Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.

Answer:

a. A point estimate of the BMI for adults in the United States can be calculated from the sample mean, which has a value M=44.57.

b. The sample standard deviation is s=79.9507.

c. The 95% confidence interval for the BMI of adults in the United States is (26.18, 62.96).

Step-by-step explanation:

We start by calculating the sample mean and standard deviation of the BMI data:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{75}(16.2+31.1+24.8+. . .+22.9)\\\\\\M=\dfrac{3343}{75}\\\\\\M=44.57\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{74}((16.2-44.57)^2+(31.1-44.57)^2+(24.8-44.57)^2+. . . +(22.9-44.57)^2)}\\\\\\s=\sqrt{\dfrac{473016.8667}{74}}\\\\\\s=\sqrt{6392.1198}=79.9507\\\\\\[/tex]

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=44.57.

The sample size is N=75.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{79.9507}{\sqrt{75}}=\dfrac{79.9507}{8.66}=9.232[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=75-1=74[/tex]

The t-value for a 95% confidence interval and 74 degrees of freedom is t=1.993.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=1.993 \cdot 9.232=18.39[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 44.57-18.39=26.18\\\\UL=M+t \cdot s_M = 44.57+18.39=62.96[/tex]

The 95% confidence interval for the BMI of adults in the United States is (26.18, 62.96).

Answer: C. y ≤ 2/3x + 1/5

Step-by-step explanation: From 1/5 on the y coordinate plane go up 2 and right 3 and it perfectly matches, so it would be C. 100% on Edge2020.

Answer:

C

Step-by-step explanation:

just did the test.

Answer:

The frequency of the resulting harmonic motion is 0.000219 Hz

Step-by-step explanation:

We are going to calculate the time it takes for one single wave ocillation.

Frequency and the time taken to finish a single wave oscillation are inversely proportional. The formula for calculating frequency when given the time taken to complete a wave cycle is written as: f = 1 / T

In this formula, f represents frequency and T represents the time period or amount of time required to complete a single wave oscillation.

I consider the initial speed to be zero, because it is of no significance compared with the free fall into the earth, through the earth and back again.

Given from Wikipedia:

The diameter of the earth is 1.2742 * 10⁴ km which is 1.27 * 10⁷ m

2 times the radius = diameter, so the radius of the earth = (1.27 * 10⁷ m) /2 = 6.4 * 10⁶ m

radius earth = r

r = 6.4 * 10⁶ m

Now imagine the tunnel and the free fall.

1. Initially the rock has no speed.

2. Due to the gravitational accelleration, the rock will increase it's speed every second by a factor of 9.8.

3. The Rock gains speed untill it reached the centre of the earth. By then it will have reached it's maximum speed and it has travelled the distance r !

4. After this moment, the Rock will be slowed down because of the negative accelleration...

After it has travelled from the centre of the earth to the other end of the earth, it will have stopped completely, and again passing the distance r.

5. Now at the other end of the earth there is the same initial situation as described at point 1, only the Rock has travelled the distance equal to the diameter of the earth, (exactly 2 times r).

So basically, the samething happens once more, only this time it starts exactly from the other end of the earth...

6. Initially the rock has no speed.

7. Due to the gravitational accelleration, the rock will increase it's speed every second by a factor of 9.8.

8. The Rock gains speed untill it reached the centre of the earth. By then it will have reached it's maximum speed.

9. By now the Rock will be slowed down because of the negative accelleration... It is moving towards the initial starting point...

After it has travelled from the centre of the earth to the other end of the earth, it will have stopped completely.

10. Now finally the Rock is exactly at the starting position.

In reality there will have been some loss of speed due to friction, so the Rock will be slightly lower then the 100 m above the ground.

let's calculate the time it takes to free fall for the distance r.

initial speed =0 and after 6.4 * 10⁶ m it's speed will be maximum. We need to find out how much time passes before that distance is passed.

r = v*t + 0.5*a*t²

r = 0 + 0.5*a*t²

0.5*a*t² = r

t² = r / ( 0.5 * a )

t² = 6.4 *10⁶ / ( 0.5 * 9.8 )

t² = 1.306 * 10 ⁶

t = 1142.86 s

Now please confirm that in order for the Rock to move back to the initial starting point it has to travel 4 times as much time. It has to travel r to centre of the earth then another r to travel to to the other side of the earth, and back again. So indeed 4 times r.

The time it will take must be the same as 4 * 1142.86 s

now this is the time of one single wave ocillation.

Since T = 4571.43 s

f = 1 / 4571.43

f = 0.00021874993164 Hz

The frequency of the resulting harmonic motion is 2.19 *10-4

The frequency of the resulting harmonic motion is 0.000219 Hz

Answer:

Assuming that the null hypothesis is true and that the new cancer drug shrinks tumors by the same amount as the gold-standard drug, the probability that the test will lead the researcher to this decision = 95%

Step-by-step explanation:

The nulll hypothesis is correct and we are not rejecting it, which means we are making the correct decision.

P(not rejecting the null | null hypothesis is true)

= 1 - P(rejecting null hypothesis | null hypothesis is true)

= 1 - P(type I error)

P(type I error) = significance level of the test = 0.05

P(not rejecting the null | null hypothesis is true)

= 1 - 0.05

= 0.95

= 95%

Hope this Helps!!!

Answer:

1057

Step-by-step explanation:

tower is 60 feet high.

angle of 3.25 degrees.

3.25/360 * 2 * pi * r = the arc length of this angle.

that would be equal to 0.0567232007* r

if we assume the arc length and the height of the tower are approximately equal, then 0.0567232007 * r = 60

solving for r, we get r = 60/0.0567232007 = 1057.768237 feet.

that's about how far the tower is from the observer.

since the arc length is going to be a little longer than the length of the chord formed by the flagpole, this means that the distance of 1057.768237 meters is going to be a little less than the actual distance.

Answer:

≈ 1058 ft

Step-by-step explanation:

Use of arc formula: s=rθ

Given:

r= s/θ= 60/0.0567 ≈ 1058 ft

Answer: 205 and 1/7

Step-by-step explanation:

Hope this helped!

<!> Brainliest is appreciated! <!>

Answer: x = 120

Step-by-step explanation:

Here we have 3 triangles, one big and two smaller ones, one at the left and other at the right.

Now, the right sides is shared by the right smaller triangle and the big triangle, if this length is Z, we have that (using the angle in top of it, A, such that 64 is adjacent to A.)

Cos(A) = 64/Z

Cos(A) = Z/(64 +225)

We can take the quotient of those two equations and get:

[tex]1 = \frac{64*(64 + 225)}{Z^2} = \frac{18496}{Z^2}[/tex]

Then:

Z = √(18,496) = 136.

now, we have that for the smaller triangle one cathetus is equal to 64 and the hypotenuse is equal to 136.

Then, using the Pythagorean theorem:

64^2 + x^2 = 136^2

x = √(136^2 - 64^2) = 120

Answer:

The percentage  is  %z [tex]= 41.9[/tex]%    

Step-by-step explanation:

From the question we are told that

     The mean is  [tex]\mu = 63.5 \ g[/tex]

     The  standard deviation is  [tex]\sigma = 12.2 \ g[/tex]

      The  random number is  x  = 66 g

Given the the population is normally distributed

   The  probability is mathematically represented as

        [tex]P(X > 66 ) = P(\frac{X - \mu }{\sigma} > \frac{x - \mu }{\sigma } )[/tex]  

Generally the z-score for this population is mathematically represented as

         [tex]Z = \frac{ X - \mu}{ \sigma}[/tex]

  So

      [tex]P(X > 66 ) = P(Z > \frac{66 - 63.5 }{12.2 } )[/tex]  

      [tex]P(X > 66 ) = P(Z > 0.2049 )[/tex]  

Now the z-value for 0.2049 from the standardized normal distribution table is  

     [tex]z = 0.41883[/tex]

=>    [tex]P(X > 66 ) = 0.41883[/tex]  

The  percentage  is

     % z     [tex]= 0.41883 * 100[/tex]  

     %z   [tex]= 41.9[/tex]%    

Answer:

$1,020

Step-by-step explanation:

0.06x + 0.16(20,000 - x) = 1500

[tex]50/20=20/x\implies50x=400\implies\boxed{x=8\mathrm{ft}}[/tex]

Hope this helps.

The length of the shadow cast by the flag pole is 6.4 feet.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

We are given that;

Height of building= 50 foot

Shadow= 20foot

Now,

Let x be the length of the shadow cast by the flag pole. Then we have:

2050​=x20​

Cross-multiplying, we get:

50x=20×20

Dividing both sides by 50, we get:

x=5020×20​

Simplifying, we get:

x=58​×4

Multiplying, we get:

x=6.4

Therefore, by the proportion the answer will be 6.4 feet.

More can be learned about proportions at;

brainly.com/question/24372153

#SPJ2

Answer:

the minimum sample size n = 11.03

Step-by-step explanation:

Given that:

approximate value of the population standard deviation [tex]\sigma[/tex] = 49

level of significance ∝ = 0.01

population mean = 38

the minimum sample size n = ?

The minimum sample size required can be determined by calculating the margin of error which can be re[resented by the equation ;

Margin of error = [tex]Z_{ \alpha /2}} \times \dfrac{\sigma}{\sqrt{n}}[/tex]

[tex]38 = \dfrac{2.576 \times 49}{\sqrt{n}}[/tex]

[tex]\sqrt{n} = \dfrac{2.576 \times 49}{38}[/tex]

[tex]\sqrt{n} = \dfrac{126.224}{38}[/tex]

[tex]\sqrt{n} = 3.321684211[/tex]

[tex]n= (3.321684211)^2[/tex]

n ≅ 11.03

Thus; the minimum sample size n = 11.03

Answer:

(1) A Normal approximation to binomial can be applied for population 1, if n = 100.

(2) A Normal approximation to binomial can be applied for population 2, if n = 100, 50 and 40.

(3) A Normal approximation to binomial can be applied for population 2, if n = 100, 50, 40 and 20.

Step-by-step explanation:

Consider a random variable X following a Binomial distribution with parameters n and p.

If the sample selected is too large and the probability of success is close to 0.50 a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:

The three populations has the following proportions:

p₁ = 0.10

p₂ = 0.30

p₃ = 0.50

(1)

Check the Normal approximation conditions for population 1, for all the provided n as follows:

[tex]n_{a}p_{1}=10\times 0.10=1<10\\\\n_{b}p_{1}=100\times 0.10=10=10\\\\n_{c}p_{1}=50\times 0.10=5<10\\\\n_{d}p_{1}=40\times 0.10=4<10\\\\n_{e}p_{1}=20\times 0.10=2<10[/tex]

Thus, a Normal approximation to binomial can be applied for population 1, if n = 100.

(2)

Check the Normal approximation conditions for population 2, for all the provided n as follows:

[tex]n_{a}p_{1}=10\times 0.30=3<10\\\\n_{b}p_{1}=100\times 0.30=30>10\\\\n_{c}p_{1}=50\times 0.30=15>10\\\\n_{d}p_{1}=40\times 0.10=12>10\\\\n_{e}p_{1}=20\times 0.10=6<10[/tex]

Thus, a Normal approximation to binomial can be applied for population 2, if n = 100, 50 and 40.

(3)

Check the Normal approximation conditions for population 3, for all the provided n as follows:

[tex]n_{a}p_{1}=10\times 0.50=5<10\\\\n_{b}p_{1}=100\times 0.50=50>10\\\\n_{c}p_{1}=50\times 0.50=25>10\\\\n_{d}p_{1}=40\times 0.50=20>10\\\\n_{e}p_{1}=20\times 0.10=10=10[/tex]

Thus, a Normal approximation to binomial can be applied for population 2, if n = 100, 50, 40 and 20.

Answer:

72

Step-by-step explanation:

45/35=x/56

9/7=x/56

7x=9*56

:7. :7

x=9*8

x=72

Answer:

A) Yes, there are a fixed number of trials and the trials are independent of each other.

Sample size 'n' = 37

probability of success  p = 0.1081

                                     q = 0.8919

Step-by-step explanation:

Explanation:-

Given data we will observe that

There are a fixed number of trials and the trials are independent of each other.

Given a state lottery randomly chooses 4 balls numbered from 1 through 37 without replacement.

Given size 'n' = 37

The probability that a state lottery randomly chooses 4 balls numbered from 1 through 37 without replacement.

Proportion

           [tex]p = \frac{x}{n} = \frac{4}{37} = 0.1081[/tex]

q = 1 - p = 1 - 0.1081 = 0.8919

Final answer:-

Sample size 'n' = 37

                     p = 0.1081

                     q = 0.8919

This question is incomplete, here is the complete question:

Suppose in the next year, 2007, College D's expenses and enrollment remain about the same, but in addition to their current revenues, they receive an additional $50,000,000 grant. This would allow them to reduce average tuition by how much?

A) $1388.89

B) $3571.43

C) $5555.56

D) $9500.00

E) $25888.89

number of students = 36,000

Answer: A) $

1388.89

Step-by-step explanation:

the college received additional grant which is $50,000,000

and the number of students is 36,000,

and we also know that expenses and enrollment remained the same.

So if we have more money (grants) and nothing changed (expenses remain the same)

dividing the grant by the number of students will show just how much the average tuition fee would be reduced

therefore R = G/n

R = 50,000,000 / 36000

R = 1,388.888 ≈  $1388.89

Answer:

  A.  (x, y) ⇒ (-x, -y)

Step-by-step explanation:

Rotation 180° in either direction is equivalent to reflection across the origin, and/or reflection across both axes (in either order). It negates both coordinates.

  (x, y) ⇒ (-x, -y) . . . . rotation 180°

Answer:

Option (4)

Step-by-step explanation:

Surface area of a prism = 2B + P×h

where B = Area of the triangular base

P = perimeter of the triangular base

h = height of the prism

B = [tex]\frac{1}{2}(\text{leg 1})(\text{leg 2})[/tex]

Since, (Hypotenuse)² + (Leg 1)² + (Leg 2)² [Pythagoras theorem]

(20)² = (12)² + (Leg 2)²

Leg 2 = [tex]\sqrt{400-144}[/tex]

          = 16 units

Therefore, B = [tex]\frac{1}{2}\times 12\times 16[/tex]

                     = 96 units²

P = 12 + 16 + 20

P = 48 units

h = 7.5 units

Surface area of the prism = 2(96) + (48×7.5)

                                           = 192 + 360

                                           = 552 units²

Therefore, surface area of the given triangular prism = 552 units²

Option (4) will be the answer.

They got 5 yards on 3 plays. For total yards multiply the 3 plays by 5 yards. The first play was negative, so add the negative value.  The answer is A.

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

246(.03)= 7.38

246+7.38= $253.38

Given Information:

Annual interest rate = r = 10%

Accumulated amount = A = $6380.00

Semi-annual compounding = n = 2

Number of years = t = 38/12 = 19/6  

Required Information

Principle amount= P = ?

Answer:

Principle amount= P = $4,684.05

Step-by-step explanation:

The principal amounts in terms of compound interest is given by  

[tex]$ P = \frac{A}{(1 + i)^N} $[/tex]

Where  

i = r/n

i = 0.10/2

i = 0.05

N = n*t

N = 2*19/6

N = 19/3

So, the principal amount is

[tex]P = \frac{6380.00}{(1 + 0.05)^{19/3}} \\\\P= \$4,684.05 \\\\[/tex]

Therefore, you need to invest $4,684.05 at 10% compounded semiannually for 38 months to get $6380.00 in savings.

Answer:

cot(A-B) = 3/19

Step-by-step explanation:

The formula for cot(A-B) = (Cot A Cot B + 1 ) / (Cot B - Cot A)

we know that cot A = 1/ Tan A

Given

tan A=2/3

therefore cot A = 1/ tan A = 1/2/3 = 3/2

tan B= -3/5  

cot B = 1/ tan B = 1/-3/5 = -5/3

Thus,

(Cot A Cot B + 1 ) = (3/2)*(-5/3 )+ 1 = -5/2 +1 = (-5+2)/2 = -3/2

(Cot B - Cot A) = -5/3 -3/2 = (-5*2) + (-3*3) / 2 = -10 -9/2 = -19/2

Thus,

cot(A-B) = (Cot A Cot B + 1 ) / (Cot B - Cot A) = -3/2  / -19/2 = 3/19

Thus,

cot(A-B) = 3/19

Answer:

  hare

Step-by-step explanation:

Their average rates are ...

  tortoise: (220 mi)/(10 h) = 22 mi/h

  hare: (90 mi)/(2 h) = 45 mi/h

The hare has a faster speed than the tortoise.

Answer:

  A. $3246.74

Step-by-step explanation:

The monthly payment can be found from the amortization formula.

  A = P(r/n)/(1 -(1 +r/n)^(-nt))

where P is the principal amount, r is the annual rate compounded n times per year for t years.

Filling in the values, we compute the monthly payment to be ...

  A = $170,000(.072/12)/(1 -(1 +.072/12)^(-12·30)) = $1153.94

__

The remaining balance after t years will be ...

  B = P(1 +r/n)^(nt) -A((1 +r/n)^(nt) -1)/(r/n)

For the given initial principal and the computed payment, after 18 years, the balance will be ...

  B = $170000(1 +.072/12)^(12·18) -$1153.94((1 +.072/12)^(12·18) -1)/(.072/12)

  B = $111,054.71

The prepayment penalty appears to be ...

  (r/2)(0.80B) = (.072/2)(0.80)($111,054.71) = $3,198.38

The closest listed answer choice is ...

  A.  $3246.74

_____

Please ask your teacher how to get the answer, since none of the offered choices appear to be correct.

Answer:

3x³(x + 5)

Step-by-step explanation:

1/x² - 4/(3x² + 15x)

Factor 3x² + 15x.

3x² + 15x

3x(x + 5)

Find the least common denominator.

(1 × 3x(x + 5))/(x² × 3x(x + 5)) - (4 × x²)/(3x² + 15x × x²)

(3x(x + 5))/(3x³(x + 5)) - (4x²)/(3x³(x + 5))

The least common denominator is 3x³(x + 5).

Answer:

The least common denominator is 3x^2(x+5)

Answer: The box with three shaded squares and one non-shaded square

Step-by-step explanation:

You are trying to find the representation of the shaded region.

The scale shows point A at 0.75, and the scale can range from 0 to 1.

0.75 is equal to 3/4 of 1

3 of the 4 squares are shaded

So, the common ratio is 3:4 or 3/4

Complete Question:

Tublu buys a cylindrical water tank of height 1.4m and diameter 1.1m to catch rainwater off his roof. He has a full 2 liters tin of paint in his store and decides to paint the tank(not the base). If he uses 250ml to cover 1m2, will he have enough paint to cover the tank with one layer of paint? Take pie as 3.142

Answer:

Yes. It will be enough to cover the tank with 1 layer of paint. The tank requires 1.21 liters of paint.

Step-by-step explanation:

Given:

Height of cylindrical tank (h) = 1.4m

Diameter = 1.1m (radius = ½ of 1.1 = 0.55 m)

Litres of paint available = 2 liters

Rate of usage of paint = 250 ml to 1 m²

π = 3.142

Required:

Determine if the available 2 liters of paint would be enough for the painting

Solution:

Step 1: calculate the curved surface area of the cylindrical tank

Curved surface area (CSA) = 2πrh

= 2*3.142*0.55*1.4

= 4.84 m²

Step 2: Calculate how many liters of paint is required to paint the cylindrical tank having a curved surface area of 4.84 m²

If 1 m² requires 250ml (0.25 liters) of paint,

4.84m² area will require 4.84*0.25 liters

= 1.21 liters of paint.

Since 2 liters of paint is available, it means the paint will be more than enough to cover the tank with 1 layer of paint.

Answer:

x = 2.

Step-by-step explanation:

3(x + 2) = 12

3x + 6 = 12

3x = 6

x = 2

Hope this helps!

Answer:

4

Step-by-step explanation:

Think about this. If we were to align the coefficients with their solutions to form this matrix, it would be the following -

[tex]\begin{bmatrix}2&-6&-2&|&1\\ 0&3&-2&|&-5\\ 0&2&2&|&-3\end{bmatrix}[/tex]

Now this is one way to assign the coefficients. As you can see, 2, - 6, - 2 are present as the coefficients for the first row. Similarly 0, 3, - 2 are present as the coefficients for the second row - ( as one term is missing from this row, it is replaced with a " 0 " ). The same applies for the third row. The end values of the system of equation is present as the last column.

The options are assigned in a manner with which the coefficients and variables are present in two columns, while the end values of the system of equation given, is present as the last column. Knowing the arrangement of both the coefficients and the end values of the system of equation, all we have to do is add these " variables " as one column -

Solution = Option B