a hollywood film producer is working on a new action film. she wants to estimate the true mean length of action films that have appeared in theatres during the past decade. she randomly selects 30 films and records the run time of each. the average time was 119 minutes with a standard deviation of 21.5 minutes. - construct a 95% confidence interval that estimates the true mean length of action films over the past decade.
1. State.
- We want to construct a ___% confidence interval for µ = ___ length of an action film over the past decade.
2. Plan
- Name : ___
- Conditions :
- Random : Randomly select 30 films
- 10% : 30 is ___ 10% of the population of all action films in the past in the past decade.
- Normal/Large sample : ____

Number of clients who do not play either the piano or the guitar is 22

To find the number of clients who do not play either instrument, we need to subtract the number of clients who play either the piano or the guitar or both from the total number of clients.

Let A be the set of clients who play the piano, and B be the set of clients who play the guitar. Then, we can use the formula A union B

|A ∪ B| = |A| + |B| - |A ∩ B|

where |A ∪ B| is the number of clients who play either the piano or the guitar or both, |A| is the number of clients who play the piano, |B| is the number of clients who play the guitar, and |A ∩ B| is the number of clients who play both instruments

Substituting the given values, we get

|A ∪ B| = 46 + 58 - 17

|A ∪ B| = 87

Therefore, the number of clients who do not play either instrument is:

109 - 87 = 22

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Answer:

9000

Step-by-step explanation:

4

largest:4/7×21000 = 12000

smallest: 1/7×21000. = 3000

12,000-3000 = 9000

Answer:

{-9.5, 1,7}

Step-by-step explanation:

For y =f(x)

domain is list of all values of x and range is list of all values of y

Given

ƒ(x) = 3x – 5

domain = {–1.5, 2, 4}.

thus,

range will be value of f(x)

when x = -1.5

x = 2 and x = 4

Thus,

for x = -1.5

ƒ(x) = 3*-1.5 – 5 = -4.5 - 5 = -9.5

\

for x = 2

ƒ(x) = 3*2– 5 = 6 - 5 = 1

for x = 4

ƒ(x) = 3*4– 5 = 12 - 5 = 7

thus,

range of ƒ(x) = 3x – 5 is {-9.5, 1,7}

the expression fir the weight  of Emmett's dog is 1.25p

Step-by-step explanation:

The weight of Jordan's dog is p pounds.

And it has been given that Emmett's dog weighs 25% more than Jordan's dog.

Hence, 25% of weight of Jordan's dog is

25% of p

= 0.25p

Now, since, Emmett's dog weighs 25% more than Jordan's dog.

Hence, the weight  of Emmett's dog is given by

Weight of  Jordan's dog + 25% of weight of Jordan's dog

= p + 0.25p

=1.25 p

Therefore, the expression fir the weight  of Emmett's dog is 1.25p

Answer:

No

Step-by-step explanation:

A quadratic equation looks something along the lines of \((a+b)^2=a^2+2ab+b^2\)

(x+1)=2(x-3) comes out to be x=-2 and that is not a quadratic equation

Answer:

C

Step-by-step explanation:

∆=b^2-4a*c=1-4*3*(-10)=121>0 có 2x

x1=-b+sprt∆/2a=1+sprt121/2*3=2

x2=-b-sprt∆/2a=1-sprt121/2*3=-5/3

The independent variable in this experiment is the ink color used to present the test (black ink or red ink).

1. The professor is conducting an experiment where the ink color used to present the test is being manipulated.

2. The students are divided into two groups: one group receives the test in black ink, and the other group receives the test in red ink.

3. By using different ink colors, the professor is creating two distinct conditions or treatments for the students.

4. The purpose of manipulating the ink color is to examine if it has any effect on the students' test scores.

5. The professor will collect and compare the test scores of both groups to determine if there are any differences between them.

6. The ink color is the independent variable because it is the variable being deliberately changed by the professor in order to observe its potential impact on the students' test scores.

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Answer:

1.6n \(\leq\) 56

Step-by-step explanation:

1.6n \(\leq\) 56

This states,

'$1.60 per notebook, but use up to 56 dollars.'

The difference between 3 and 12​" translates as 12 while​ "the difference between 12 and 3 translates as 12.

So, according to mathematical expressions:  the difference between 3 and 12​" translates as 12 while​ "the difference between 12 and 3 translates as 12.

Therefore, the difference between 3 and 12​" translates as 12 while​ "the difference between 12 and 3 translates as 12.

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The rate of change of the radius is 1.32cm²/s

The formula for calculating the volume of a sphere is expressed as:

The rate of change of the volume is given as:

Given the following paramters;

dv/dt = 23cm³/s

Volume = 7cm³

Get the radius of the sphere:

7 = 4/3 πr³\

21 = 4πr³

r³ = 21/4π

r = 1.18 cm

Get the rate of change of the radius to have:

\(23 = 4(3.14)(1.18)^2 \frac{dr}{dt} \\23 = 17.48 \frac{dr}{dt} \\\frac{dr}{dt}=1.32cm^2/s\)

Hence the rate of change of the radius is 1.32cm²/s

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Answer:

y = 3/2x - 1/2

all steps explained in pic attached below :)

The estimate of the impact that a successful preventive program might have can be derived from

attributable risk.

In epidemiology, attributable risk or excess risk is a phrase equivalent with risk difference, which has also been used to express the attributable proportion among the exposed and the population.

Attributed risk assists in determining how much of an outcome is attributable to a certain risk factor (i.e., an estimate of the excess risk) in a population exposed to that factor.

The rate (percentage) of a health result (illness or death) in exposed persons that can be linked to the exposure is known as the attributable risk (AR). Attribitable risk measures how much more common a result is in absolute terms among the exposed than the non-exposed.

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Answer:

The length of the side along the river is 140 m

Step-by-step explanation:

Equations

To solve the problem, we need to recall the area of a trapezium is:

\(\displaystyle A=\frac{b1+b2}{2}.h\)

Where b1 and b2 are the lengths of the parallel sides and h is the height of the trapezium.

The field to be bought by Mohan has a trapezium shape with a side along the road of side x and a side along the river of side 2x, as stated in the problem.

Knowing the height is h=100 m, and the area is 10500 m2:

\(\displaystyle \frac{x+2x}{2}\cdot 100=10500\)

Simplifying:

\(\displaystyle (3x)\cdot 50=10500\)

\(150x=10500\)

Dividing by 150:

\(x = 10500 / 150 = 70\)

x = 70 m

2x = 140 m

The length of the side along the river is 140 m

The simplified form of the given fraction \(\frac{4^{11} }{4^{-8} }\) is given by 4¹⁹.

As given in the question,

Given fraction :\(\frac{4^{11} }{4^{-8} }\)

Simplify the given fraction using the formula of exponents

\(\frac{x^{a} }{x^{b} } =x^{a-b}\)

The simplified form of the given fraction is given by :

\(\frac{4^{11} }{4^{-8} }\)

Substitute the value in the formula of exponent we get:

Here the value of x= 4 ,value of a=11 and value of b= -8

=(4¹¹ ⁻ ⁽⁻⁸⁾)

=(4¹¹ ⁺ ⁸)

=4¹⁹

Therefore, the simplified form of the given fraction \(\frac{4^{11} }{4^{-8} }\) is given by 4¹⁹.

The complete question is:

Simplify the given fraction in simplified form: \(\frac{4^{11} }{4^{-8} }\).

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The possible range for x, in the terms, of BC is 6BC<x<8BC.

The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.

Given that, a triangle has side lengths AB, BC, and x, where AB=7BC.

The question gives three sides: AB (L₁), BC (L₂) and x (L₃). Also, you know that AB=7BC.

L₁+L₂>L₃ ------(1)

L₁+L₃>L₂ ------(2)

L₂+L₃>L₁ ------(3)

Applying the equation (1) of rule for triangle side lengths, we get

L₁+L₂>L₃

AB+BC >x

7BC+BC>x

8BC >x

x<8BC

Applying the equation (2) of rule for triangle side lengths, we get

L₁+L₃>L₂

AB+x >BC

7BC+x >BC

x > -6BC

Applying the equation (3) of rule for triangle side lengths, we get

L₂+L₃>L₁

BC+x>AB

BC+x>7BC

x>6BC

Now, 6BC<x<8BC

Therefore, the possible range for x, in the terms, of BC is 6BC<x<8BC.

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Answer:

72 pencils

Step-by-step explanation:

i used a calculator

Answer:

72 pencils

Step-by-step explanation:

8-3

x-27

cross multiple

x×3=8×27

x×3=216

x=216/3

x=72

From the given information provided, the approximate volume of the cone is 94.24777 cubic inches.

The volume of a cone can be calculated using the formula V = (1/3) × π × r² × h, where "r" is the radius of the base of the cone, "h" is the height of the cone, and "π" is the mathematical constant approximately equal to 3.14159.

Radius r= 3 inches

Height h= 10 inches

π = 3.14159

Using the formula for the volume of a cone, V = (1/3) × π × r² × h, we can substitute the given values to calculate the volume of the cone:

V = (1/3) × 3.14159 × 3² × 10

V ≈ 94.24777 cubic inches

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Each box has 5 crayon

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The large box contain 48 crayons while its 75% of crayon i.e. 36 crayon is stored in small box.

Independent events are those events whose occurrence is not dependent on any other event. For example, if we flip a coin in the air and get the outcome as Head, then again if we flip the coin but this time we get the outcome as Tail. In both cases, the occurrence of both events is independent of each other.

Events A and B are independent if: knowing whether A occured does not change the probability of B. Mathematically, can say in two equivalent ways: P(B|A) = P(B) P(A and B) = P(B ∩ A) = P(B) × P(A).

Two events are independent if the occurrence of one does not change the probability of the other occurring. An example would be rolling a 2 on a die and flipping a head on a coin. Rolling the 2 does not affect the probability of flipping the head.

Here the Independent event is 36 crayons in small box

The dependent event is large box = 75/100 = 36/x

75x = 3600

x = 3600/75

x = 48

Thus, the large box contain 48 crayons while its 75% of crayon i.e. 36 crayon is stored in small box.

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The probability of exactly one success in the binomial experiment would be 20. 4 %.

The probability that there is one success in a binomial probability which has a chance of success of 5 % can be found by the formula :

P ( X = 1) = (5 choose 1) x ( 0.05 ) x  (0.95 ) ⁴

= ( 0.05 ) x  ( 0. 95 ) ⁴

= 0.05 x 0.8145

= 0.040725

Multiplying both gives:

P(X = 1) = 5 x 0.040725

= 0.203625

In conclusion, the probability of one success is 0.203625 or 20. 4 %.

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Answer:

Step-by-step explanations:

The sum of 5/6 and 2/9 is: C. 1 1/18.

The sum of 1/2 and 2/3 is 7/6.

The fraction of the boys that have either blue or hazel eyes is: B. 1/2.

The sum of 7/10 and 1/4 is: D. 19/20.

The sum of 3/5 and 1/5 is 11/10.

In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

Based on the information provided above, each of the sums can be calculated as follows;

Fraction = 5/6 + 2/9

Fraction = (15 + 4)/18

Fraction = 19/18 = 1 1/18.

Fraction = 1/2 + 2/3

Fraction = (3 + 4)/6

Fraction = 7/6

Fraction = 1/5 + 3/10

Fraction = (2 + 3)/10

Fraction = 1/2

Fraction = 1/4 + 7/10

Fraction = (5 + 14)/20

Fraction = 19/20

Fraction = 3/5 + 1/2

Fraction = (6 + 5)/10

Fraction = 11/10

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At 8000 feet MSL in the teardrop could a descent to 3,200 feet commence.

What is aircraft?

A vehicle that can fly is known as an aircraft. It does so by getting help from the air. It does this by either employing static lift, the dynamic lift of an airfoil or, in a few rare instances, the downward push from jet engines. Aerial vehicles include, but are not limited to, planes, helicopters, airships (including blimps), gliders, paramotors, and hot air balloons.

As given, your aircraft was cleared for the ils rwy 18 at Lincoln municipal and crossed the Lincoln Vortac at 5,000 feet MSL.

Therefore, at 8000 feet MSL in the teardrop could a descent to 3,200 feet commence.

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Answer:

£0.34

£0.43

€3.04

£3.40

£4.03

Step-by-step explanation:

One pound (€) is less than one Pound Sterling (£), so 3.04 pounds is worth less than 3.40 Pound Sterlings.

The following data shows the daily production of cell phones. 7, 10, 12, 15, 18, 19, 20. Mean The formula for finding the mean is: mean = (sum of observations) / (number of observations).

Therefore, the mean for the daily production of cell phones is: Mean = (7+10+12+15+18+19+20) / 7

= 101 / 7

Mean = 14.43

Variance The formula for finding the variance is: Variance = (sum of the squares of the deviations) / (number of observations - 1) Where the deviation of each observation from the mean is: deviation = observation - mean First, calculate the deviation for each observation:7 - 14.43

= -7.4310 - 14.43

= -4.4312 - 14.43

= -2.4315 - 14.43

= 0.5718 - 14.43

= 3.5719 - 14.43

= 4.5720 - 14.43

= 5.57

Now, square each of these deviations: 56.25, 19.62, 5.91, 0.33, 12.75, 20.9, 30.96 The sum of these squares of deviations is: 56.25 + 19.62 + 5.91 + 0.33 + 12.75 + 20.9 + 30.96

= 147.72

Therefore, the variance for the daily production of cell phones is: Variance = 147.72 / (7-1) = 24.62 Standard deviation ) Mean = 14.43b) Variance per Day = 24.62c) Standard Deviation = 4.96

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a. The truck rental cost when you drive 85 miles is  $85.7.

b. The number of miles driven when the cost is $65.96 is 0.42x.

a. To find the truck rental cost when driving 85 miles, we can substitute the value of x into the given function.

f(x) = 0.42x + 50

Substituting x = 85:

f(85) = 0.42(85) + 50

= 35.7 + 50

= 85.7

Therefore, the truck rental cost when driving 85 miles is $85.70.

b. To determine the number of miles driven when the cost is $65.96, we can set up an equation using the given function.

f(x) = 0.42x + 50

Substituting f(x) = 65.96:

65.96 = 0.42x + 50

Subtracting 50 from both sides:

65.96 - 50 = 0.42x

15.96 = 0.42x

To isolate x, we divide both sides by 0.42:

15.96 / 0.42 = x

38 = x

Therefore, the number of miles driven when the cost is $65.96 is 38 miles.

In summary, when driving 85 miles, the truck rental cost is $85.70, and when the cost is $65.96, the number of miles driven is 38 miles.

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A statistical hypothesis test can be performed to determine whether a given hypothesis is true or false. A p-value is a probability value that reflects the strength of evidence against the null hypothesis.

Step 1: WXYZ's current audience share is 25%.Ha: WXYZ's current audience share is not 25%.

Step 2: \(z = (146 - n*p) / sqrt(n*p*q)\)
Where \(n = 400, p = 0.25, and q = 1 - p = 0.75z = (146 - 400*0.25) / sqrt(400*0.25*0.75)z = -2\)

Step 3: We are given that the z-score is -0.62. Since this is a two-tailed test, we need to find the area to the left of -2 and to the right of 2 in the standard normal distribution table.
By adding these two areas, we get the p-value. p-value =
\(P(Z < -2) + P(Z > 2)Where P(Z < -2) = 0.0228\)
(from standard normal distribution table)
\(P(Z > 2) = 0.0228\)
\(p-value = 0.0228 + 0.0228p-value = 0.0456\)

Step 4:The p-value is 0.0456 which is less than the significance level of 0.05. we reject the null hypothesis.

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At μ = 10.0932 level should the mean be set if it is required that only 1% of the bags weigh less than 9.5 kg.

Given Data:

σ = 0.04 kg

x = 9.5 kg

We want to determine μ such that: P(X ≤ 9.5)= 1% = 0.01

Thus, we know here probability of x is 0.1 which is  less than 9.5

so here Z is -2.326 by the standard table

Determine the z-score in the normal probability table in the appendix that has a probability closest to 0.01:

Then, we have here 1% to left when Z is - 2.326

Now,

The value corresponding to the z-score is then the mean increased by the product of the z-score and the standard deviation:

x = μ+ zσ

= μ− 2.33(0.04) = μ - 0.0932

Since , P(X ≤ 9.5) = 0.95% = 0.095, we know that x also has to be equal to 9.5:

   μ− 0.0932 = 9.5

Add 0.0932 to each side of the previous equation:

μ = 10+ 0.0932

= 10.0932

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