A coin is flipped 150 times. The results of the experiment are shown in the following table:

Heads Tails
84 66

Which of the following statements best describes the experimental probability of getting heads?

Group of answer choices

It is equal to the theoretical probability.

It is 6% lower than the theoretical probability.

It is 6% higher than the theoretical probability.

The experimental probability cannot be concluded from the data in the table.

Sorry I did it wrong.

Answer:

(0, -5) and (-16, -17)

Step-by-step explanation:

You can plug in the points into the function to test them.

(0, -5)

3(0) - 4(-5) - 8 = 12

20 - 8 = 12

12 = 12

(8, 2)

3(8) - 4(2) - 8 = 12

24 - 8 - 8 = 12

8 ≠ 12

(-16, -17)

3(-16) - 4(-17) - 8 = 12

-48 + 68 - 8 = 12

12 = 12

3(-1) - 4(-8) - 8 = 12

-3 + 32 - 8 = 12

21 ≠ 12

3(-40) - 4(-34) - 8 = 12

-120 + 136 - 8 = 12

8 ≠ 12

Answer:

A

Step-by-step explanation:

Answer:

Type 1 error.

Step-by-step explanation:

H0 : μ = 5.1

H1 : μ ≠ 5.1

The Pvalue of the test = 0.003

Decision made by the researcher was conclude that mean weight is not as advertised, that is the researcher rejected the Null hypothesis.

However, when the Pvalue is < α - value , we reject the null ; The type of error the researcher could have made is that ; The mean weight may be truly as advertised, Hence, leading us to make a false positive error, thus is rejecting a true null. This is a TYPE 1 error.

Answer:

D = L/k

Step-by-step explanation:

Since A represents the amount of litter present in grams per square meter as a function of time in years, the net rate of litter present is

dA/dt = in flow - out flow

Since litter falls at a constant rate of L  grams per square meter per year, in flow = L

Since litter decays at a constant proportional rate of k per year, the total amount of litter decay per square meter per year is A × k = Ak = out flow

So,

dA/dt = in flow - out flow

dA/dt = L - Ak

Separating the variables, we have

dA/(L - Ak) = dt

Integrating, we have

∫-kdA/-k(L - Ak) = ∫dt

1/k∫-kdA/(L - Ak) = ∫dt

1/k㏑(L - Ak) = t + C

㏑(L - Ak) = kt + kC

㏑(L - Ak) = kt + C'      (C' = kC)

taking exponents of both sides, we have

[tex]L - Ak = e^{kt + C'} \\L - Ak = e^{kt}e^{C'}\\L - Ak = C"e^{kt} (C" = e^{C'} )\\Ak = L - C"e^{kt}\\A = \frac{L}{k} - \frac{C"}{k} e^{kt}[/tex]

When t = 0, A(0) = 0 (since the forest floor is initially clear)

[tex]A = \frac{L}{k} - \frac{C"}{k} e^{kt}\\0 = \frac{L}{k} - \frac{C"}{k} e^{k0}\\0 = \frac{L}{k} - \frac{C"}{k} e^{0}\\\frac{L}{k} = \frac{C"}{k} \\C" = L[/tex]

[tex]A = \frac{L}{k} - \frac{L}{k} e^{kt}[/tex]

So, D = R - A =

[tex]D = \frac{L}{k} - \frac{L}{k} - \frac{L}{k} e^{kt}\\D = \frac{L}{k} e^{kt}[/tex]

when t = 0(at initial time), the initial value of D =

[tex]D = \frac{L}{k} e^{kt}\\D = \frac{L}{k} e^{k0}\\D = \frac{L}{k} e^{0}\\D = \frac{L}{k}[/tex]

Answer:

0.16 probability that in a sample of 25 mosquitoes the mean body temperature is greater than 59∘F, assuming the underlying distribution is normal.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The body temperatures of all mosquitoes in a county have a mean of 57∘F and a standard deviation of 10∘F.

This means that [tex]\mu = 57, \sigma = 10[/tex]

Sample of 25:

This means that [tex]n = 25, s = \frac{10}{\sqrt{25}} = 2[/tex]

of 25 mosquitoes the mean body temperature is greater than 59∘F, assuming the underlying distribution is normal?

This is 1 subtracted by the pvalue of Z when X = 59. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{59 - 57}{2}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.84

1 - 0.84 = 0.16

0.16 probability that in a sample of 25 mosquitoes the mean body temperature is greater than 59∘F, assuming the underlying distribution is normal.

Multiply the length by the height:

6.5 x 2 = 13

The width is the volume divided by 13

Width = 52/13 = 4 m

Answer:

a) The total engine volume is 30.3265 in³

b) the mass of air contained in the engine is 0.00129 lbm

c) The efficiency of the engine is 55.6%

Step-by-step explanation:

Given the data in the question;

The configuration is in line with four-stroke, four-cylinder engine.

Bore ( d ) = 3.17 in

Stroke ( L ) = 3.48 in

compression ratio ( r ) = 10.6 : 1

First, we calculate the swept Volume V₁ = π/4 × d²L

we substitute

V₁ = π/4 × (3.17 )² × (3.48) = 27.4655 in³

Now, Compression Ration; r = Vs + Vc / Vc

r = (V₁ + V₂) / V₂

we substitute

10.6 = (27.4655 + V₂) / V₂

10.6V₂ = 27.4655 + V₂

10.6V₂ - V₂ = 27.4655

9.6V₂ = 27.4655

V₂ = 2.861 in³

So

a) total engine volume

[tex]V_{BDC[/tex] = V₁ + V₂

we substitute

[tex]V_{BDC[/tex] = 27.4655 in³ + 2.861 in³

[tex]V_{BDC[/tex] = 27.4655 in³ + 2.861 in³

[tex]V_{BDC[/tex] = 30.3265 in³

Therefore, The total engine volume is 30.3265 in³

b) The mass of air

given that; T = 540°R, P = 14.7 psia

we know that; PV = mRT   { R is constant }

we solve for m

m = PV / RT

we substitute

m = (14.7 × 30.3265)  / ( 0.3704 × 1728 )540

m = 445.79955 / 345627.648

m = 0.00129 lbm

Therefore, the mass of air contained in the engine is 0.00129 lbm

c) The efficiency

from table { properties of air}

At 540°R; u₁ = 92.04 BTu/lbm, u[tex]_r[/tex]₁ = 144.32

Now process 1 - 2 ( Isentropic )   u[tex]_r[/tex]₁ / u[tex]_r[/tex]₂  = V₁/V₁ = r

so,  u[tex]_r[/tex]₁ / u[tex]_r[/tex]₂ = r

144.32  / u[tex]_r[/tex]₂ = 10.6

u[tex]_r[/tex]₂ = 144.32/10.6

u[tex]_r[/tex]₂ = 13.61

Thus, at u[tex]_r[/tex]₂ = 13.61, u₂ = 235 BTU/lbm, T₂ = 1340°R

Now, we know that;

P₁V₁/T₁ = P₂V₂/T₂  ⇒ (P₁/V₁)r = P₂/T₂

⇒ ( 14.7 / 540 )10.6 = P₂/1340

P₂ = 386.664 psia  

process 2 - 3; constant volume heat addition;

Now, At T₃ = 3600°R, u₃ = 721.44 BTU/lbm, u[tex]_r[/tex]₃ = 0.6449

so, [tex]q_{in[/tex] =  u₃ -  u₂

we substitute

so, [tex]q_{in[/tex] =  721.44  -  235  = 486.44 BTU/lbm

Next, process 3 - 4; Isentropic  

u[tex]_r[/tex]₄/u[tex]_r[/tex]₃ = V₄/V₃ = r

u[tex]_r[/tex]₄ / 0.6449  = 10.6

u[tex]_r[/tex]₄ = 6.8359

At u[tex]_r[/tex]₄ = 6.8359; u₄ = 308 BTU/lbm

∴

Heat Rejection [tex]q_{out[/tex] = u₄ - u₁ = 308 - 92.04 = 215.96 BTU/lbm

so, [tex]W_{net[/tex] = [tex]q_{in[/tex] - [tex]q_{out[/tex]

[tex]W_{net[/tex] = 486.44 - 215.96

[tex]W_{net[/tex] = 270.48 BTU/lbm

so the efficiency; η[tex]_{thermal[/tex] = ([tex]W_{net[/tex] / [tex]q_{in[/tex] ) × 100%

η[tex]_{thermal[/tex] = ( 270.48 / 486.44  ) × 100%

η[tex]_{thermal[/tex] = ( 0.55604  ) × 100%    

η[tex]_{thermal[/tex] = 55.6%

Therefore, The efficiency of the engine is 55.6%

Answer:

V= 160 ft

Step-by-step explanation:

First 10×8×6 then ÷ 3 = 160

Answer: Midpoint: (2, 1)

Step-by-step explanation:

Midpoint formula: ((x1 + x2)/2 , (y1 + y2)/2)

(-4 + 8)/2 = 2

(-8 + 10)/2 = 1

Answer: (2, 1)

Answer:

d

Step-by-step explanation:

V=whl=3·4·6=72

D. 6*4*6≠72

Answer:

D 6x6x4

Step-by-step explanation:

the dimensions are 3x6x4 so 6x6x4 is not the volume of this rectangular prism

Answer:

the answer is c square root 52

Step-by-step explanation:

just got a 100

The distance from Beth’s house to the coffee shop, which are graphed on a coordinate plane is √(52) units.

The distance formula is used to measure the distance between the two points on a coordinate plane.

Let the two coordinate  point on a coordinate plane is ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]). Thus, the distance between these two can be given as,

[tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]

When graphed on a coordinate plane Beth’s house is located at (4, 3) and the coffee shop is located at the point (–2, –1).

Here, each grid line on the coordinate plane represents 1 mile.

Using the distance formula for these point, the distance from Beth’s house to the coffee shop can be given as,

[tex]d=\sqrt{(4-(-2)^2)+(3-(-1))^2}\\d=\sqrt{6)^2+(4)^2}\\d=\sqrt{36+16}\\d=\sqrt{52}[/tex]

Hence, the distance from Beth’s house to the coffee shop, which are graphed on a coordinate plane is √(52) units.

Learn more about the distance formula here;

https://brainly.com/question/661229

Answer:

The 4th one (bottom)

Step-by-step explanation:

[tex]\frac{2}{3}x - 5 > 3\\\frac{2}{3}x > 3 + 5\\\frac{2}{3}x > 8\\x > 8 / \frac{2}{3} \\x > 12\\[/tex]

> sign means an open circle over 12, shaded/pointing to the right. The 4th option is your answer

Answer:

45

Step-by-step explanation:

1/2×9×10

since the formula says half base times height, so therefore

Area =45

Answer:

x = 13/8

Step-by-step explanation:

(4x−1)(2)=11

Simplify both sides of the equation.

(4x−1)(2)=11

(4x)(2)+(−1)(2)=11 (Distribute)

8x+−2=118x+−2=11

8x−2=11

Add 2 to both sides.

8x−2+2=11+2

8x=13

Divide both sides by 8.

8x/8 = 13/8

which brings you to the answer of

x = 13/8

(Note:If this was a little confusing,feel free to ask me any questions revolving around this topic)

Answer:

1 1/4, -1, -1/4, 0, 1/4, 1

Step-by-step explanation:

Answer:

-1 1/4, -1, -1/4, 0, 1/4, 1,

Step-by-step explanation:

Answer:

$192

Step-by-step explanation:

Answer:

Answer:

a) σ  =  4933,64

b) CI 99%  = ( - 5746  ;  7194 )

c) No difference in brands

Step-by-step explanation:

Brand 1:

n₁   =  8

x₁   = 38222

s₁   = 4974

Brand 2:

n₂  = 8

x₂  = 37498

s₂  = 4893

As n₁  =  n₂  = 8       Small sample  we work with t -student table

degree of freedom      df  = n₁  +  n₂  - 2    df = 8 +8 -2  df = 14

CI = 99 %   CI  =  0,99

From  t-student table we find   t(c)  = 2,624

CI  =   (  x₁  -  x₂ ) ±  t(c) * √σ²/n₁   +  σ²/n₂

σ² = [( n₁  -  1 ) *s₁² +  ( n₂  -  1  ) * s₂² ] / n₁ +n₂ -2

σ² = 7* (4974)² + 7*( 4893)² / 14

σ² = 24340783       σ  =  4933,64

√ σ²/n₁  +  σ²/n₂     =  √ 24340783/8   +  24340783/8

√ σ²/n₁  +  σ²/n₂     =  2466

CI 99%  =  (  x₁  -  x₂ ) ± 2,624* 2466

CI 99%  =   724  ± 6470

CI 99%  = ( - 5746  ;  7194 )

As we can see CI 99% contains 0 and that means that there is not statistical difference between mean life of the two groups

[tex]\huge{\textbf{\textsf{{\color{navy}{An}}{\purple{sw}}{\pink{er}} {\color{pink}{:}}}}}[/tex]

C. 4.

Answer:

27) x = 2^(y) – 5.

Asymptote: x = -5.

D: x > -5; (-5, infinity).

R: -infinity < f(x) < infinity; ARN;

(-infinity, infinity).

x → -infinity, f(x) → -infinity.

x → +infinity, f(x) → +infinity.

________________________

28) x = 2^-(y–3).

Asymptote: x = 0.

D: x > 0; (0, infinity).

R: -infinity < f(x) < infinity; ARN;

(-infinity, infinity).

x → -infinity, f(x) → +infinity.

x → +infinity, f(x) → -infinity.

________________________

29) x = 4^(y–2) + 1.

Asymptote: x = 1.

D: x > 1; (1, infinity).

R: -infinity < f(x) < infinity; ARN;

(-infinity, infinity).

x → -infinity, f(x) → -infinity.

x → +infinity, f(x) → +infinity.

________________________

Answer:

D

Step-by-step explanation:

80 miles per hour, each hour it will travel 80 miles so for two hours tou do

80 x 2 = 160

Answer:

D

Step-by-step explanation:

80x2=40

it's just simple multiplecation but then again I cant spell multiplication so I mean

Answer: C. 10x-3

Step-by-step explanation: I got this question correct on Edmentum.

The value of the expression will be 10x – 3. Then the correct option is C.

The value that approaches the output for the given input value. Limits are a very important tool in calculus.

The function is defined as,

f(x) = 5x² – 3x + 2

Then the value of the expression will be

[tex]\rightarrow \displaystyle \lim_{h \to 0} \dfrac{f(x+h)-f(x)}{h}[/tex]

Substitute the value of the function, then the value of the expression will be

[tex]\rightarrow \displaystyle \lim_{h \to 0} \dfrac{5(x+h)^2 - 3(x + h) + 3- 5x^2 + 3x - 3}{h}\\\\\\\rightarrow \displaystyle \lim_{h \to 0} \dfrac{5x^2 + 5h^2 + 10xh - 3x - 3h + 3- 5x^2 + 3x - 3}{h}\\\\\\\rightarrow \displaystyle \lim_{h \to 0} \dfrac{ 5h^2 + 10xh - 3h }{h}\\[/tex]

Simplify the equation further, then we have

[tex]\rightarrow \displaystyle \lim_{h \to 0} 5h + 10x - 3 \\[/tex]

Substitute the value of the h = 0, then the value of the expression will be

⇒ 5(0) + 10x – 3

⇒ 10x – 3

Then the correct option is C.

More about the limit link is given below.

https://brainly.com/question/8533149

#SPJ2

Answer:

3

Step-by-step explanation:

For x<=0, f is constant: f(x) =3

-4<0, so f(-4)=3

Answer: 120cm squared

Step-by-step explanation: To do this you can cut off one of the 'triangle ends' on the trapezoid and add it to the other side to make a rectangle. Since the top is 10cm, each triangle will have a base of 5cm, so the bases will be 15cm when you subtract 20-5. Then you just have 8 * 15 which is 120cm SQUARED. This may have been a little confusing so i attachecd a diagram.

Answer:1,250

Step-by-step explanation:

Answer:

15 x /2

Step-by-step explanation:

Answer:

Option B and D are correct

Step-by-step explanation:

Exponential functions are really useful in the real world situation. They can be used to solve following

a) Population Models

b) Determination of area and perimeters

c) Determine time related things such as half life, time of happening of an event etc.

d) Useful for solving financial problems such as computing investments etc.

Hence, option B and D