A survey was conducted of 250 pediatricians on the average age of their patients. A sample mean of 8. 3 years was determined, with a standard deviation of 1. 8 years. Assuming a 90% confidence level, which of the following statements holds true? A. As the sample size is too small, the margin of error cannot be trusted. B. As the sample size is too small, the margin of error is ±1. 29. C. As the sample size is appropriately large, the margin of error is ±0. 187. D. As the sample size is appropriately large, the margin of error is ±0. 14.

Answer:

Step-by-step explanation:

Given  the inequality function 12x+7< -11 and 5x-8>40, we are to solve for the value of x. To solve for x, the following steps must be followed.

For the inequality 12x+7< -11

Step 1: Subtract 7 from both sides of the inequality

12x+7-7< -11-7

12x < -18

Step 2: Divide both sides of the inequality by 12

12x/12 < -18/12

x < -3/2 .............. 1

For the inequality 5x-8> 40;

Step 1: Add 8 to both sides of the inequality

5x-8+8 > 40+8

5x > 48

Step 2: Divide both sides of the inequality by 5

5x/5 > 48/5

x>48/5....... 2

Combining equation 1 and 2, we will have;

x < -3/2 and x>48/5

If x>48/5 then 48/5<x

Combining 48/5<x with x < -3/2  will give  48/5<x<-3/2

Answer:

there are no soulutions

Step-by-step explanation:

The center and the radius by completing the square of the given equation of circle is x² + y² - 32x+24y +396 = 0 is C( -16, 12) and radius is 2.

The equation of the circle is given as x² + y² - 32x+24y +396 = 0.

Comparing the given equation with general equation of circle, x² + y² + 2gx + 2fy + c = 0.

The center of circle is C = (-g, -f)

The radius of circle is r = √g² + f² - c

Therefore, from the given equation,

2g = -32

g = -16

2f = 24

f = 12

C( -16, 12)

And the radius is

r = √(-16)² + (12)² - 396

= √256 + 144 -396

=√4

= 2

Hence, the center and the radius by completing the square of the given equation of circle is x² + y² - 32x+24y +396 = 0 is C( -16, 12) and radius is 2.

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Answer:-3

Step-by-step explanation: -3 because when you do it I really don't know how to explain it srry

The two-way relative frequency table should look like

                          play a sport            Not play a sport           Total

Honor Roll             10%                       10%                             20%

Not Honor Roll     30%                      50%                              80%

Total                      40%                       60%                              100%

A two-way relative frequency table is a table that shows the relative frequency distribution of two category variables.

The table tells us how frequent each the combination of  categories for the two variables happens  when we look at the total percentage.  

Looking at the table, we were total that only 20% of the student surveyed are on the honor roll, and we were also told that  10% of student survey play sport and are in the honor roll. This means that additional 10% of student that don't play sport are on the honor roll too.

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Answer:

Order from greatest to least: 10.5, \(3\pi +1\), \(\sqrt{105}\)

Step-by-step explanation:

step 1 simplify each number

3π + 1  = 10.4247779

*round to the nearest tenth*

3π + 1 = 10.4

\(\sqrt{105} =10.2469507\)

*round to the nearest tenth*

\(\sqrt{105} =10.2\)

10.5 = 10.5

Now that we have simplified each number we can easily put them in order from greatest to least

10.5 is the greatest number

10.4 is the middle number

10.2 is the lowest number

so 10.5, 10.4, 10.2

Now we put them back in the original form

10.5 = 10.5

10.4 = 3π + 1

10.2 = \(\sqrt{105}\)

Your answer is

10.5 , 3\(\pi\) + 1, \(\sqrt{105}\)

A job that takes approximately 22 hours would result in the same cost for both yard cleanup services.

To determine when the two yard cleanup services have the same cost, you'll need to set up an equation using the given fees and hourly rates

. For the first service, the cost is $254 (fee) + $19.25 per hour (rate).

For the second service, the cost is $133 (fee) + $24.75 per hour (rate).

Let x represent the number of hours for the job.

The equation would be: 254 + 19.25x = 133 + 24.75x

To solve for x, subtract 19.25x from both sides and simplify: 121 = 5.5x

Now, divide both sides by 5.5 to find the number of hours: x ≈ 22 hours

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The missing side is  6√13 in the given right-angled triangle.

If one of a triangle's angles is a right angle (90 degrees), the triangle is known as a right-angled triangle or just a right triangle, according to the definition of a right triangle. Triangle ABC is a right triangle that contains the base, altitude, and hypotenuse in the example image.

Base AB, altitude AC, and hypotenuse BC are shown in this equation. The largest side and the side that faces away from the right angle in a right triangle is the hypotenuse, and it is this side that is significant.

Given that A right angle triangle has sides 12cm and 18 cm

y = \(\sqrt{12^2 + 18^2}\)

y = 6√13

Thus, the missing side y is  6√13.

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Check the picture below.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{6.6+x}\\ a=\stackrel{adjacent}{6.6}\\ o=\stackrel{opposite}{8.8} \end{cases} \\\\\\ (6.6+x)^2= (6.6)^2 + (8.8)^2\implies (6.6+x)^2=121\implies (6.6+x)^2=11^2 \\\\\\ 6.6+x=11\implies x=4.4\)

Answer:

g=-4/5

Step-by-step explanation:

-25/32g=5/8

-200g=160

g=-4/5

Answer:

the answer is g= -4/5 if u want decimal form its g=-0.8

The optimal point values for x1, x2, λ, and μ (Lagrange multipliers) in the given problem are:

x1 = 1

x2 = 1

λ = -4

μ = 2

To solve the optimization problem using the Lagrange multipliers technique, we first construct the Lagrangian function L(x1, x2, λ) by incorporating the equality constraint:

L(x1, x2, λ) = f(x1, x2) - λ(g(x1, x2))

Where f(x1, x2) is the objective function, g(x1, x2) is the equality constraint, and λ is the Lagrange multiplier.

In this case, the objective function is f(x1, x2) = 2x1^2 - 2x1x2 + 2x2 - 6x1 + 6, and the equality constraint is g(x1, x2) = x1 + x2 - 2.

The Lagrangian function becomes:

L(x1, x2, λ) = 2x1^2 - 2x1x2 + 2x2 - 6x1 + 6 - λ(x1 + x2 - 2)

To find the optimal values, we need to find the critical points by taking partial derivatives of L with respect to x1, x2, and λ and setting them equal to zero. Solving these equations simultaneously, we get:

∂L/∂x1 = 4x1 - 2x2 - 6 - λ = 0

∂L/∂x2 = -2x1 + 2 + λ = 0

∂L/∂λ = -(x1 + x2 - 2) = 0

Solving these equations, we find x1 = 1, x2 = 1, and λ = -4. Substituting these values into the equality constraint, we can solve for μ:

x1 + x2 - 2 = 1 + 1 - 2 = 0

Therefore, μ = 2.

The optimal point values for the variables in the optimization problem are x1 = 1, x2 = 1, λ = -4, and μ = 2. The Lagrange multipliers λ and μ represent the rates of change of the objective function and the equality constraint, respectively, with respect to the variables. They provide insights into the sensitivity of the objective function to changes in the constraints and can indicate the impact of relaxing or tightening the constraints on the optimal solution. In this case, the Lagrange multiplier λ of -4 indicates that a small increase in the equality constraint (x1 + x2 - 2) would result in a decrease in the objective function value. The Lagrange multiplier μ of 2 indicates the shadow price or the marginal cost of satisfying the equality constraint.

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The linear function relating the variables C and S is given as follows:

C(S) = 5000 + 200S.

The graph of the linear function is given by the image at the end of the answer.

The linear function in this problem is defined in the slope-intercept as follows:

y = mx + b.

In which the coefficients of the function are defined as follows:

In the context of this problem, the variables are given as follows:

It will cost $5000 to rent trucks, hence the intercept is of:

b = 5000.

It will cost an additional $200 for each ton of sugar transported, hence the slope is of:

m = 200.

Then the equation is defined as follows:

C(S) = 5000 + 200S.

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Answer:

33.02 cm in 13inches

Step-by-step explanation:

3Justin's estimated Vo2 max is 25.8(mL*kg*min)

What is Vo2 max ?

 The amount (volume) of oxygen used by your body while exercising as hard as you can is referred to as VO2 max. It's a common tool for determining your level of fitness. Knowing your VO2 max can assist you in training for sports, tracking fitness progress, and improving your heart health.

Here using vo2 max fomula 1.5 miles ,

=> VO2 max = 3.5+483/Time

Here Time= 11 min 25 sec = 25/60 = 0.41 min

Then time=11.42 mins. Now,

=> VO2 max = 3.5+ 483/11.41

=> VO2 max = 3.5+42.3

=>VO2 max = 25.8(mL*kg*min)

Hence His estimated Vo2 max is 25.8(mL*kg*min)

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if length of the diagonal is 10 inch then the side will be 5\(\sqrt{2}\) ,

we came to this conclusion by using Pythagoras theorem.

in a square the diagonal intersect each other at right angle so we can apply Pythagoras theorem.

Answer:

A=50 B=40 C=90

Step-by-step explanation:

B is a right angle so its automatically 90 degrees since A=50 and a triangle has to be 180 degrees 90+50= 140, 180-140=40.

Answer:

[3/3+5](2-(-14))+(-14)

Step-by-step explanation:

3:5 Ratio means that the m/m+n would be 3/3+5.

Then X2 is 2 and X1 is -14.

X2-X1 is 2-(-14)

Step-by-step explanation:

explain what 7 c is please and I'll write the answer in the comments:))

The percentage change in frequency is 0%.Hence, the natural frequency of torsional vibration of the custen is given by f = 25.7 / L₀^(1/2) and the percentage change in frequency is 0%.

We are given that:

Total moment of inertia of moving parts = I = 1 kgm²

Moment of inertia of air-screw = I = 18 kgm²

Outer diameter of hollow shaft = D₀ = 80 mm

Inner diameter of hollow shaft = Dᵢ = 35 mm

Length of hollow shaft = L = 0.30 m

Stiffness of the crank-throw = K = 2.5 × 10⁴ Nm/rad

Shear modulus of elasticity = G = 83000 N/mm²

We need to calculate the natural frequency of torsional vibration of the custen.

The formula for natural frequency of torsional vibration is: f = (1/2π) [(K/L) (J/GD)]^(1/2)

Where, J = Polar moment of inertia

J = (π/32) (D₀⁴ - Dᵢ⁴)

The formula for equivalent length of hollow shaft is given by:

q₁ = q₁₁ + q₁₂

Where, q₁₁ = (π/32) (D₀⁴ - Dᵢ⁴) / L₁q₁₂ = (π/64) (D₀⁴ - Dᵢ⁴) / L₂

L₁ = length of outer diameter

L₂ = length of inner diameter

For the given shaft, L₁ + L₂ = L

Let L₁ = L₀D₀ = D = 80 mm

Dᵢ = d = 35 mm

So, L₂ = L - L₁= 0.3 - L₀...(1)

For the given crank-throw, q₁ = (π/32) (D⁴ - d⁴) / L, where D = 80 mm and d = 80 mm

Hence, q₁ = (π/32) (80⁴ - 35⁴) / L

Therefore, q₁ = (π/32) (80⁴ - 35⁴) / L₀...(2)

From the formula for natural frequency of torsional vibration, f = (1/2π) [(K/L) (J/GD)]^(1/2)

Substituting the values of K, J, G, D and L from above, f = (1/2π) [(2.5 × 10⁴ Nm/rad) / (L₀) ((π/32) (80⁴ - 35⁴) / (83000 N/mm² (80 mm)³))]^(1/2)f = (1/2π) [(2.5 × 10⁴ Nm/rad) / (L₀) (18.12)]^(1/2)f = 25.7 / L₀^(1/2)...(3)

Now, if we assume that the air-screw mass is infinite, then the moment of inertia of the air-screw is infinite.

Therefore, the formula for natural frequency of torsional vibration in this case is:

f = (1/2π) [(K/L) (J/GD)]^(1/2)Substituting I = ∞ in the above formula, we get:

f = (1/2π) [(K/L) (J/GD + J/∞)]^(1/2)f = (1/2π) [(K/L) (J/GD)]^(1/2)f = 25.7 / L₀^(1/2)

So, in this case also the frequency is the same.

Therefore, the percentage change in frequency is 0%.Hence, the natural frequency of torsional vibration of the custen is given by f = 25.7 / L₀^(1/2) and the percentage change in frequency is 0%.

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each large envelope costs $1.60.

What did we do?

Let's represent the cost of a postcard by "p" and the cost of a large envelope by "e".

From the information given, we can create a system of equations:

17p + 4e = 13.88 (equation 1)

10p + 12e = 23.60 (equation 2)

To solve for "e", we can use the method of elimination.

First, let's multiply equation 1 by 3:

51p + 12e = 41.64 (equation 3)

Now, we can subtract equation 3 from equation 2:

10p + 12e = 23.60

-(51p + 12e = 41.64)

-41p = -18.04

Dividing both sides by -41, we get:

p = 0.44

Substituting this value into equation 1:

17(0.44) + 4e = 13.88

7.48 + 4e = 13.88

4e = 6.4

Therefore, the cost of each large envelope is:

e = 6.4/4 = 1.6

So each large envelope costs $1.60.

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Answer:

5

Step-by-step explanation:

-9-(-9)+5=5

Answer:

231

Step-by-step explanation:

because the whole circle has an area of 360 so on the right side there is half and a little more so you would cut it in half so you have 180 and on the right side you still have a little left so thats about 10 so now you have 190 then you add 21 +20 you have 41 +190 =231 hope this helps

In order to calculate the area of the rhombus, first let's draw the diagonal BD.

This diagonal and the diagonal AC will intersect at point M, which is the midpoint of each diagonal.

Since M is midpoint of AC, we have AM = MC = 7 cm.

Now, let's calculate the length of BM, using the Pythagorean theorem in the right triangle BMC:

Calculating the area of this triangle, we have:

The triangles BMC, BMA, DMC and DMA are all congruent, so the area of the rhombus is:

Answer:

Step-by-step explanation:

Average = sum of number/total number

Given 07 number are= 98, 100, 100, 79, 85, 79, 83

average=98+100+100+79+85+79+83/7=89

Grounded average=89% answer

Answer:

Pack of 6

Step-by-step explanation:

Pack of 4 = £1

Packs of 6 = £1.20

Price per unit of each pack:

Pack of 4 ;

Unit price : cost / units

Unit price = £1 / 4 = £0.25

Pack of 6 ;

Unit price : cost / units

Unit price = £1.20 / 6 = £0.20

Pack of 6 is the best value for money as it has a lower unit price

Answer:

No. of ticket bought is 4

Step-by-step explanation:

Let the no. of ticket bought be x

Given cost of 1 ticket = $12

Therefore cost x ticket = x*cost of 1 ticket = x*$12 = $12x

parking fee = $5

given that it is flat so, whatever be the no. of ticket bought or family member,

the parking cost will remain $5 only.

Total money paid by family  = parking charge + cost x ticket = 5+12x

But , given that family paid total of $53

then

5 + 12x = 53

=> 12x = 53-5 = 48

=> x = 48/12 = 4

Thus, no. of ticket bought is 4.

This can be validated as  shown below

cost of 4 ticket as 12 each will be = 12*4 = 48

thus total money paid = $(48+5 )= $53

Answer:

x= -3 / 8

Step-by-step explanation:

5x+7+3x-4=0

Sum 5x and 3x

8x+7-4=0

Subtract 7-4

8x+3=0

Move the constant to the other side and change his symbol with his opposite

8x=-3

8 is multiplying x, the opposite of multiplying is dividing, so it divide the -3 (under it)

x= -3 / 8