-step explanation: Hope this help :D
I need this done today please help!
Answer:
1.
2. 4:7
3.
4.10:4
5.
id k the rest sorry :/
PLEASE SHOW YOUR WORK!!! WILL MARK BRAINLIEST!!!
On a youth soccer team 3 out of 12 team members have played in previous years. Based on this information, if 180 kids are in the youth soccer league, then how many could be expected to have played the year before?
Answer:
45
Step-by-step explanation:
3 out of 12 is 1/4, or 0.25, so if you divide 180 by 4, then using the same logic, you can expect 45 kids to have played last year.
3 = 1/4 OR .25 of 12, 12 divided by 4 = 3
180 divided by 4 = 45
Answer:
yes its 45 i did the test and i got an 100
Step-by-step explanation:
heres proof
PLEASE MARK BRAINLIEST!!!!!!what is 22/25 as a equivalent fraction out of 100
Answer:
hope this helps :)
Step-by-step explanation:
18 x 1/6 simplify if can thank u
Answer:
3
Step-by-step explanation:
[tex]18*\frac{1}{6} \\\\3[/tex]
Answer:
=3x
Step-by-step explanation:
18x^1 / 6
=3x
An object is acted upon by the forces F1=(10,6,3), and F2=(0,4,9). Find forces F3 that must act on the object so that the sum of the forces is zero.
The forces [tex]F_3[/tex] that must act on the object so that the sum of the forces is zero are [tex]F_3[/tex] = (-10, -10, -12).
To find the forces [tex]F_3[/tex] that must act on the object so that the sum of the forces is zero, we need to find a vector [tex]F_3[/tex] that satisfies the equation
[tex]F_1 + F_2 + F_3 = 0.[/tex]
Given the forces:
[tex]F_1[/tex] = (10, 6, 3)
[tex]F_2[/tex] = (0, 4, 9)
We can rearrange the equation to solve for [tex]F_3[/tex]:
[tex]F_3 = -F_1 - F_2[/tex]
Now, let's calculate [tex]F_3[/tex]:
[tex]F_3[/tex] = -(10, 6, 3) - (0, 4, 9)
= (-10, -6, -3) - (0, 4, 9)
= (-10-0, -6-4, -3-9)
= (-10, -10, -12)
Therefore, the forces [tex]F_3[/tex] that must act on the object so that the sum of the forces is zero are [tex]F_3[/tex] = (-10, -10, -12).
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Please help I will give brainliest!
Answer:
Step-by-step explanation:
Distributive Property
commutative property of addition.
assosciative property of addition
Answer:
distrubutive property
Step-by-step explanation:
help plzzzzzzzzzzzzz
Answer:
Building new bike paths.
Step-by-step explanation:
The reason I choose this answer was because the other ones would all use more gas when bike paths would limit the amount of driving and add to the amount of biking done.
NEED HELP ASAP!!!!
A rectangular billboard for a high school is 10 feet high and 20 feet long. In a scale model of the school, the billboard is 3.5 inches long. How many inches tall is the scale model?
-i got 1.75
Answer:
I got 1.75 too
Step-by-step explanation:
20/3.5 is 5.7
10/5.7 is 1.75
The rectangular billboard is 1.75 inches tall in the scale model.
What is scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
The fundamental equation to determine a figure's scale factor is written as, Scale factor is equal to the ratio between the dimensions of the new and old shapes.
Given that, a rectangular billboard for a high school is 10 feet high and 20 feet long.
In a scale model of the school, the billboard is 3.5 inches long.
So, the scale factor = 3.5/20
= 0.175 inches
Thus, the height is 10×0.175
= 1.75 inches
Therefore, the rectangular billboard is 1.75 inches tall in the scale model.
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Determine in each case for the linear system X′ = AX whether the
equilibrium point is a sink, a source, a saddle, or a nodal source
(centre), and draw the respective phase diagram.
Equilibrium point is a sink, a source, a saddle, or a nodal source (centre).
The equilibrium point is a sink in a phase diagram. A sink is a point towards which any system that begins near it will converge. This is a stable point that attracts nearby systems towards it. When the system comes close to the sink, it will slow down as it approaches, then stop at the sink. A sink is a stable equilibrium point. This is also known as an attractor that attracts nearby points. The phase diagram is a visual representation of the equilibrium point's behavior in the system. The arrows that come into or go out of the sink are pointing towards it, and they represent the direction of the flow of the system. Thus, the sink's shape is inward, indicating that any system near it will converge towards it.
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PLEASE ANSWER THIS ASAP I WILL MARK YOU THE BRAINLIEST
SHOW YOUR WORK!!!
Calculate the volume of the following three-dimensional object
Answer:
2305.33π square inches
Step-by-step explanation:
The volume of a sphere is V = (4/3) πr ^ 3
Because the diameter is 24, the radius is 12.
Substituting 12 for r in the above equation:
V = (4/3) π (12 ^ 3) = (4/3) (1728) π = 2305.33π square inches, or 7238.23 square inches.
Answer:
Measure the length, width and height of the square or rectangle prism or object in inches. Record each of these on paper. Multiply the three measurements together to find the volume using either paper and pencil or a calculator. This is the equation: Volume = length x width x height.
I think that is:
24/2 = 12² = 144 x 3.14 = 452.16.
¯\_(ツ)_/¯
What is the measure of the other acute angle ?
4.
Which properties of equality justify steps c and f?
A. Multiplication Property of Equality; Division Property of Equality
B. Addition Property of Equality; Division Property of Equality
C. Subtraction Property of Equality; Multiplication Property of Equality
D. Addition Property of Equality; Subtraction Property of Equality
Answer:
B. Addition Property of Equality; Division Property of Equality
Step-by-step explanation:
The answer is D, because in step c. you add to both sides to get rid of the on the right hand, so you use the fact that you can add the same number to both sides of an equation.
Likewise, in step f. you divided both sides by to get rid of the coefficient, so you use the fact that you can divide both sides of an equation by the same number.
...............................................................................................................................................
Answer:
Option C and B
Step-by-step explanation:
In the question step C is 23 + 11 = -11 +(-4x) + 11
which is in the form of a + b = c + a
In step C we have added 11 on both the sides to eliminate 11 from right side of the equation.
property which signifies this step is
Addition property of equality :
In step 'f' expression is
In this step equation has been divided by -4 on both the sides to eliminate 4 from the numerator.
In this step division property of equality has been applied.
Therefore Option C and B are the correct options.
Answer:
B. Addition Property of Equality; Division Property of Equality
Step-by-step explanation:
hope it helps...
Can someone plzzz helpppp!!!!
Answer:
[tex] m\angle SXW =113\degree [/tex]
Step-by-step explanation:
In circle with center X, VS is diameter.
So [tex] \widehat {SWV} [/tex] is a semicircular arc.
[tex] \therefore m\widehat{SWV} = 180\degree [/tex]
[tex] \therefore (12x+7)\degree + (21x +8)\degree = 180\degree [/tex]
[tex] \therefore (33x+15)\degree = 180\degree [/tex]
[tex] \therefore 33x+15 = 180 [/tex]
[tex] \therefore 33x = 180-15 [/tex]
[tex] \therefore 33x = 165 [/tex]
[tex] \therefore x =\frac{165}{33} [/tex]
[tex] \therefore x =5 [/tex]
[tex] m\angle SXW =m\widehat{SW} [/tex]
(Measure of central angle is equal to the measure of its corresponding minor arc)
[tex] m\angle SXW =(21x + 8)\degree [/tex]
[tex] m\angle SXW =(21\times 5+ 8)\degree [/tex]
[tex] m\angle SXW =(105+ 8)\degree [/tex]
[tex] m\angle SXW =113\degree [/tex]
Please Help!!! Unit 8: Right Triangles & Trigonometry Homework 6: Trigonometry Review
The value of x from the figure is [tex]cos^-1(\frac{14}{13} )[/tex]
Triangles and AnglesFrom the given diagram, we have the following
Adjacent = 14Hypotenuse = 13The required angle is x
Using the SOH CAH TOA identity
[tex]cos \theta =\frac{adj}{hyp}\\ cos \theta =\frac{14}{13}\\ \theta = arccos(\frac{14}{13} )[/tex]
Hence the value of x from the figure is [tex]cos^-1(\frac{14}{13} )[/tex]
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Confidence intervals based on pivotal quantities. Let Y1, Y2, . . . , Yn follow an Exponential distribution with parameter β. Note that βYn ∼ Gamma(n, n) and 2nβYn ∼ χ 2 df=2n are both pivotal quantities. (a) Explain why both statistics are indeed pivotal quantities. (b) Construct a 95% confidence interval for β using each pivot and provide interpretations. (c) Compare both intervals. Which one would you recommend using? Explain why
In the context of the Exponential distribution with parameter β, the statistics βYn and 2nβYn are both pivotal quantities. They can be used to construct confidence intervals for β.
A pivotal quantity is a function of the data and a parameter that has a known distribution regardless of the parameter's true value. In this case, both βYn and 2nβYn are pivotal quantities because their distributions (Gamma and chi-squared, respectively) do not depend on the unknown parameter β.
To construct a 95% confidence interval for β using the first pivot, βYn, we can utilize the properties of the Gamma distribution. The interval will be of the form [a, b], where a and b are the lower and upper bounds determined based on the cumulative distribution function of the Gamma distribution. This interval represents a range of plausible values for the parameter β.
Similarly, to construct a 95% confidence interval using the second pivot, 2nβYn, we can employ the chi-squared distribution. The interval will have the form [c, d], where c and d are the lower and upper bounds determined based on the cumulative distribution function of the chi-squared distribution. This interval also represents a range of plausible values for β.
When comparing both intervals, considerations such as width, interpretability, and efficiency are important. The recommended interval would be the one that is narrower (smaller width) and easier to interpret. Additionally, the efficiency of the estimators used in constructing the intervals should be taken into account.
In conclusion, both pivotal quantities, βYn and 2nβYn, can be used to construct 95% confidence intervals for β. The choice between them depends on factors such as width, interpretability, and efficiency. A comprehensive analysis considering these factors will determine the most suitable interval to use.
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help please i have 0 clue on what to do
Answer:
Step-by-step explanation:
[tex]9x6x12[/tex]= 648 the length(12m), width(6m), and height(9m) that all i can give you for now because this got me losing brain sells
Answer:
for the first question the answer is 3
for the second question the answer is 9
Step-by-step explanation:
12/4=3, 6/2=3, 9/3=3
8+8+12+12+6+6 = 52 & 108 + 108 + 72 + 72 + 54 + 54= 468
468 / 52 = 9