An object is traveling at a steady speed of 9 4/5 mi/h. How long will it take the object to travel 2 1/5 mi? First round to the nearest integer to find the estimated answer. Then find the exact answer.

The number of ways to chose a president, vice president, secretary, and treasurer of the club, where no person can hold more than one office is 11880.

If the person cannot hold more than one office.

Then the number of ways of selecting a president, vice president, secretary and treasurer of the club from the club consisting of 12 member is given by the permutation ¹²P₄.

Because we have to select four member out of 12,

So, solving further,

= ¹²P₄

= 12!/(12-4)!

= 12!/8!

= 12 x 11 x 10 x 9

= 11880.

So, there are a total of 11880 ways to chose the members.

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Complete question - A club has 12 members A president, a vice president, a secretary, and a treasurer are to be chosen from these members. A member cannot serve for more than one position. In how many ways can this be down?

Answer:

$42 dollars is the cost per dozen.

Step-by-step explanation:

3.50 is the cost for ONE muffin and we know that 12 goes into a dozen. Simply multiple 3.50 by 12 (3.50 X 12) to get your answer 42.

Answer:

42 dollars

Step-by-step explanation:

A dozen is equal to 12. A muffin is equal to 3.5 dollars each. Therefore, you have to multiply them together. 12 times 3.5 is equal to 42. Therefore, it is 42 dollars a dozen.

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The distance between the initial position and the final position is 72.1ft

The initial position is (0ft, 0ft). Where the notation used is:

(horizontal position, vertical position).

Martha climbs 40 steps, then the final position is:

(40*1ft, 40*1.5ft) = (40ft, 60ft)

The distance between the initial position and the final position is:

\(d = \sqrt{(40ft - 0ft)^2 + (60ft - 0ft)^2} = 72.1ft\)

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The value of x is after solving the logarithm equation logx⁽⁵¹²⁾ = 3 is 8.

A logarithmic equation is an equation that involves the logarithm of an expression containing a variable.

To solve the logarithm equation, we follow the steps below.

Given:

Step 1:

Therefore,

Step 2:

Convert 512 to index form. (i.e 8³)

Comparing both side of equation 1,

Hence, the value of x is 8.

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Answer: $7,500

Step-by-step explanation:

Use the formula: SI = P(1 + rt)

SI = 5000(1 + 0.05[10])

SI = 5000 + 2500

SI = $7,500

After 10 years, your balance should be $7,500

Answer:

\(60n - 97\)

Step-by-step explanation:

\(3 - 5( - 3n + 5)3 - 5( - 3n + 5)\)

\(3 + (15n - 25)3 + 15n - 25\)

\(3 + 45n - 75 + 15n - 25\)

\(60n - 97\)

The value of ∫∫df(x)g(y)da is -20.

The value of ∫∫df(x)g(y)da, where d is the rectangle: −2≤x≤−1, 1≤y≤5, is 20.What is the solution to the given problem?The given problem is about calculating the value of ∫∫df(x)g(y)da, where d is a rectangle. The limits for x and y are given.

We have to use the given values to find the solution. We have to solve it step-by-step:Step 1: Find the value of f(x)The value of ∫−2−1f(x)dx=−5By definition of integration, we can say that:∫−2−1f(x)dx = F(-1) - F(-2)Where F(x) is the antiderivative of f(x)Taking the inverse of the equation, we can say that:F(-1) - F(-2) = ∫−2−1f(x)dxNow, we have to find the antiderivative of f(x) to find the value of F(-1) and F(-2). Let's suppose, the antiderivative of f(x) is F(x).

Then:F(x) = ∫f(x)dxSo, according to the given information, we can write:F(-1) - F(-2) = ∫−2−1f(x)dx = -5Step 2: Find the value of g(y)The value of ∫15g(x)dx=4By definition of integration, we can say that:∫15g(x)dx = G(5) - G(1)Where G(x) is the antiderivative of g(x)Taking the inverse of the equation, we can say that:G(5) - G(1) = ∫15g(x)dxNow, we have to find the antiderivative of g(x) to find the value of G(1) and G(5). Let's suppose, the antiderivative of g(x) is G(x).

Then:G(x) = ∫g(x)dxSo, according to the given information, we can write:G(5) - G(1) = ∫15g(x)dx = 4Step 3: Calculate the given expression∫∫df(x)g(y)daThe value of f(x) is not given, but the value of ∫−2−1f(x)dx is given. Similarly, the value of g(x) is not given, but the value of ∫15g(x)dx is given. So, we can replace the given values in the expression.

Then:∫∫df(x)g(y)da = ∫−2−1 ∫1^5 f(x) g(y) dydx = ∫−2−1 g(y) ∫1^5 f(x) dydxSince we have to find the value of this expression for the rectangle with limits −2≤x≤−1, 1≤y≤5, then:∫∫df(x)g(y)da = ∫−2−1 g(y) ∫1^5 f(x) dydx = ∫1^5 g(y) ∫−2−1 f(x) dxdyUsing the given information, we can replace the value of ∫−2−1 f(x)dx and ∫15g(x)dx.

Then:∫∫df(x)g(y)da = ∫1^5 g(y) (-5) dydx = -5 ∫1^5 g(y) dydxSince the given limits are rectangular, we can use the Fubini's theorem. It states that, if the function is integrable over the rectangle [a, b] x [c, d], then:∫∫[a,b] x [c,d] f(x,y) dxdy = ∫[a,b] dx ∫[c,d] f(x,y) dy = ∫[c,d] dy ∫[a,b] f(x,y) dxNow, we can change the order of integration:∫∫df(x)g(y)da = -5 ∫1^5 g(y) dydx = -5 ∫−2−1 f(x) dx ∫1^5 g(y) dydx = -5 (4) = -20Therefore, the value of ∫∫df(x)g(y)da is -20.Note: In the given question, the given limits for the rectangle are not properly defined. So, we have to consider that the limits are rectangular.

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Result of the problem   is  f = u + iv is a constant function on D.

To show that f is a constant function, we can use the Cauchy-Riemann equations. Since f is analytic on D, we know that it satisfies the Cauchy-Riemann equations, which state that u_x = v_y and u_y = -v_x.

Taking the partial derivative of u with respect to x and v with respect to y, we get:

u_xx = v_yx
and
v_yy = -u_xy

Since f is analytic, its second partial derivatives exist and are continuous. Therefore, we can substitute these equations into each other and get:

u_xx = -u_xy

Using the mixed partial derivative theorem, we know that u_xy = u_yx, so we can rewrite the above equation as:

u_xx = -u_yx

Since u and v are both real-valued functions, they are continuous on D. Therefore, we can apply the mean value theorem for partial derivatives to both sides of the above equation to get:

0 = u_xx(x,y) + u_yx(x,y) / 2

Since this holds for all (x,y) in D, we can conclude that u is a harmonic function on D. By Liouville's theorem, since u is a bounded harmonic function, it must be constant.

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The values of the trigonometric ratio is 1/4 , √15 / 4 , 4 .

When a Triangle is a right angled Triangle then the ratios used to determine the sides and the angles of the triangle are called Trigonometric Ratio.

It is given that in triangle EFG , right angled at F ,

EG = 8 , FG = 2

By Pythagoras theorem

The length of EF is

8² = 2² + EF²

EF = √(64-4) = √60 = 2√15

The value of the trigonometric ratios is

sin E = Perpendicular / Hypotenuse

sin E = 2 / 8 = 1/4

sin G =  2√15 / 8 = √15 / 4

sec G = 1 / cos G = Hypotenuse / Base = 8 / 2 = 4

Therefore the values of the trigonometric ratio is 1/4 , √15 / 4 , 4 .

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Given that we have to find the probability of each of the following when we roll a pair of fair dice:

Probability of getting a sum of 1 = 0

Probability of getting a sum of 5= {4}/{36}=0.1111

Probability of getting a sum of 12= {1}/{36}= 0.0278

Explanation: When we roll a pair of dice, there are 36 possible outcomes or events. When we roll the dice, the number on the dice will be an integer from 1 to 6.

The following table represents the possible outcome when we roll a pair of dice.

There is only one way to obtain the sum of 1, i.e., when both dice show 1. As there is only one way, the probability is 0.

There are 4 possible ways to obtain the sum of 5. They are (1,4),(2,3),(3,2),(4,1). The probability is 4/36.

There is only one way to obtain the sum of 12, i.e., when both dice show 6. As there is only one way, the probability is 1/36.

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Because he multiplied the triangle's base by its height, Kelvin's solution is incorrect

Use the equation area = 1/2 * bases * altitude to determine a triangle's surface area Choose which side will be the triangle's base, and then measure the height of the triangle from that base.. After that, enter the height and base measurements you have into the formula.

Area of triangle= 1/2 base × height

The base of the triangle= 5 in

The height of the triangle = 8 in

Area of triangle= 1/2 base × height

=  1/2 × 5 in × 8 in

=  1/2 × 40 square inches

= 20  square inches

As a result, Kelvin's estimation of the triangle's area is incorrect.

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The point on the curve where the tangent line has a slope of 1/2 is (x, y) = (7, -7).

To find the point on the curve x = 3t^2 + 4, y = t^3 - 8 where the tangent line has a slope of 1/2, we need to determine the value of t at which this occurs. First, we find the derivatives of x and y with respect to t:
dx/dt = 6t
dy/dt = 3t^2
Next, we compute the slope of the tangent line by taking the ratio of dy/dx, which is equivalent to (dy/dt) / (dx/dt):
slope = (dy/dt) / (dx/dt) = (3t^2) / (6t) = t/2
Now, we set the slope equal to 1/2 and solve for t:
t/2 = 1/2
t = 1
With t = 1, we find the corresponding x and y values:
x = 3(1)^2 + 4 = 7
y = (1)^3 - 8 = -7
So, the point on the curve where the tangent line has a slope of 1/2 is (x, y) = (7, -7).

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Therefore, the probability that someone who brings a laptop on vacation also uses a cell phone is 3.52 or 352%.

To find the probability that someone who brings a laptop on vacation also uses a cell phone, we need to use conditional probability.

Let's denote the events:

A: Bringing a laptop

B: Using a cell phone

We are given the following information:

P(A) = 25% = 0.25 (Probability of bringing a laptop)

P(B) = 30% = 0.30 (Probability of using a cell phone)

P(A ∩ B) = 88 out of 100 who bring a laptop also check work email (88/100 = 0.88)

P(B | A) = ? (Probability of using a cell phone given that someone brings a laptop)

We can use the conditional probability formula:

P(B | A) = P(A ∩ B) / P(A)

Substituting the given values:

P(B | A) = 0.88 / 0.25

Calculating the probability:

P(B | A) = 3.52

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The exact value of a trig function can be found by using the unit circle, the trigonometric identities, tables or a calculator.

To find the exact value of a trigonometric function, there are several methods you can use. Below are a few:

1. Using the Unit Circle: The unit circle is a circle with radius 1 centered at the origin in the coordinate plane. The angles in the unit circle are measured in radians and the coordinates of points on the circle can be used to find the exact values of trigonometric functions. For example, given an angle θ in the unit circle, the x-coordinate of the point on the circle corresponding to θ is cos(θ) and the y-coordinate is sin(θ).

2. Using the Trigonometric Identities: There are several trigonometric identities that relate the values of the six trigonometric functions to one another. These identities can be used to find the exact value of a trigonometric function for certain angles. For example, the Pythagorean identity states that for any angle θ, sin²(θ) + cos²(θ) = 1.

3. Using Tables or a Calculator: Trigonometric tables or a scientific calculator can be used to find the exact values of trigonometric functions for certain angles. The values are often given in degrees, so it is important to convert the angle to radians if necessary.

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The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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Answer:

Step-by-step explanation:

Begin by transferring 1/10 x to the right hand side.

y = - 1/10 x + 3

Since the equations are identical, they have infinitely many solutions.

Answer:

let c is a point between a and b we can find the coordinates of c by using mid-point formula

the coordinate x of c is equal to

x=(x1+x2)÷2

x=(3+27)÷2

x=30÷2

x=15

the coordinate y of c is equal to

y=(y1+y2)÷2

y=(2+30)÷2

y=32÷2

y=16

so the coordinates of c are (15,16)

Answer: 15.9 feet

Step-by-step explanation:

Answer:

15.9

Step-by-step explanation:

The probability that the bag is not orange is given as follows:

p = 5/12.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

In this problem, the parameters are given as follows:

Hence the probability that the bag is not orange is given as follows:

p = 5/12.

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The blanks in this two-column proof should be filled as follows:

Statements                                             Reasons_______________

m∠1 = m∠3                                                Given

m∠CBA = m∠ABE + m∠CBD            Angle Addition Postulate  

m∠ABE = m∠3 + m∠2              Substitution Property of Equality          

m∠CBD = m∠3 + m∠2              Substitution Property of Equality

m∠ABE ≅ m∠CBD                    Transitive Property of Equality

In Mathematics, the Angle Addition Postulate states that the measure of an angle formed by two (2) angles that are placed side by side to each other is equal to the sum of the measures of the two (2) angles.

This ultimately implies that, the Angle Addition Postulate can be used to determine the measurement of a missing angle in a geometric figure or it can be used for calculating an angle that is formed by two (2) or more angles such as m∠CBA = m∠ABE + m∠CBD.

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The total amount Mr Page paid for the oil he bought in February was $21,580.

Since Mr Page uses oil to heat his home, and at the beginning of November there were 1000 liters of oil in his oil tank, and Mr Page bought enough oil to fill the tank completely, and he has paid $50 per liter for this oil, and he has paid a total amount of $750, while at the end of February Mr Page had 600 liters of oil in the tank, and he has bought enough oil to fill the tank completely, and the cost of oil had increased by 4%, to determine the total amount Mr Page paid for the oil he bought in February, the following calculation must be performed:

Therefore, the total amount Mr Page paid for the oil he bought in February was $21,580.

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Because r must be between -1.00 and +1.00 and the closer to either indicates a stronger relationship, the strongest must be -0.74. It is a strong negative correlation.

Any statistical association, whether causal or not, between two random variables or bivariate data is referred to in statistics as correlation or dependency. A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate). It's a typical technique for describing straightforward connections without explicitly stating cause and consequence.

A relationship between two variables is said to have a positive correlation when both variables move in the same direction. Consequently, when one variable rises as the other rises, or when one variable falls while the other falls. The link between height and weight is a good example.

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The correct statement is: b. The uncertainty will be larger in Study 1 than in Study 2.

This is because Study 2 used a larger random sample (100 cigarettes) compared to Study 1 (10 cigarettes), resulting in a more accurate estimate of the mean nicotine content and reduced uncertainty.

The uncertainty will be larger in study 1 than in study 2. This is because the sample size in study 1 is smaller than in study 2, which means there is more variability in the estimates due to the smaller sample size. In general, larger sample sizes lead to more precise estimates with less uncertainty.

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Answer:

the set of all possible outputs for a function is the range

The area of the regular polygon from the radius is 50 square units

From the question, we have the following parameters that can be used in our computation:

Half diagonal = 5

This means that

Diagonal = 10

The side length is the calculated as

Length = Diagonal/√2

So, we have

Length = 10/√2

For the area, we have

Area = (10/√2)^2

Evaluate

Area = 50

Hence, the area is 50 square units

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