Fill in the table by converting from 12 hour clock to 24 hour clock and vice versa ​

Answer: \(\frac{8}{3}\ ft/s\)

Step-by-step explanation:

Given

length of shadow =22 ft

height of woman =5.5 ft

speed of woman \(\frac{dy}{dt}=8\ ft/s\)

from the figure, we can write

\(\frac{22}{x+y}=\frac{5.5}{x}\)

at given instant

y=20 ft

so, using similar triangle properties

\(\frac{22}{x+20}=\frac{5.5}{x}\\22x=5.5x+110\\16.5x=110\\x=6.67\ ft\)

Again we can write

\(\dfrac{22}{x+y}=\dfrac{5.5}{x}\\22x=5.5x+5.5y\\16.5x=5.5y\\3x=y\\\text{differentiate w.r.t time} \\3\frac{dx}{dt}=\frac{dy}{dt}\\\frac{dx}{dt}=\frac{1}{3}\times 8=\frac{8}{3}\ ft/s\ \text{away from the woman}\)

Answer:

Yes

Step-by-step explanation:

Let's take any random multiple of 4 as an example:

8 = 2 • 4

64 = 2 • 32

20 = 2 • 10

Try any multiple of 4—this pattern continues.

We want to see if the given statement is true or not, and we will prove that it is true.

A number N has 2 as a factor if we can rewrite:

N = 2*k

Where k is an integer.

Now we want to see if all multiples of 4 have 2 as a factor.

A multiple of 4 can be written as:

N = 4*p

Where p is an integer.

And we know that:

4 = 2*2

Then we rewrite:

N = (2*2)*p = 2*(2*p)

Then a multiple of 4 is written as: 2*(2*p)

2 times an integer, so yes, 2 is a factor of this number, thus, Lindsay is correct.

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Answer: P (3 or 9) = 1/6

Step-by-step explanation:

Concept:

Here, we need to know the idea of probability.

Probability is a measure of the likelihood of an event to occur.

If you are still confused, please refer to the attachment below for a graphical explanation.

Solve:

The numbers on a dice: 1, 2, 3, 4, 5, 6

Total numbers = 6

Number of 3 = 1

Number of 9 = 0

P (3 or 9) = Favorable / Total (refer to the attachment below)

P (3 or 9) = (1 + 0) / (6)

P (3 or 9) = 1 / 6

Hope this helps!! :)

Please let me know if you have any questions

Answer:

False

Step-by-step explanation:

False - one has nothing to do with the other. None of the data points can lie on the regression line,

and you can have the coeff. of determination be 0.5.

Based on the given simple statements, "The scroll is open" and "The writings are visible," we can determine which compound statements would also be true.

The scroll is not open or the writings are visible.

This compound statement would be true. Since the first simple statement states that the scroll is open, the negation of this statement would be that the scroll is not open. The second simple statement states that the writings are visible, which aligns with this compound statement. Therefore, this compound statement is true.

The scroll is open or the writings are not visible.

This compound statement would not be true. Both simple statements state that the scroll is open and the writings are visible. So, the second part of this compound statement contradicts the given information.

The scroll is open or the writings are visible.

This compound statement would be true. It directly matches the given simple statements, where both the scroll being open and the writings being visible are mentioned. Therefore, this compound statement is true.

The scroll is not open or the writings are not visible.

This compound statement would not be true. Both simple statements state that the scroll is open and the writings are visible. So, neither part of this compound statement aligns with the given information.

The compound statements that would be true are:

The scroll is not open or the writings are visible.

The scroll is open or the writings are visible.

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No, they are not congruent.

Because congruent shapes have the same size and shape.I hope this helps you.

Answer:

NO

Step-by-step explanation:

64/12=5.333333

18x5.333333=95.999994

95.999994 is not 98

The linear equation y = 4x - 10 represents the graph z. Then the correct option is D.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

\(\text{y}=\text{mx}+\text{c}\)

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given below.

\(\sf y - 6 = 4(x - 4)\)

Convert the equation into slope-intercept form. Then we have:

\(\sf y - 6 = 4(x - 4)\)

\(\sf y - 6 = 4x - 16\)

\(\sf y = 4x - 16 + 6\)

\(\sf y = 4x - 10\)

The slope of the line is 4 and the y-intercept of the line is negative 10. Then the equation represents the graph z, then option D is correct.

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y – 6 = 4(x - 4)

Which of the following shows a graph of the equation above?

\(f(4c+1)=9(4c+1)+5=36c+9+5=36c+14\)

you can choose to add the common factor which is 2(18c+7)

Answer:

Step-by-step explanation:

SOLVING

================================================================

6=-2(7-c)

Use distribution to multiply -2 by parenthesis

6=-14+2c

Add to both sides 14

20=2c

Divide 2 into both sides

10=c

5(h-4)=8

Use distribution to multiply 5 by the parenthesis

5h-20=8

Add to both sides 20

5h=28

Divide 5 into both sides

\(h=\frac{28}{5}\)

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Answer
Y. Answer:

y=30

Step-by-step explanation:

(3)^2 equals 9, so the first blank is 9.

You then multiply it by the 2, so second blank is 18.

18+15=33

33-3=30=y

Answer:

30

Step-by-step explanation:

first space should be 9 since 3² is 9

second space should be 18 since 2×9=18

final space should be 30 since 18+15 is 33-3=30

Answer:

25.6 minutes

Step-by-step explanation: add 11.7 and 2.2 then add 11.7 again

The system of inequalities that will model the given scenerio are -

S + L < 30

13S + 18L ≥ 350

Equation modelling is the process of writing a given mathematical statement (or word problem) in the form of a mathematical equation for the correct analysis of the given problem (or situation).

Given is that Jordan's t-shirt business sells long sleeve shirts for $18 and short sleeve shirts for $13. He needs to make at least $350 to buy a new heat press machine.

Let {S} represent the short sleeves and {L} represents the long sleeves. So, we can model the equations as -

S + L < 30

13S + 18L ≥ 350

Therefore, the system of inequalities that will model the given scenerio are -

S + L < 30

13S + 18L ≥ 350

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(a) Expected utility is calculated as the weighted average of the utilities of all possible outcomes.

According to the problem, Sam's utility function is u(100) = 1 and u(200) = 2.

The lottery L1 = ( £100, w.p. 0.6; £200, w.p. 0.4 ) has two outcomes with the probabilities of 0.6 and 0.4.

Therefore, the expected utility of the lottery L1 is:

Expected utility of L1 = 0.6 × u(100) + 0.4 × u(200)= 0.6 × 1 + 0.4 × 2= 1.4

Since Sam is willing to pay at most £120 for the lottery L1, this indicates that the expected utility of L1 is worth £120 to Sam. Thus:1.4 = u(£120)

Since we know u(100) = 1 and u(200) = 2, we can linearly interpolate to find u(£120):

u(£120) = u(100) + [(120 - 100)/(200 - 100)] × (u(200) - u(100))= 1 + [(120 - 100)/(200 - 100)] × (2 - 1)= 1.3

Therefore, the expected utility of the lottery L2 = ( £100, w.p. 0.6; £120, w.p. 0.4 ) is:

Expected utility of L2 = 0.6 × u(100) + 0.4 × u(£120)= 0.6 × 1 + 0.4 × 1.3= 0.78

So, Sam's expected utility for the lottery L2 is 0.78

.(b) The risk preferences of Sam can be determined by comparing the utility of the lottery L1 and the sure outcome that gives the same expected value as the lottery L1.

The expected value of the lottery L1 is:Expected value of L1 = 0.6 × £100 + 0.4 × £200= £140

Therefore, Sam needs to be indifferent between the lottery L1 and the sure outcome of receiving £140. Since the expected utility of L1 is 1.4, Sam's utility for receiving £140 must also be 1.4.

This can be represented as:u(£140) = 1.4From part (a), we know that u(£120) = 1.3.

Therefore, the difference between the two utility values is:u(£140) - u(£120) = 1.4 - 1.3= 0.1

The difference in utility is positive but not enough to reflect risk-loving behavior. Therefore, Sam is risk-averse.

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The width and length of the rectangle is 27 cm and 36 cm. respectively.

To solve the problem, we can use the Pythagorean theorem since the diagonal, width, and length of the rectangle form a right triangle. The Pythagorean theorem states that:
a² + b² = c²
where a and b are the legs of the right triangle and c is the hypotenuse (diagonal of the rectangle).

Let's denote the width of the rectangle as w, the length as l, and the diagonal as d. According to the problem, we have:
d = w + 18
l = w + 9

Substituting these equations into the Pythagorean theorem, we get:
(w + 9)² + w² = (w + 18)²

Expanding and simplifying the equation, we get:
w² - 18w - 243 = 0

We can solve for w by factoring the expression:
(w - 27)(w + 9) = 0

w = 27 or w = -9

The positive solution for w is 27. We can use this value to find the length of the rectangle:
l = w + 9
l = 27 + 9
l = 36

Therefore, the width of the rectangle is 27 cm, and the length of the rectangle is 36 cm.

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Answer:

(-3,-5)

Step-by-step explanation:

subtract y1 from y2 and you get -5. Now subtract x1 from x2 and you get -3. Now put the x value first and then the y value.

Answer:

Step-by-step explanation:

\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(10,\:10\right),\\\:\left(x_2,\:y_2\right)=\left(7,\:5\right)\\\\m=\frac{5-10}{7-10}\\\\Simplify\\\\m = \frac{-5}{-3} \\\\m=\frac{5}{3}\)

The probability that Julien samples an equal number of real and fake gold coins from the random sample of four is approximately 0.463.

To calculate this probability, we can consider two cases: sampling from Treasure Chest A and sampling from Treasure Chest B.

For Treasure Chest A:

The probability of sampling an equal number of real and fake coins can be calculated using combinations. Out of the 15 gold coins in Treasure Chest A, 40% are real and 60% are fake. The probability of selecting 2 real and 2 fake coins can be calculated as (0.4^2) * (0.6^2) * (4 choose 2).

For Treasure Chest B:

The probability of sampling an equal number of real and fake coins can be calculated in a similar way. Out of the 8 gold coins in Treasure Chest B, 75% are real and 25% are fake. The probability of selecting 2 real and 2 fake coins can be calculated as (0.75^2) * (0.25^2) * (4 choose 2).

Finally, we can add the probabilities of the two cases together to get the overall probability is approximately 0.463.

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Answer:  b = 14/3 = 4.667 feet

The decimal value is approximate. In reality the 6's go on forever. Round that however you need to.

================================================

Work Shown:

b = unknown base

h = height = 6 ft

A = area = 14 sq ft

A = b*h/2

14 = b*6/2

14 = b*3

14 = 3b

3b = 14

b = 14/3

This approximates to 14/3 = 4.667 ft

Answer:

Step-by-step explanation:

– 3 – 90 Answer is B

To find the area of triangle ΔABC, we can use the formula for the area of a triangle given its side lengths, also known as Heron's formula. Heron's formula states that the area (A) of a triangle with side lengths a, b, and c is:

A = \(\sqrt{(s(s-a)(s-b)(s-c))}\)

where s is the semi perimeter of the triangle, calculated as:

s = (a + b + c)/2

In this case, we have the side lengths b = 12, a = 9, and c = 15.2, and we know that ∠C = 68°.

s = (9 + 12 + 15.2)/2 = 36.2/2 = 18.1

Using Heron's formula, we can calculate the area:

A = \(\sqrt{(18.1(18.1-9)(18.1-12)(18.1-15.2))}\)

A ≈ 49.9

Therefore, the area of triangle ΔABC, rounded to the nearest tenth, is approximately 49.9 square units.

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Answer:

The equation is "\(\bold{p^2-5p-36=0}\)"

Step-by-step explanation:

Given:

\(\to p=3x+4\)

evaluate \((3x+4)^2-36=15x+20\) in terms of p=?

\(\to (3x+4)^2-36=15x+20\\\\\to (3x+4)^2-36=5(3x+4)\\\\\to p^2-36=5p\\\\\)

Expression in terms of p:

\(\to \bold{p^2-5p-36=0}\\\\\)

\(\to p^2-(9-4)p-36=0\\\\\to p^2-9p+4p-36=0\\\\\to p(p-9)+4(p-9)=0\\\\\to (p-9)(p+4)=0\\\\\to p-9=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \to p+4=0\\\\\to \bold{p=9 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \to p=-4}\\\\\to 3x+4=9 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \to 3x+4=-4\\\\\to 3x=5 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \to 3x=-8\\\\\to x=\frac{5}{3} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \to x=- \frac{8}{3}\\\\\)

The value of p: 9 and -4

Equation is: \(\bold{p^2-5p-36=0}\)

Answer: 20 weeks in 1 week

in 2 weeks 40

Step-by-step explanation:

This proves that the equation is true

Answer:

400

Step-by-step explanation:

percent means per one hundred so

p/100=5/8

p=500/8

p=62.5%

so, 62.5% have paid their yearly fees .

400(5/8) =200

250 member paid their fees .

Answer:

250

Step-by-step explanation:

If a group contains 400 members

Then the 5/8 of 400 who didn't pay the fees are as follows:-

=5/8*400

=5*50

=250 out of 400

So, the fees is only paid by 250 members out of 400.

Given the function f(x)=sin(2πx), with x = 0.3, f(x) = 0.951057. The objective is to approximate the value of f(0.2) using the first two terms in the Taylor series and Vx=0.1.

We know that the Taylor series for a function f(x) can be written as:f(x)=f(a)+f′(a)(x−a)+f′′(a)2(x−a)2+…+f(n)(a)n!(x−a)n+…The first two terms of the Taylor series are given by:f(x)=f(a)+f′(a)(x−a)The first derivative of f(x) is given by:f′(x)=2πcos(2πx)On substituting x = a = 0.1, we get:f′(0.1) = 2πcos(2π * 0.1) = 5.03118603447The value of f(x) at a=0.1 is given by:f(0.1) = sin(2π * 0.1) = 0.587785252292With a=0.1, the first two terms of the Taylor series become:f(x)=0.587785252292+5.03118603447(x−0.1) = 0.587785252292+0.503118603447x−0.503118603447×0.1Using x=0.2 and substituting the values of a and f(a) in the equation above, we get:f(0.2)=0.587785252292+0.503118603447*0.2−0.503118603447×0.1=0.712261After approximating the value of f(0.2) using the first two terms in the Taylor series,

we can conclude that the value of f(0.2) = 0.712261 with a = 0.1, with an error of approximately 0.012796.

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Given statement solution is :- a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

Set A: {apple, banana}, Set B: {cat, dog}

Power set of A: {{}, {apple}, {banana}, {apple, banana}}

Power set of B: {{}, {cat}, {dog}, {cat, dog}}

Set A: {red, blue}, Set B: {circle, square}

Power set of A: {{}, {red}, {blue}, {red, blue}}

Power set of B: {{}, {circle}, {square}, {circle, square}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}

Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}

Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}

Set A: {red, blue, green}, Set B: {circle, square, triangle}

Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}

Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

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1. The fundamental risk question that has V(s) as the answer is this:

B. What can happen?

2. The analytic technique that is an essential part of the weighted ranking method is: C.Ratio Method

3. The statement that is likely true about the change in the value of the Phillies ball cap relative to the Yankees ball cap is this: A. The value of Phillie's ball cap increases while the value of the Yankee's cap decreases

4. Economics prefer to think of value in the subjective sense, whereas philosopher prefers to think of value in the objective sense.

Economists tend to think of value in the subjective sense, which means relative to an individual. When thinking of the value of goods and services, economists try to ascertain whether the consumers are satisfied or not.

Also, for philosophers, value is viewed in the objective sense. This means that they try to analyze the inherent value of things as against individual opinions of what is valuable.

Fundamental risk refers to the kind of risks that can impact an entire economy. V in the equation represents what can happen given a particular economic move.

The ratio method is a weighted ranking method where the things that are to be decided upon are first ranked and weights such as 10 are assigned to each of them. To determine a change in value in the Yankees and Phillies, the first value is obtained and then compared with the most current value.

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The area of one of the bases of the hexagonal prism is approximately 7.39 units^2.

To solve this problem, we can use the formula for the volume of a hexagonal prism:

V = (3√3/2) * a^2 * h

where V is the volume, a is the length of one side of the hexagonal base, and h is the height of the prism.

We are given that the height of the prism is 4 units and the volume is 98 units^3. Plugging these values into the formula, we can solve for the length of one side of the base:

98 = (3√3/2) * a^2 * 4
a^2 = 98 / (12√3)
a ≈ 2.95

Now that we know the length of one side of the base, we can find the area of the hexagon by using the formula:

A = (3√3/2) * a^2

where A is the area of one of the bases. Plugging in the value we found for a, we get:

A = (3√3/2) * (2.95)^2
A ≈ 7.39

Therefore, the area of one of the bases of the hexagonal prism is approximately 7.39 units^2.

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Answer:

13 and 1/3

Step-by-step explanation:

2×5=10

2/3 ×5 =10/3

10/3 simplifies to 3 and 1/3

Add them together to get 13 and 1/13

To solve the equation 10sin(2θ)=9 for the smallest positive value of θ, we need to isolate θ on one side of the equation. First, let's divide both sides by 10:

sin(2θ) = 0.9

Now, we can use the inverse sine function (sin⁻¹) to solve for θ:
2θ = sin⁻¹(0.9)
θ = sin⁻¹(0.9)/2

Using a calculator, we find that sin⁻¹(0.9) ≈ 1.1198 radians or 64.26 degrees. Therefore, the smallest positive value of θ in radians is:
θ = 1.1198/2 ≈ 0.5599 radians

And in degrees:
θ = 64.26/2 ≈ 32.13 degrees

So, the solution to the equation 10sin(2θ)=9 for the smallest positive value of θ is θ ≈ 0.5599 radians or θ ≈ 32.13 degrees.

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The total number of different permutations of the set is 5040

The set of elements is given as

Set =  {a, b, c, d, e, f, g}.

The cardinality of the above set is

n = 7

So, the total number of different permutations of the set is

Permutation = n!

This gives

Permutation = 7!

Expand

Permutation = 7 * 6 * 5 * 4 * 3 * 2 * 1

Evaluate

Permutation = 5040

Hence, the total number of different permutations of the set is 5040

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