A pilot is flying from Phoenix, Arizona, to Louisville, Kentucky. The aircraft cannot take off
or land if the temperature on the field is not within its operating limitations. The aircraft
cannot operate if the temperature is at or below -40 degrees, or at or above 118 degrees.
A) Write an inequality to represent the temperatures in which the pilot can take off &
land. (2pts)

B) Describe the graph of the inequality. Use terms such as open/closed circles and
shading directions. Explain what the solutions to the inequality represent (4pts)

Answer:

180°

Step-by-step explanation:

JM is the diameter of the circle with center L.

\( \huge \red{ \boxed{\therefore m\widehat{(JKM)} = 180\degree}} \\ \)

Answer:

Step-by-step explanation:

JLM is diameter so  arc JKM is half of circle

measure of arc JKM = 0.5m•360° = 180°

The ways that we can choose 2 red, 1 yellow, and 2 blue marbles is ³C₂ ×  ⁵C₁ ×  ⁸C₂ / ¹⁶C₅

According to the question,

In a bag there are three different color of marbles

Number of red color marbles = 3

Number of yellow color marbles = 5

Number of blue color marbles = 8

Total number of marbles = 3 + 5 + 8

=> 16

We have to find number of ways to choose 2 red, 1 yellow, and 2 blue marbles

For choosing 2 red marbles from total 3 ,

Number of ways = ³C₂

For choosing 1 yellow marbles from total 5 ,

Number of ways = ⁵C₁

For choosing 2 blue marbles from total 8 ,

Number of ways =  ⁸C₂

Total number of ways to choose 5 marbles from 16 = ¹⁶C₅

Therefore , Numbers of ways we can choose n 2 red, 1 yellow, and 2 blue marbles =  ³C₂ ×  ⁵C₁ ×  ⁸C₂ / ¹⁶C₅

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There is sufficient evidence to suggest that the proportion of university students engaging in binge drinking has decreased at a 5% level of significance.

A hypothesis test will be conducted to determine whether the proportion of university students who engage in binge drinking has decreased or not.

Null hypothesis: H0: p = 0.62 (proportion of students who engage in binge drinking at least once a month has not decreased).

Alternative hypothesis: H1: p < 0.62 (proportion of students who engage in binge drinking at least once a month has decreased).

The proportion of students who engaged in binge drinking at least once in the last month, according to the survey, is 1954/3500 = 0.558 or 55.8 percent, which is less than 0.62.

The sample size is greater than 30, therefore the z-test can be utilized.

To perform a hypothesis test, the following z-statistic is employed:

\(z = (p - P) / sqrt(PQ/n)\)

Where:

P = 0.62 (hypothesized proportion)

P = 0.38 (1 - P)

Q = 0.38 (1 - P)

n = 3500

z = (0.558 - 0.62) / sqrt((0.62 × 0.38) / 3500)

= -9.57

The p-value for a one-tailed z-test with a test statistic of -9.57 is practically zero (less than 0.00001).

Therefore, at a 5% level of significance, the null hypothesis is rejected.

There is sufficient evidence to suggest that the proportion of university students engaging in binge drinking has decreased at a 5% level of significance.

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Answer:

A = 8 km^2

B = 12 km

Step-by-step explanation:

The point in polar coordinates (2, 13π/6) can be matched with the point A.

Explanation:

Here, (2, 13π/6) is given in polar coordinates.

So, we need to convert it into rectangular coordinates (x, y) to plot the given point in the cartesian plane.

The relation between polar and rectangular coordinates is given below:  

x = r cos θ, y = r sin θ

where r is the distance of the point from the origin, and θ is the angle made by the line joining the point and the origin with the positive x-axis.  

Therefore,

we have:

r = 2, θ = 13π/6  

Substituting these values in the above equations,

we get:  

x = 2 cos (13π/6)

  = 2(-√3/2)

  = -√3  y

  = 2 sin (13π/6)

  = 2(-1/2)

  = -1

So, the rectangular coordinates of the given point are (-√3, -1).  

Now, let's look at the given points A, B, C, and D.

A(-√3, -1) B(√3, 1) C(-√3, 1) D(√3, -1)

The rectangular coordinates of the given point match with point A.

Therefore, the given point in polar coordinates (2, 13π/6) can be matched with the point A.

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Answer:

3. y = 2x - 2

4. y = \(\frac{4}{3}x-1\)

Step-by-step explanation:

3. Slope = 2

Y-intercept = -2

4. Slope = \(\frac{4}{3}\)

Y-intercept = -1

Answer:

3). y = 2x - 2

4). y = (4/3)x - 1

Step-by-step explanation:

3).

First find the slope

(y2 - y1) / (x2 - x1)  or rise/run

(0 - (-2)) / (1 - 0) = 2

2 is your slope

Now use the equation below for using coordinates for finding slope intercept form.

y - y1 = m(x - x1)

y1 = y number of given coordinate

x1 = x number of given coordinate

m = slope

y - 0 = 2(x - 1)

Distribute

y - 0 = 2x + (-2)

Get y by itself by adding 0 to both sides.

y - 0 = 2x + (-2)

  +0           +0

y = 2x - 2

4).

Repeat the same process for 4 as done in 3

Find the slope

(y2 - y1) / (x2 - x1)  or rise/run

(3 - (-1)) / (3 - 0) = 4/3

4/3 is your slope

Now use the equation below for using coordinates for finding slope intercept form.

y - y1 = m(x - x1)

y1 = y number of given coordinate

x1 = x number of given coordinate

m = slope

y - 3 = (4/3)(x - 3)

Distribute

y - 3 = (4/3)x + (-4)

Get y by itself by adding 3 to both sides.

y - 3 = (4/3)x + (-4)

  +3                  +3

y = (4/3)x - 1

Answer:

16x2=32 - 4=28

Step-by-step explanation:

Answer:

x = 17.5°

Step-by-step explanation:

complementary means their sum is 90°.

x + 3x + 20° = 90°

4x = 70°

x = 17.5°

Answer:

B.

Step-by-step explanation:

We can start by dividing 3.5 and 0.75.

3.5/0.75 is 4.67.

Now, we multiply 4.67 by 1 since we are finding how much she walks in 1 hour.

1*4.67 is 4.67.

The statement, "When using binomial distribution, maximum possible number of "success" is number of trials." is, True because number of success is equal to number of trials.

When using the binomial distribution, the maximum possible number of successes is equal to the number of trials.

In each trial, there are two possible outcomes: success or failure.

The probability of success in each trial is denoted by "p" and the probability of failure is denoted by "q" (where q = 1 - p).

The binomial distribution calculates the probability of obtaining a specific number of successes in a fixed number of trials.

Since the number of possible successes is limited to the number of trials, the statement is true.

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Answer:

5: 4

Step-by-step explanation:

original ratio: 3:5

new ratio: 5:4

hope it helps!

Therefore , the solution of the given problem of equation comes out to be it mean that you owe 36 amount of money to bank.

When the equals sign (=) is used to denote equality, an algebraic theorem resembles a rule joining two statements. An algebraic equation is a factual assertion that shows the equivalence of multiple numerical variables. The values ob d + 6 and 12 are separated by an equal sign in the calculation data logger + 6 = 12. The number of syllables that correspond to each side of each letter can be expressed numerically. The message of a symbol is frequently its complete opposite.

Here,

Given :

After a few weeks, you create and calculate an equation

so determine how much money is in your bank account.

M equals -36, as you discover.

Thus,

It mean that you owe 36 amount of money to bank.

Therefore , the solution of the given problem of equation comes out to be it mean that you owe 36 amount of money to bank.

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The number of new phone sold is 1 and the number of old phone sold is 5, if the sales for the day totals $625.

It is given that

A new phone sells for $250

and a used one sells for $75

Let number of new phone is sold = x

and number of old phone is sold = y

Here the total profit for the day is $625

So, 250x + 75y = 625

or 10x + 3y = 25

Now the value of x  and y satisfy the above equation, if we take x = 2 and more than 2, it is clear that it not satisfy the above equation. So we made a conclusion here x must be equal to 1 here.

Now, if x = 1

10(1) + 3y = 25

3y = 15

y = 5

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Answer:

If two individual forces are of equal magnitude and opposite direction, then the forces are said to be balanced. An object is said to be acted upon by an unbalanced force only when there is an individual force that is not being balanced by a force of equal magnitude and in the opposite direction.

Answer:

Step-by-step explanation:

H

Complete Question:

If all other factors specified in an attribute sampling plan remain constant, changing the expected population deviation rate from 1 percent to 2 percent and changing the tolerable deviation rate from 7 percent to 6 percent would cause the required sample size to:

a. Increase.

b. Decrease.

c. Remain the same.

d. Change by 2 percent.

The required sample size should increase.

The sample size is directly influenced by the projected population deviation rate, but the tolerated deviation rate has the opposite impact. The sample size will therefore increase as the projected population deviation rate rises and the acceptable deviation rate falls.

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The circumference formula for a circle is C=πd where C is the circumference, d is the diameter of the circle and π is a constant. If you plug in 6 for C and solve the equation for d like:

6= πd and then divide both sides of the equation by π you get that d = 1.90

To find the central angle of an arc you would use the equation S = rθ where S is the length of the arc, r is the radius of the circle, and θ is the measure of the angle which in this case is unknown. So with S = 1 and r = d/2 = 1.90/2 = 0.9549 you would have an equation that looks like this:

1 = 0.9549θ

Answer:

60

Step-by-step explanation:

1/6 x 360

Central angle is equal to measure of intercepted arc.

60 degrees

The weakest correlation is represented by the value of c. 0.11.

The weakest correlation is represented by the value that is closest to zero, as it indicates a weaker relationship between the variables. In this case, the answer is: c. 0.11

A correlation coefficient of 0.11 is closer to zero than the other options provided, indicating a weaker correlation compared to the rest. The negative values (-0.75 and -0.27) represent negative correlations, but their magnitudes are larger than 0.11, making them stronger correlations (although still considered weak in general). The positive value of 0.54 represents a moderate positive correlation.

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers. To calculate the t-value, the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

Given, M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers.

To calculate the t-value,

the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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Answer:

c. Smaller than the fraction

Step-by-step explanation:

have a great night :)

The probability that each player has a 5-card hand an ace when the 52 cards is 5/13.

Given is 52 cards of a standard deck, we need to find the probability of picking an ace,

so,

There are 4 aces in the 52-card deck so the probability of dealing an ace is 4/52 = 1/13.

In a 5-card hand, each card is equally likely to be an ace with probability 1/13. So together, the expected number of aces in a 5-card hand is 5 * 1/13 = 5/13.

Hence the probability that each player has a 5-card hand an ace when the 52 cards is 5/13.

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The limit of the function as x approaches 9 is; 4

Let y = f(x) be a function of x.

If at a point x = b, f(x) takes an indeterminate form, then we can truly consider the values of the function which is very near to b. If these values tend to some definite unique number as x tends to b, then that obtained unique number is called the limit of f(x) at x = B.

Now we are given the function as;

√(25 - x) lim x->9

Thus,we plug in 9 for x into the function to get;

√(25 - 9)

= √16

= 4

Thus,that is the limit of the function as x approaches 9.

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To find the length of the curve given by r(t) = cos(7t) i + sin(7t) j + 7 ln(cos(t)) k, 0 ≤ t ≤ π/4, we need to use the formula for arc length:

L = ∫[a,b] √[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 dt

In this case, we have:

dx/dt = -7 sin(7t)
dy/dt = 7 cos(7t)
dz/dt = -7 sin(t) / cos(t)

So,

[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 = 49 sin^2(7t) + 49 cos^2(7t) + 49 sin^2(t) / cos^2(t)
= 49 [sin^2(7t) + cos^2(7t) + sin^2(t) / cos^2(t)]
= 49 [1 + sin^2(t) / cos^2(t)]

Now, using the identity sin^2(t) + cos^2(t) = 1, we can rewrite this as:

[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 = 49 cos^2(t)

Therefore, the length of the curve is:

L = ∫[0,π/4] √[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 dt
= ∫[0,π/4] 7 cos(t) dt
= 7 [sin(t)]|[0,π/4]
= 7 sin(π/4) - 7 sin(0)
= 7 (√2/2)
= 7√2/2

So the length of the curve is 7√2/2.

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Answer:

p^2

Step-by-step explanation:

Answer:

$9.98 :)

Step-by-step explanation:

just multiply the tax (0.085) by the price ($9.20) then add the initial price ($9.20) to that.

The minimal number of simple transpositions needed to write τ as a product of simple transpositions is 3. τ is not in A₅ because it contains an odd number of transpositions. τσ₁τ⁻¹ = σ₂, showing that the conjugation by τ maps σ₁ to σ₂. σ₁ and σ₂ belong to A₅, and (34)τ belongs to A₅. Also, product is computed τ₁σ₁τ₁⁻¹ = σ₂ by using transpositions with σ₁,σ₂ ∈ A₅ and τ1 is (34)τ ∈ A5.

To write τ as a product of simple transpositions, we can use the following formula τ = (a₁ a₂)(a₁ a₃)(a₂ a₄)(a₃ a₅)

Using this formula with a₁=1, a₂=3, a₃=2, a₄=4, and a₅=5, we get:

τ = (13)(12)(34)(25)

Therefore, we need four simple transpositions to write τ as a product of simple transpositions.

To show that τ is not in A₅, we can use the fact that the parity of a permutation is equal to the parity of the number of inversions in the permutation. The number of inversions in τ is 3, which is odd, so τ is not in A₅.

To show that τσ₁τ⁻¹ = σ₂, we can simply compute the product

τσ₁τ⁻¹ = (13)(245)(1)(2)(345)(24)(13) = (3)(4)(152) = σ₂

To show that σ₁,σ₂ ∈ A₅, we can check that they are even permutations. Both σ₁ and σ₂ are products of three disjoint transpositions, so they have order 2 and are even. Therefore, σ₁,σ₂ ∈ A₅.

To compute τ₁ = (34)τ, we can first compute τ, and then apply the transposition (34) to the result

τ = (13)(245) = (13)(24)(45)

τ₁ = (34)(13)(24)(45) = (14)(23)(45)

Finally, to show that τ₁σ₁τ₁⁻¹ = σ₂, we can compute the product

τ₁σ₁τ₁⁻¹ = (14)(23)(45)(1)(2)(345)(23)(14)(45) = (3)(4)(152) = σ₂

Therefore, τ₁σ₁τ₁⁻¹ = σ₂, as required.

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Test of significance is  the observed effect due to chance. Option (c) is correct .

What is a significance test?

What makes significance significant?

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The number of free throws that adam can expect to make if he attempts 20 free throws is 14.

Probability is a metric used to express the possibility or chance that a particular event will occur. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given the probability that the person making a free throw is 70%. The question asks to estimate how many of his 20 free throw attempts will be successful.

Then, the number of free throws is calculated as follows,

\(\begin{aligned}\text{70\% of 20}&=\frac{70\times20}{100}\\&=14\end{aligned}\)

Then, the number of successful free throws is 14.

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The probability of event A occurring is 1/3, the probability of event B occurring is 5/18, and the probability of event AB occurring is 1/9.

The probability of an event occurring is the number of favorable outcomes divided by the total number of possible outcomes. In this case, we have an unfair die where the even numbered sides are twice as likely as the odd numbered sides. We can use this information to find the probabilities of events A and B.

Event A = {odd numbered side} = {1, 3, 5, 7, 9, 11}

Event B = {4, 5, 6, 7, 8}

(a) To find the probability of event A occurring, we need to find the number of favorable outcomes and the total number of possible outcomes. There are 6 odd numbered sides on the die, so the number of favorable outcomes is 6. However, since the even numbered sides are twice as likely as the odd numbered sides, we need to account for this in the total number of possible outcomes. The total number of possible outcomes is 12 + 6 = 18. Therefore, the probability of event A occurring is 6/18 = 1/3.

(b) To find the probability of event B occurring, we need to find the number of favorable outcomes and the total number of possible outcomes. There are 5 sides in event B, so the number of favorable outcomes is 5. The total number of possible outcomes is the same as in part (a), which is 18. Therefore, the probability of event B occurring is 5/18.

(c) To find the probability of event AB occurring, we need to find the intersection of events A and B. The intersection of events A and B is {5, 7}, so the number of favorable outcomes is 2. The total number of possible outcomes is the same as in parts (a) and (b), which is 18. Therefore, the probability of event AB occurring is 2/18 = 1/9.

So, the probability of event A occurring is 1/3, the probability of event B occurring is 5/18, and the probability of event AB occurring is 1/9.

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