A Triangle has two sides of lengths of 5 and 13. What value could the length of the third side be? Check all that apply.
19
5
24
10
8
2

We are 99% confident that the true average stance duration among elderly individuals lies within the range of 744.56 ms to 857.44 ms.

To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test. The null hypothesis (H0)

Using the t-test, we compare the means and standard deviations of the two samples and calculate the test statistic

a) To calculate a 99% confidence interval for the true average stance duration among elderly individuals, we can use the sample mean, sample standard deviation, and the t-distribution.

Given:

Older adults: n = 28, sample mean = 801, sample standard deviation = 117

Using the formula for a confidence interval for the mean, we have:

Margin of error = t * (sample standard deviation / √n)

Since the sample size is relatively large (n > 30), we can use the z-score instead of the t-score for a 99% confidence interval. The critical z-value for a 99% confidence level is approximately 2.576.

Calculating the margin of error:

Margin of error = 2.576 * (117 / √28) ≈ 56.44

The confidence interval is then calculated as:

Confidence interval = (sample mean - margin of error, sample mean + margin of error)

Confidence interval = (801 - 56.44, 801 + 56.44) ≈ (744.56, 857.44)

b) To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test.

The null hypothesis (H0): The true average stance duration among elderly individuals is equal to or less than the true average stance duration among younger individuals.

The alternative hypothesis (Ha): The true average stance duration among elderly individuals is larger than the true average stance duration among younger individuals.

. With the given data, perform the t-test and obtain the p-value.

c) To construct a 95% confidence interval for the difference in means between older and younger adults, we can use the formula for the confidence interval of the difference in means.

Given:

Older adults: n1 = 28, sample mean1 = 801, sample standard deviation1 = 117

Younger adults: n2 = 16, sample mean2 = 780, sample standard deviation2 = 72

Calculating the standard error of the difference in means:

Standard error = √((s1^2 / n1) + (s2^2 / n2))

Standard error = √((117^2 / 28) + (72^2 / 16)) ≈ 33.89

Using the t-distribution and a 95% confidence level, the critical t-value (with degrees of freedom = n1 + n2 - 2) is approximately 2.048.

Calculating the margin of error:

Margin of error = t * standard error

Margin of error = 2.048 * 33.89 ≈ 69.29

The confidence interval is then calculated as:

Confidence interval = (mean1 - mean2 - margin of error, mean1 - mean2 + margin of error)

Confidence interval = (801 - 780 - 69.29, 801 - 780 + 69.29) ≈ (-48.29, 38.29)

Comparison with part (b): In part (b), we performed a one-tailed test to determine if the true average stance duration among elderly individuals is larger than among younger individuals. In part (c), the 95% confidence interval for the difference in means (-48.29, 38.29) includes zero. This suggests that we do not have sufficient evidence to conclude that the true average stance duration is significantly larger among elderly individuals compared to younger individuals at the 95% confidence level.

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To solve the given initial value problem using the Laplace transform, the Laplace transform of the differential equation.   L(y'') - 2L(y') - 3L(y) = 0. By  by taking the Laplace transform of the differential equation, we obtain the equation Y = 8/(s - 3).

Let Y be the Laplace transform of y(t), i.e., Y = L(y(t)). Taking the Laplace transform of the differential equation y'' - 2y' - 3y = 0, we get: L(y'') - 2L(y') - 3L(y) = 0.

Now, let's apply the properties of the Laplace transform to each term: L(y'') = \(s^2\)Y - sy(0) - y'(0), L(y') = sY - y(0), L(y) = Y. Using the initial conditions y(0) = 8 and y'(0) = -4, we can substitute these values into the Laplace transform equation:

\(s^2\)Y - s(8) + 4 - 2(sY - 8) - 3Y = 0.

Simplifying the equation, we get:

\(s^2\)Y - 2sY - 3Y - 8s + 16 - 24 = 0.

Combining like terms:

(\(s^2\)- 2s - 3)Y - (8s + 8) = 0.

Now, we can factor the quadratic term:

(s - 3)(s + 1)Y - 8(s + 1) = 0.

Factoring out the common factor (s + 1), we have:

(s + 1)(s - 3)Y - 8(s + 1) = 0.

Now, we can solve for Y:

Y = (8(s + 1))/(s - 3)(s + 1).

Simplifying further, we get: Y = 8/(s - 3).

Therefore, by taking the Laplace transform of the differential equation, we obtain the equation Y = 8/(s - 3).

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Complete question is :"Use the Laplace transform to solve the following initial value problem: y′′−2y′−3y=0,y(0)=8,y′(0)= -4

(1) First, using Y for the Laplace transform of y(t), i.e., Y=L(y(t))

find the equation you get by taking the Laplace transform of the differential equation to obtain = 0"

Answer:

28

Step-by-step explanation:

You can split the figure up

3*4/2 = 6

3*4/2 = 6

8*2 = 16

6+6+16 = 28

Answer:

0

Step-by-step explanation:

Since

1

is constant with respect to

A

, the derivative of

1

with respect to

A

is

0

.

0

I'm not sure though, I was just trying.

To determine whether the series ∑(8(4n + 15 - n)), n = 1 to ∞ converges or diverges, we can analyze its behavior. Let's simplify the series: ∑(8(4n + 15 - n)) = ∑(32n + 120 - 8n) = ∑(24n + 120).  series ∑(8(4n + 15 - n)), n = 1 to ∞ diverges.

The series can be separated into two parts: ∑(24n) + ∑(120). The first part, ∑(24n), is an arithmetic series with a common difference of 24. The sum of an arithmetic series can be calculated using the formula: Sn = (n/2)(2a + (n - 1)d), where Sn is the sum of the series, n is the number of terms, a is the first term, and d is the common difference.

In this case, a = 24 and d = 24. Since we have an infinite number of terms, n approaches infinity. Plugging in these values, we have: ∑(24n) = lim(n→∞) (n/2)(2 * 24 + (n - 1) * 24). Simplifying further: ∑(24n) = lim(n→∞) (n/2)(48 + 24n - 24). ∑(24n) = lim(n→∞) (n/2)(24n + 24).

As n approaches infinity, the terms involving n^2 (24n * 24) will dominate the series, and the series will diverge. Therefore, ∑(24n) diverges.

Now, let's consider the second part of the series, ∑(120). This part does not depend on n and represents an infinite sum of the constant term 120. An infinite sum of a constant term diverges. Therefore, ∑(120) also diverges.

Since both parts of the series diverge, the entire series ∑(24n + 120) diverges. In summary, the series ∑(8(4n + 15 - n)), n = 1 to ∞ diverges.

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Complete question is " Determine whether the series is converges or diverges  8( 4n + 15-n) - n = 1"

The circumference of the circle is 50. 24 Inches

It is important to note that the circumference of a circle is represented with the formula;

C = 2πr or πd

Given that;

Also, the formula for calculating the radius of the circle given the diameter is expressed as;

Radius = diameter /2

Now, let's substitute the values into the formula, we get;

Circumference, C = 2 × 3. 14 × 8

Multiply the values

Circumference, C = 50. 24 Inches

Hence, the value is 50. 24 Inches

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Juanita will stuff 1/2 of the envelopes when working together with Sally and Abdul.

To determine the fraction of envelopes that Juanita will stuff when working together with Sally and Abdul, we need to consider their individual rates of work.

Let's denote the number of envelopes as E.

Sally can stuff all the envelopes in 3 hours, which means she can stuff E envelopes in 3 hours. Thus, Sally's rate of work is E/3 envelopes per hour.

Similarly, Abdul can stuff all the envelopes in 4 hours, so his rate of work is E/4 envelopes per hour.

Juanita can stuff all the envelopes in 6 hours, so her rate of work is E/6 envelopes per hour.

When they work together, their rates of work are cumulative. Therefore, the combined rate of work when all three work together is:

Sally's rate + Abdul's rate + Juanita's rate = E/3 + E/4 + E/6.

To find the fraction of envelopes stuffed by Juanita, we need to consider her rate of work in relation to the total combined rate of work:

Juanita's rate / Combined rate = (E/6) / (E/3 + E/4 + E/6).

Simplifying the expression, we get:

Juanita's rate / Combined rate = 1/2.

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Another possible vertex of the square is determined as (2, 1).

option B is the correct answer.

The vertex of a figure is the point of intersection of two sides of the shape.

The perimeter of the square is given as 12 units, the length of each side of the square is calculated as follows;

P = 12 units

a side length = 12 units / 4 = 3 units

To determine another possible vertex of the square, the length between the points must be equal to 3.

Let's consider point A;

A = (1, 2)

given vertex = (-1, 1)

distance between the points = √ (-1 -1)² + (1 - 2)² = √5

Let's consider point B;

B = (2, 1)

given vertex = (-1, 1)

distance between the points = √ (-1 -2)² + (1 - 1)² = √9 = 3

Thus, point B is another possible vertex of the square.

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Answer:

JT=19

Step-by-step explanation:

3x+6+3x+7=37

6x+6+7=37

6x+13=37

    -13  -13

6x=24

6x/6=24/6

x=4

3x+7

3(4)+7

12+7

JT=19

A third-degree polynomial in standard form is expressed as ax^3 + bx^2 + cx + d. The closure property of polynomials ensures that operations on polynomials result in another polynomial.

A third-degree polynomial in standard form is represented by the expression ax^3 + bx^2 + cx + d, where the coefficients a, b, c, and d are constants and a ≠ 0. This form ensures that the terms are arranged in descending order of degree and includes coefficients for each term. The closure property of polynomials states that the sum, difference, and product of two polynomials always yield another polynomial.

This property guarantees that when adding, subtracting, or multiplying polynomials, the resulting expression remains within the set of polynomials. It ensures that operations on polynomials maintain their polynomial nature and prevent results from falling outside the polynomial set.

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Answer:

z=6  

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

5(z + 1) = 3(z + 2) + 11

5z + 5 = 3z + 6 + 11

5z + 5 = 3z + 17

5z = 3z + 12

2z = 12

2z/2 = 12/2

z = 6

:)

Answer:

z= 6

Step-by-step explanation:

5(z + 1) = 3(z + 2) + 11

Distribute

5z+5 = 3z+6+11

Combine like terms

5z+5 = 3z+17

Subtract 3z from each side

5z+5-3z = 3z-3z+17

2z+5 = 17

Subtract 5 from each side

2z+5-5 = 17-5

2z = 12

Divide each side by 2

2z/2 =12/2

z = 6

The first statement is always true.

If m ∠m = 64° then m ∠F = 64°.

What is isomorphic triangles?

If there is an isomorphism connecting the vertices of P and Q, and that isomorphism has the property that three vertices of P form a triangle in Tp if and only if the mapping of the three vertices in Q, then the triangulations of two simple polygons, Tp and Tq, are said to be isomorphic (or occasionally compatible).

Given: ΔDEF ≅ ΔJAM

As the triangles are isomorphic that means that each angle of the triangle are same.

⇒ ∠D = ∠J

∠E = ∠A

∠F = ∠M

Hence, If m ∠m = 64° then m ∠F = 64° is true.

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Answer:

Step-by-step explanation:

v(t) =  25,000×1.035^t

The function to model the value of home is v(t) = 25000 \((1+ 0.0.35)^t\).

The worth of a current asset at some point in the future based on an estimated rate of growth is known as future value (FV). For investors and financial planners, the future value is crucial because they use it to predict how much an investment made now will be worth in the future.

Investors can make wise investment choices based on their projected demands by knowing the future worth.

Given:

P = $25, 000.

The value of the home has increased by approximately 3.5% per year since.

So, using the future value the function to model the value of home

v(t) = 25000 \((1+ 0.0.35)^t\)

where t is time in years.

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Answer:

The amount of deposit required is R37,999  for both

The percentage of purchase price for the required deposit is 20%

Therefore, deposit required=20%*R189,995

                                              =R37,999

The balance owed is the outstanding balance after payment of deposit plus the interest, bearing in mind that interest is computed using the simple interest approach

I=PRT

balance after payment of deposit=R189,995-R37,999

                                                       =R151,996

R=13.5% per year

T=48 months and 54 months

Interest on 48 month option=151,996*13.5%*48/12

                                              = R82,077.84

Interest on 54 month option=151,996*13.5%*54/12

                                              = R 92,337.57

The total payment without the initial deposit is the outstanding balance after payment of deposit plus the interest

Total payment for 48 month option=R151,996+R 92,337.57

                                                          =R  244,333.57

Total payment for 54 month option=R151,996+R82,077.84

                                                          =R 234,073.84

                                              Hope it helped!

Answer:

The equation that represents the relation is x = 3y - 5, where x is the number of plates and y is the number of cups

Step-by-step explanation:

To solve this question chose a variable represents the number of the plates and another variable represents the number of the cups

Assume that the number of plates is x and the number of cups is y

∵ The number of plates = x

∵ The number of cups = y

∵ The number of plates is 5 less than 3 times the number of cups

→ That means x is less than 3 times y by 5

∵ 3 times y = 3 × y = 3y

∵ x is less than 3y by 5

→ Remember is means equal and "less" means subtract 5 from 3y

∴ x = 3y - 5

The equation that represents the relation is x = 3y - 5, where x is the number of plates and y is the number of cups

Answer:

5,500

Step-by-step explanation:

2,500 + 3,000:

2000 + 3000 + 500

5000 + 500

5500

Easy!

The correct hypothesis relation is  is H₀ : μ ≥ 2,412. and Ha : μ < 2,412

According to the United States Census Bureau, the average area = 2, 412 square feet

Then the null hypothesis is

H₀ :μ ( mean ) area is greater than or equal to 2,412

H₀ : μ ≥ 2,412.

But, according to Jane, in her area, still families want a small home comparison to average.

Alternative hypothesis is that, mean area is less than 2,412 .

Ha : μ < 2,412.

Therefore,  H₀ : μ ≥ 2,412. and Ha : μ < 2,412

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84 km/h divided by 24 equals 3.5 hours.To express the answer in units, we need to consider the units of the given quantity and the units we want to express the result in.

Given: 84 km/h (kilometers per hour)

We want to find the time taken for a distance of 84 km at a speed of 84 km/h.

To calculate the time, we divide the distance by the speed:

Time = Distance / Speed

Distance = 84 km

Speed = 84 km/h

Time = 84 km / 84 km/h

When we divide the distance by the speed, the unit of kilometers cancels out, leaving us with just the unit of hours.

Therefore, the answer in units is:

Time = 1 hour

So, 84 km/h divided by 24 equals 3.5 hours.

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Answer:huh

Step-by-step explanation:

Answer:

Find the answers below

Step-by-step explanation:

Using m<X as the reference angle

Opposite YZ = 7

Adjacent  XY = 10

Hypotenuse XZ = √149

Using the SOH CAH TOA identity

sinX = opp/hyp

sinX =YZ/XZ

sinX = 7/√149

For cos X

cos X = adj/hyp

cos X =10/√149

Using m<Z as reference angle;

Opposite XY = 10

Adjacent  YZ = 7

Hypotenuse XZ = √149

Using the SOH CAH TOA identity

sinZ = opp/hyp

sinZ =10/√149

sinZ = 7/√149

For cos Z

cosZ = 7/√149

Answer and Step-by-step explanation:

What the question is asking is that it wants you to make the equation show equal to n.

We can do that by dividing both sides by RT, to get n by itself.

\(PV = nRT\\\\\\\frac{PV}{RT} = n\)⇔ This is the answer.

#teamtrees #PAW (Plant And Water)

Answer:

-5 and 5

Step-by-step explanation:

you basically just subtract 5 from 5 and you get 0

Answer:

5 , -5

Step-by-step explanation:

The pair of numbers that  has a sum of 0 is 5, -5 this is because a negative number plus a positive that is the same number will automatically be zero.

Answer:

x = 3; y = -4

Step-by-step explanation:

2(10x - 6y = 54) = ( 20x - 12y = 108)

4(-4x + 3y = -24) = ( -16x + 12y = -96)

                                   4x = 12

                                     x = 3

-4(3) + 3y = -24

-12 + 3y = -24

+12           +12

3y = -12

y = -4

Answer:

negative

Step-by-step explanation:

a posotive times a negative is a negative

Answer:

positive

Step-by-step explanation:

I hope this helps!

Answer:

m = -3

Step-by-step explanation:

We Know

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (0,15) (2,9)

We see the y decrease by 6, and the x increase by 2, so the slope is

m = -6/2 = -3

So, the slope of the line representing the data is -3.

Answer:

y = 2x - 12

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 2, then

y = 2x + c ← is the partial equation

To find c substitute (3, - 6) into the partial equation

- 6 = 6 + c ⇒ c = - 6 - 6 = - 12

y = 2x - 12 ← equation of line

Answer:

y=2x-12

Step-by-step explanation:

slope=m=y-(-6)/x-3

2=y+6/x-3

y+6=2(x-3)

y=2x-12

Answer:

90 = a + t

Step-by-step explanation:

admission + ticket book = $90

Answer:

Step-by-step explanation:

find the gradient of given equation:

3y+4x=12

3y= -4x+12

y= -4/3x+4

gradient= -4/3

perpendicular gradient:

m1xm2=-1

-4/3m2=-1

-4m2=-3

m2= 3/4

find y-intercept by inputting coordinates in y=mx+c

5=3/4(3)+c

5=9/4+c

5-9/4=c

c= - 11/4

equation:

y=3/4x-11/4