the sum of two consecutive integers is 187. find the integers ​

The table that shows the correct t and d values is

Distance Covered (m)           Time Taken (hr)

8                                               6

32                                              15

The table of values is given as:

Distance Covered (m)           Time Taken (hr)

8                                               6

16                                              12

32                                              15

48                                              18

The distance covered in 15 hours is 32 m and the time taken to cover 8 m is 6 hours

When these values are extracted, we have:

Distance Covered (m)           Time Taken (hr)

8                                               6

32                                              15

The above represents the table that shows the correct t and d values

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Using the tangent relation,

The angles subtended by the major and minor arc sums up to 360 degrees.

That means, the angle subtended by the major arc

While the angle subtended by the minor arc is

Applying the tangent relation above

Therefore, t

Answer:

1) cpk < 1.33, therefore it is not capable

b) cpk = 1.33, therefore it is capable

c) cpk < 1.33, therefore it is not capable

2) Cpk can never be greater than the Cp, but can be equal to it

Step-by-step explanation:

Upper limit (USL) = 47 minutes and Lower limit (LSL) = 30 minutes

1)

a) mean (μ) = 37 minutes, standard deviation (σ) = 3 minutes

\(cpk=min(\frac{USL-\mu}{3\sigma}, \frac{\mu - LSL}{3\sigma})=min(\frac{47-37}{3*3},\frac{37-30}{3*3} )=min(1.11,0.78)=0.78\)

\(cp=(\frac{USL-LSL}{6\sigma})=\frac{47-30}{6*3}=0.94\)

cpk < 1.33, therefore it is not capable

b) mean (μ) = 38 minutes, standard deviation (σ) = 2 minutes

\(cpk=min(\frac{USL-\mu}{3\sigma}, \frac{\mu - LSL}{3\sigma})=min(\frac{47-38}{3*2},\frac{38-30}{3*2} )=min(1.5,1.33)=1.33\)

\(cp=(\frac{USL-LSL}{6\sigma})=\frac{47-30}{6*2}=1.42\)

cpk = 1.33, therefore it is capable

c) a) mean (μ) = 38.5 minutes, standard deviation (σ) = 2.9 minutes

\(cpk=min(\frac{USL-\mu}{3\sigma}, \frac{\mu - LSL}{3\sigma})=min(\frac{47-38.5}{3*2.9},\frac{38.5-30}{3*2.9} )=min(0.98,0.98)=0.98\)

\(cp=(\frac{USL-LSL}{6\sigma})=\frac{47-30}{6*2.9}=0.98\)

cpk < 1.33, therefore it is not capable

2) Cpk can never be greater than the Cp, but can be equal to it

Answer:its 309

Step-by-step explanation:

a) To maximize profits, 10 units should be sold in market 1 and 5 units in market 2.

b) The corresponding prices are $180 in market 1 and $160 in market 2.

c) If it becomes illegal to discriminate, the profit loss is $50.

d) The imposition of a tax of $5 per unit sold in market 1 would likely decrease the monopolist's profit and potentially lead to adjustments in prices and quantities sold in both markets.

a) To maximize profits, the monopolist should set marginal revenue equal to marginal cost in each market.

In this case, marginal revenue is equal to the derivative of the demand function with respect to quantity, and it can be calculated as MR = dP/dQ.

For market 1:

MR₁ = dP₁/dQ₁ = -2

For market 2:

MR₂ = dP₂/dQ₂ = -4

Setting MR equal to marginal cost, which is the derivative of the cost function with respect to quantity, gives:

MR₁ = -2 = dC/dQ₁ = 20

MR₂ = -4 = dC/dQ₂ = 20

Solving these equations, we find:

Q₁ = 10

Q₂ = 5

Therefore, the monopolist should sell 10 units in market 1 and 5 units in market 2 to maximize profits.

b) To determine the corresponding prices, we substitute the quantities obtained in part (a) into the demand functions:

For market 1:

P₁ = 200 - 2Q₁ = 200 - 2(10) = 180

For market 2:

P₂ = 180 - 4Q₂ = 180 - 4(5) = 160

Therefore, the corresponding prices are $180 in market 1 and $160 in market 2.

c) To calculate the profit lost if it becomes illegal to discriminate, we need to compare the profits under discrimination with the profits under non-discrimination.

Under discrimination, the monopolist charges different prices in each market, while under non-discrimination, the same price is charged in both markets.

Under discrimination:

Profit = Total revenue - Total cost

For market 1:

Total revenue₁ = P₁ \(\times\) Q₁ = 180 \(\times\) 10 = $1

For market 2:

Total revenue₂ = P₂ \(\times\) Q₂ = 160 \(\times\) 5 = $800

Total revenue = Total revenue₁ + Total revenue₂ = $1800 + $800 = $2600

Total cost = C = 20(Q₁ + Q₂) = 20(10 + 5) = $300

Profit = Total revenue - Total cost = $2600 - $300 = $2300

Under non-discrimination:

Since the same price is charged in both markets, we take the average price:

Average price = (P₁ + P₂) / 2 = (180 + 160) / 2 = $170

Total revenue = Average price \(\times\) (Q₁ + Q₂) = $170 \(\times\) (10 + 5) = $2550

Total cost remains the same at $300.

Profit = Total revenue - Total cost = $2550 - $300 = $2250

Therefore, the profit lost if discrimination becomes illegal is $2300 - $2250 = $50.

d) The imposition of a tax of $5 per unit sold in market 1 would increase the cost per unit for the monopolist.

This would affect the profit-maximizing quantity in market 1 and potentially lead to a change in prices.

The monopolist would compare the new marginal cost, which includes the tax, with the marginal revenue to determine the new profit-maximizing quantities and prices.

The tax would likely reduce the monopolist's profits and could potentially result in adjustments in production and pricing strategies.

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Each ticket costs $37.5 according to the calculation t = ($175 - $25)/4.

Equation is a mathematical statement that expresses two expressions as equal. It consists of two expressions separated by an equal sign (=). An equation is used to solve for a unknown value by using known values and following the rules of algebra and arithmetic. Equations can be used to solve for a single unknown, multiple unknowns, and even non-numeric values.

Given that the total cost for parking and four tickets to a baseball game is $175.00.

$25 is the parking fee.

4 tickets cost $175 - $25.

Suppose that each ticket costs t.

t =($175 - $25)/4

Each ticket costs $37.5.

The equation follows.Each ticket costs $37.5 according to the calculation t = ($175 - $25)/4.

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Answer:

B is the correct answer

Step-by-step explanation:

hope this helps :)

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Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

Integer Part: 4

Fractional Part: 377

To round 4.377 to the nearest hundredth means to round the numbers so you only have two digits in the fractional part. Use the rule (B) "If the last digit in the fractional part of 4.377 is 5 or more and the second digit in the fractional part is less than 9, then add 1 to the second digit of the fractional part and remove the third digit." With 4.377, rule B applies and 4.377 rounded to the nearest hundredth is: 4.38

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Have a great day/night!

❀*May*❀

Answer:

Step-by-step explanation:

Hope it helps!!

Triangle ABC with vertices A(2, 7), B(6,5) and C(4, 1): 90° counterclockwise transformation is A'(-7, 2), B'(-5, 6) and C'(-1, 4).

Given that, triangle ABC with vertices A(2, 7), B(6,5) and C(4, 1).

Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).

90° counterclockwise rotation: (x, y) becomes (-y, x)

A(2, 7) → A'(-7, 2)

B(6, 5) → B'(-5, 6)

C(4, 1) → C'(-1, 4)

Therefore, triangle ABC with vertices A(2, 7), B(6,5) and C(4, 1): 90° counterclockwise transformation is A'(-7, 2), B'(-5, 6) and C'(-1, 4).

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Answer:

its B.

Step-by-step explanation:

all you have to do is y divided by x to find the constant of proportionality

so it would be two  y=2x

The rise from the ground by the skateboard is 5.5 inches

The length of the skateboard is given as:

Length (l) = 18 inches

The angle of elevation (x) is

x = 17∘

Represent the height with h.

The value of h is calculated using the following tangent ratio:

tan(x) = h/l

Make h the subject

h = l * tan(x)

Substitute known values

h = 18 * tan(17)

Evaluate

h = 5.5

Hence, the rise from the ground by the skateboard is 5.5 inches

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Answer: 5.3

Step-by-step explanation:

S​OH-CAH-TOAsin 17=oppositehypotenuse=x18sin 17=hypotenuseopposite​=18x​sin 17=sin 17=  x1818x​sin 171=1sin 17​=  x1818x​18 sin 17=18 sin 17=  xxx=5.262690...≈5.3x=5.262690...≈5.3

The value of x = 2nπ,  (n ∈ Z) and

\(x=2(n\pi+(-1)^{n} \pi /6)\),  (n ∈ Z)

What are Trigonometric Identities?

Trigonometric Identities are useful whenever trigonometric functions are involved in an expression or an equation. Trigonometric Identities are true for every value of variables  being on both sides of an equation. Geometrically, these identities involve certain trigonometric functions(  similar as sine, cosine, tangent ) of one or  further angles.

According to question

⇒ sin(x/2) + cos(x) - 1 = 0

⇒ sin(x/2) + cos(x) - 1 = 0

{ cos(2x) = 1 - 2sin²(x) }

cos(x) = 1 - 2sin²(x/2)

⇒ sin(x/2) + cos(x) - 1 = 0

⇒ sin(x/2) + 1 - 2sin²(x/2) - 1 = 0

⇒ - 2sin²(x/2) + sin(x/2) + 1 - 1 = 0

⇒ - 2sin²(x/2) + sin(x/2)  = 0

⇒ sin(x/2)(- 2sin(x/2) + 1)  = 0

⇒ sin(x/2) = 0 , x = 2nπ (n ∈ Z)

and

⇒ sin(x/2) = 1/2 , \(x=2(n\pi+(-1)^{n} \pi /6)\) (n ∈ Z)

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The equation for the relationship between the number of bracelets made and the number of beads is y = 21x.

First, the rate of change

= (483 - 210) / (23 - 10)

= 273 / 13

= 21

So, the equation for the relationship between the number of bracelets made and the number of beads used.

(y - 210) = 21 (x-  10)

y - 210 = 21x - 210

y = 21x

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we make a relation

now we make a relation between the number of gallons on 1 day

where x is the number of gallons on 1 day

Join it

and use cross multiplication to solve, multipli the numbers on the diagonal where isnt the missing number. and divide by the number on diagonal of the missing number, to find the Value of the missing number

to simplify the operations we change the mixed number to decimal

then...

and do the operations to find the unknow

the reounded number of gallons for one day are

Answer:

-1 1/2 (-3/2), -1 1/3 (-4/3) -1 1/4 (-5/4), -1 1/5 (-6/5), -1 1/6 (-7/6)

Step-by-step explanation:

Answer:

f(x)^-1=\(\sqrt[3]{x}\)-1

f(x)=x^3+1+3x^2+3x

Step-by-step explanation:

Answer:

Therefore, the correct statements are A, B, and E.

Explanation:

Based on my knowledge, a vector is a quantity that has both magnitude and direction. A scalar is a quantity that has only magnitude. When a vector is multiplied by a scalar, the magnitude of the vector is multiplied by the absolute value of the scalar, and the direction of the vector is either preserved or reversed depending on the sign of the scalar.

To answer your question, we need to find the component form, magnitude, and direction of the scalar product –4⇀

.

- The component form of −4⇀

is obtained by multiplying each component of ⇀

by –4. Therefore, −4⇀

= ⟨–8, –12⟩. This means that statement A is true.

- The magnitude of −4⇀

is obtained by multiplying the magnitude of ⇀

by 4. The magnitude of ⇀

is √(2^2 + 3^2) = √13. Therefore, the magnitude of −4⇀

is 4√13. This means that statement B is true.

- The direction of −4⇀

is opposite to the direction of ⇀

because the scalar –4 is negative. This means that statement C is false.

- The vector −4⇀

is in the third quadrant because its components are both negative. This means that statement D is false.

- The direction of −4⇀

is 180° greater than the inverse tangent of its components because it is opposite to ⇀

. The inverse tangent of its components is tan^(-1)(–12/–8) = tan^(-1)(3/2). Therefore, the direction of −4⇀

is 180° + tan^(-1)(3/2). This means that statement E is true.

Therefore, the correct statements are A, B, and E.

After answering the presented question, we can conclude that probability Therefore, the probability of 30 or more seconds between vehicle arrivals is approximately 0.0498.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many fields, including statistics, economics, science, and engineering.

Sketch of exponential probability distribution with mean of 12 seconds:

   |                            

   |                            

   |              .            

   |             . .            

   |             . .            

   |             . .            

   |             . . .          

   |             . . .          

   |             . . .          

   |             . . .          

   |             . . .          

   |             . . . .        

   |             . . . .        

   |             . . . .        

   |             . . . . .      

   |             . . . . .      

   |_____________. . . . . . .

        0       12             X

The X-axis represents the time between vehicle arrivals, and the Y-axis represents the probability density. The peak of the distribution is at 12 seconds, which is the mean.

b. Probability of the arrival time between vehicles being 12 seconds or less:

Since the mean of the exponential distribution is 12 seconds, we can use the cumulative distribution function (CDF) to find the probability of the arrival time being 12 seconds or less:

\(P(X < = 12) = 1 - e^(-12/12) = 1 - e^(-1) ≈ 0.6321\)

Therefore, the probability of the arrival time between vehicles being 12 seconds or less is approximately 0.6321.

c. Probability of the arrival time between vehicles being 6 seconds or less:

\(P(X < = 6) = 1 - e^(-6/12) = 1 - e^(-0.5) ≈ 0.3935\)

Therefore, the probability of the arrival time between vehicles being 6 seconds or less is approximately 0.3935.

d. Probability of 30 or more seconds between vehicle arrivals:

\(P(X > = 30) = e^(-30/12) ≈ 0.0498\)

Therefore, the probability of 30 or more seconds between vehicle arrivals is approximately 0.0498.

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Answer:

2:1

6:3

8:4

Step-by-step explanation:

24 divided by 12 is 2, so equivalent ratio should also be 2

2 divided by 1 is 2

6 divided by 3 is 2

8 divided by 4 is 2

Answer:

A. 36, -36

Step-by-step explanation:

y = x^2 - 12x - 5

steps to complete the square

add a 5 to both sides to move the constant

x^2 - 12x = 5

Then take -12, the coefficient of the variable and divide by 2 and square.

12/2 = 6, 6^2 = 36

Then add 36 to both sides.

x^2 - 12x + 36 = 5 + 36

Then subtract the 5 and 36 from both sides.

x^2 - 12x + 36 - 36 - 5

Answer:

38°

Step-by-step explanation:

y = 142°

x + y = 180°{ being supplementary angles }

x + 142° = 180°

x = 180° - 142°

x = 38°

Hope it will help :)

The correct answer is (C) The cost of hot dog combos less than an $18 coupon split by 5 people.

Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

Using the Law of Sines, we get an angle of 2.41 degrees and no triangles are produced.

Option (C) is the correct one.

Given, Two sides and an angle are given below.

we have to determine whether the given information results in one​ triangle, two​ triangles, or no triangle at all.

If b = 5, c = 6 and B = 20 degrees in the triangle.

On using the concept of Laws of Sines, we get

sinA/a = sinB/b = sinC/c

sin 20°/5 = sin C/6

0.34/5 = sin C/6

0.007 = sin C/6

sin C = 0.042

C = 2.41

So, the angle C be 2.41 degrees.

which implies that no triangle can be formed or produced with the given data of the triangle.

Hence, No triangles are produced.

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Answer:

70cm

Step-by-step explanation:

10 times 7 = 70

Answer:

The answer is option C

Step-by-step explanation:

To find the length of AB we use sine

sin∅ = opposite / hypotenuse

From the question

The hypotenuse is AB

The opposite is AC

So we have

sin 54 = AC/AB

sin 54 = 16 / AB

AB = 16/sin 54

AB = 19.777

Hope this helps you

Answer:

AB = 19.78

Step-by-step explanation:

From the diagram (Right-angle triangle):

AC = 16

AB = ?

Angle = 54°

Applying trig ratio:

Tan 54° = 16/BC

1.376381920 = 16/BC

Therefore;

BC = 16/1.376381920

BC = 11.62

To solve the length AB:

Cos 54° = BC/AB

0.587785252 = 11.62/AB

Solving AB gives:

AB = 11.62/0.587785252

AB = 19.78

The probabilities are:

1. P(yellow) = 2/5

2. P(red) = 3/10

3. P(blue) = 3/10

4. P(blue or yellow) = 7/10

5. P(red or blue) = 3/5

To find the probability that a person in each color seat would receive the free tickets, we need to calculate the probabilities of each event.

1. P(yellow): There are 8 yellow seats out of a total of 20 seats in Section A. Therefore, the probability of selecting a yellow seat at random is P(yellow) = 8/20 = 2/5.

2. P(red): There are 6 red seats out of a total of 20 seats in Section A. Therefore, the probability of selecting a red seat at random is P(red) = 6/20 = 3/10.

3. P(blue): There are 6 blue seats out of a total of 20 seats in Section A. Therefore, the probability of selecting a blue seat at random is P(blue) = 6/20 = 3/10.

4. P(blue or yellow): To calculate the probability of selecting a blue or yellow seat, we add the individual probabilities of selecting a blue seat and a yellow seat: P(blue or yellow) = P(blue) + P(yellow) = 3/10 + 2/5 = 7/10.

5. P(red or blue): To calculate the probability of selecting a red or blue seat, we add the individual probabilities of selecting a red seat and a blue seat: P(red or blue) = P(red) + P(blue) = 3/10 + 3/10 = 6/10 = 3/5.

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Answer:

The answer would be B. With equations, what you do to one side you have to do to the other.

Answer:

Step-by-step explanation:

X: -2, -1, 0, 1, 2,...

Y: -2, -1, 0, 1, 2,...

(y=x)