The base of a triangular prism has an area of 35 m2. This triangular prism has a height of 7 m. What is the volume of this triangular prism? ​

Answer:

a) 272 used at least one prescription​ medication.

b) The 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication is (85.6%, 87.6%).

Step-by-step explanation:

Question a:

86.6% out of 3149, so:

0.866*3149 = 2727.

272 used at least one prescription​ medication.

Question b:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 3149, \pi = 0.866[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.866 - 1.645\sqrt{\frac{0.866*0.134}{3149}} = 0.856[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.866 + 1.645\sqrt{\frac{0.866*0.134}{3149}} = 0.876[/tex]

For the percentage:

0.856*100% = 85.6%

0.876*100% = 87.6%.

The 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication is (85.6%, 87.6%).

The number of subjects in the study who used at least one prescription medication is 2727 approx. The needed 90% confidence interval is:  [0.8560, 0.8758] or in percentage as: 85.6% to 87.58%

Suppose that we have:

Then, we get:

[tex]CI = \hat{p} \pm Z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

where [tex]Z_{\alpha/2}[/tex] is the critical value of Z at specified level of significance and is obtainable from its critical value table(available online or in some books)

For this case, we have:

Part (a):

The number of subjects used at least one prescription​ medication is:

[tex]\dfrac{3149}{100} \times 86.6 \approx 2727[/tex]

Thus, the sample proportion we get is:

[tex]\hat{p} = \dfrac{2727}{3149} \approx 0.8659[/tex]

For level of significance 0.10, we get: [tex]Z_{\alpha/2} = 1.645[/tex]

Thus, the confidence interval needed is:

[tex]CI = \hat{p} \pm Z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\CI \approx 0.8659\pm 1.645 \times \sqrt{\dfrac{0.8659(1-0.8659)}{3149}}\\\\\\CI \approx 0.8659 \pm 0.0099[/tex]

Thus, CI is [0.8659 - 0.0099, 0.8659 + 0.0099] = [0.8560, 0.8758]

Thus, the number of subjects in the study who used at least one prescription medication is 2727 approx. The needed 90% confidence interval is:  [0.8560, 0.8758] or in percentage as: 85.6% to 87.58%

Learn more about population proportion here:

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Answer:

C

Step-by-step explanation:

We see that the y-intercept is 3. So it is either A of B.

Plug in the point that is on the line (1, -2), we see that the point works for C.

Answer:

41

136

155

193

Step-by-step explanation:

use the equation 19*d+22=h

19 represents the number of hats knitted per day

22 represents the already made hats

Answer:

hhhhhhhhhhhhhhhhhhu

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]Sin \ 30 = \frac{opposite \ side}{hypotenuse}\\\\\frac{1}{2}=\frac{h}{6}\\\\\frac{1}{2}*6=h\\\\3 = h[/tex]

h = 3 cm

Area of parallelogram = b * h

                                    = 6 * 3

                                     = 18 sq.cm

Answer:

5/3

Step-by-step explanation:

3^5 = 27 ^x

Rewrite 27 and 3^3

3^5 = 3^3^x

We know that a^b^c = a^(b*c)

3^5 = 3^(3x)

The bases are the same so the exponents are the same

5 = 3x

Divide by 3

5/3 =x

Answer:

x = [tex]\frac{5}{3}[/tex]

Step-by-step explanation:

[tex]3^{5} = 27^{x}[/tex]

These problems are getting you ready to work with exponential functions,

and ultimately with logarithms. The point here is that with variable exponents (notice the exponent is an x (on the right one) and not a number. Variable exponents can not be solved with regular algebra "rules" you need new ones.

The new ones will be Logs....

For now (until you learn logs) , you have to use some "tricks"

the "trick" in this problem is that you have to realize that 27 = [tex]3^{3}[/tex]...

with "common bases" this problem becomes trivial

[tex]3^{5} =(3^{3} ) ^{x}[/tex]

so now the bases are the same and the equals sign suggests that

3x = 5

thus x = [tex]\frac{5}{3}[/tex]

Answer:

1) -7929

2) -2401

3)-5414

4) -7592

5) 12888

6)-237726

7) 7287

8)-4588

9)-394495

10) 891856

Answer:

The vertex appears to be (-1,-5)   (The lowest point of line)

Axis of symmetry is x = -1   (Notice that the x value of the vertex is same)

y-intercept is (0, -3)     (where the line crosses the y-axis)

Answer:

4 + x =5

Step-by-step explanation:

By adding a variable you can set up an addition sentence

Answer:

25.

Step-by-step explanation:

Let the number of pupils be x, then:

there are 0.6x girls and 0.4x boys.

From the given information:

0.6x - 0.4x = 5

0.2x = 5

x = 5/0.2

= 50/2

= 25.

Answer:

D. [tex] \frac{15}{8} [/tex]

Step-by-step explanation:

Recall: SOH CAH TOA

Thus,

Tan A = Opposite/Adjacent

Reference angle (θ) = A

Length of side Opposite to <A = 15

Length of Adjacent side = 8

Plug in the known values

[tex] Tan(A) = \frac{15}{8} [/tex]

7.7cm

the rest is vastly (a and d) off or just enough off (can't be less then 5.2, because that's already the shortest side), to solve this by looking at it

hope this helps! feel free to clarify if unsure

Answer:

QXV=WXV

Step-by-step explanation:

a=132°

b=20°

Answer:

Solution given:

a=132°[exterior angle of a cyclic quadrilateral is equal to the opposite interior angle]

again

In ∆ BCO is similar to ∆ BOE

so

b=20°[corresponding angle of similar triangle are equal]

Answer:

115

Step-by-step explanation:

When x = -11, x^2 = 121. y = 121 - 6 = 115.

Hope this helped,

~cloud

Answer:

115

Step-by-step explanation:

y = x^2 - 6

Let x = -11

y = (-11)^2 - 6

y = (121) -6

   = 115

The area of the triangle is (A) [tex]73.6ft^{2}[/tex].

Area = [tex]\frac{1}{2}[/tex] × [tex]a[/tex] × [tex]b[/tex] × [tex]sin[/tex] (θ)

Now, out the values in the formula for the solution.

[tex]A=\frac{1}{2} (16)(10)sin(67^{o} )\\A= 80sin(67^{o} )\\[/tex]

[tex]A=73.6ft^{2}[/tex]

Therefore, the area of the given triangle is (A) [tex]73.6ft^{2}[/tex].

Know more about the area of triangles here:

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#SPJ2

Answer:

The height above sea level at B is approximately 1,604.25 m

Step-by-step explanation:

The given length of the mountain railway, AB = 864 m

The angle at which the railway rises to the horizontal, θ = 120°

The elevation of the train above sea level at A, h₁ = 856 m

The height above sea level of the train when it reaches B, h₂, is found as follows;

Change in height across the railway, Δh = AB × sin(θ)

∴ Δh = 864 m × sin(120°) ≈ 748.25 m

Δh = h₂ - h₁

h₂ = Δh + h₁

∴ h₂ ≈ 856 m + 748.25 m = 1,604.25 m

The height above sea level of the train when it reaches B ≈ 1,604.25 m

Answer:

210 Km

Step-by-step explanation:

Distance travelled is calculated as

distance = speed × time ( time is in hours )

              = 90 × 2 [tex]\frac{1}{3}[/tex]

             = 90 × [tex]\frac{7}{3}[/tex]

            = 30 × 7

            = 210 Km

Answer:

102

Step-by-step explanation:

Exterior angle is sum of interior angles.

∠1 = 51 + 51

∠1 = 102

Answer: m∠1 = 102°

Step-by-step explanation:

The inside angles of a triangle always add up to 180°

so get the 3rd inside angle with

[tex]180-51-51=78[/tex]

And we know that a straight line in 180° on each side

So we take 180° and subtract 78° to get our answer 102°

Answer:

value of K =16

I hope it's helps you

Answer:

[tex]\sqrt{89}[/tex] = 9.83

Step-by-step explanation:

[tex]\sqrt{89}[/tex]

[tex]\sqrt{25 + 64} \\\sqrt{5^2 + 8^2}[/tex]

Answer: 89

Step-by-step explanation:

Answer:

b:    [tex]\frac{5-\sqrt{11} }{2}[/tex]< x < [tex]\frac{5+\sqrt{11} }{2}[/tex]  

c:  x < -5 , x > 7

Step-by-step explanation:

Answer:

For a give event with outcomes:

{x₁, x₂, ..., xₙ}

Each with probabilities:

{p₁, p₂, ..., pₙ}

The expected value is:

Ev = x₁*p₁ + ... + xₙ*pₙ

Here we have the outcomes and probabilities:

win $1, with a probability 20%/100% = 0.2

win $2, with a probability 25%/100% = 0.25

win $5, with a probability of 35%/100% = 0.35

do not win, with a probability of 20%/100% = 0.2

Then the expected value of the game is:

Ev = $1*0.2 + $2*0.25 + $5*0.35 + $0*0.2 = $2.45

And if we know that the game costs $2, then the expected value is:

Ev = $2.45 - $2 = $0.45

The expected value is  $0.45

Answer:

336π square millimeters

Answer:

A

Step-by-step explanation:

Answer:

Triangle ISK

Step-by-step explanation:

Answer:

Triangle ISK

Step-by-step explanation:

if the angles and sides of one triangle are equal to the corresponding sides and angles of the other triangle, they are congruent.

∠Q = ∠I

∠R = ∠S

∠S = ∠K

Step-by-step explanation:   The standard formula for geometric sequence is an = a1 * r^(n-1) where r is the geometric factor and n is an integer. In this problem, upon substitution, an = 4*2^(n-1).

Answer:

-0.301

Step-by-step explanation:

Correct Question :-

If log 2 = 0.301 , find log 0.5

Solution :-

We are here given that the value of log 5 is 0.699 . Here the base of log is 10 .

[tex]\rm\implies log_{10}2= 0.301 [/tex]

And we are supposed to find out the value of log 0.5 . We can write it as ,

[tex]\rm\implies log_{10}(0.5) = log _{10}\bigg( \dfrac{5}{10}\bigg)[/tex]

Simplify ,

[tex]\rm\implies log _{10}\bigg( \dfrac{1}{2}\bigg)[/tex]

This can be written as ,

[tex]\rm\implies log_{10} ( 2^{-1})[/tex]

Use property of log ,

[tex]\rm\implies -1 \times log_{10}2 [/tex]

Put the value of log 2 ,

[tex]\rm\implies -1 \times 0.301 =\boxed{\blue{-0.301}} [/tex]

Hence the value of log (0.5) is -0.301 .

*Note -

Here here there was no use of log 5 in the calculation .