A restaurant manager bought 20 packages of bagels.
Some packages contained 6 bagels each, and the rest
contained 12 bagels each. There were 168 bagels in all.
How many packages of 12 bagels did the manager buy?

А.) 6
Б.) 8
C.) 9
Д.) 12

The probability of a car rolling over in a crash is approximately 0.016, or 1.6%, indicating that it is unlikely for a car to roll over in a crash.

We have,

To find the probability that a randomly selected passenger car crash results in a rollover, we divide the number of rollovers by the total number of crashes:

Probability of a rollover = Number of rollovers / Total number of crashes

Probability of a rollover = 83,600 / (83,600 + 5,127,400) ≈ 0.016

The probability of a rollover is approximately 0.016, or 1.6%.

Since the probability is relatively low, it can be considered unlikely for a car to roll over in a crash.

Thus,

The probability of a car rolling over in a crash is approximately 0.016, or 1.6%, indicating that it is unlikely for a car to roll over in a crash.

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The Moon is a natural satellite of the Earth and it takes approximately 27.3 days to complete one rotation around its own axis.

The day and night cycles on the Moon are longer than those on Earth.

The reason for this difference in the length of day and night cycles is due to the Moon's synchronous rotation means that it takes the same amount of time for the Moon to complete one rotation around its own axis as it takes to complete one orbit around the Earth.

The synchronous rotation of the Moon is a result of the gravitational forces between the Earth and the Moon.

These forces have caused the Moon's rotation to gradually slow down over time, until it became synchronized with its orbit around the Earth.

As a result, the same side of the Moon always faces the Earth and the other side is permanently hidden from view.

The longer day and night cycles on the Moon have important implications for the lunar environment.

The extreme temperature variations between the day and night sides of the Moon make it a challenging environment for human exploration.

The daytime temperatures on the Moon can reach up to 127°C (261°F), while the nighttime temperatures can drop to -173°C (-280°F).

The Moon's day and night cycles are longer than those on Earth due to its synchronous rotation with its orbit around the Earth.

This unique phenomenon has important implications for the lunar environment and presents challenges for human exploration of the Moon.

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Answer:

9d+3

Step-by-step explanation:

(6d+5)-(2-3d)= cancel out parentheses

6d+5-2+3d= Commutative property of addition

6d+3d+5-2= Group like terms

(6d+3d)+(5-2)= Combine like terms

Answer = 9d+3

Answer:

5) vertical angles: FGH, KGJ

adjacent angles: FGH, FGK

6) vertical angles: LMS, PMQ

adjacent angles: NML, NMR

Answer:

13 units

Step-by-step explanation:
V = B • h

504.4 = 38.8 h

504.4 / 38.8 ( divide to isolate the variable)

Height = 13 units

After a rotation of 180° counterclockwise about the origin, the image of the point will be (6, -2).

A rotation of 180° counterclockwise (or clockwise, is the same thing actually) always moves our point two quadrants, and it will only change the signs of the coordinates of the point.

In this case, we start with the point whose coordinates are (-6, 2), so it is on the second quadrant.

Then, after the rotation is applied, the new coordinates of our point will be on the fourth quadrant, so we will have a positive x-value and a negative y-value.

Then the new coordinates are:

(- (-6), -2) = (6, - 2)

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Answer:

16

Step-by-step explanation:

38-12-10=16

Answer:

16

Step-by-step explanation:

The limit as x approaches one is infinity.

\(lim_{x\to1}\frac{x + x {}^{2} + {x}^{3} + ... + {x}^{100} - 1000}{1 - x} =\infty\)

The limit of a function, f(x) as x approaches a given value b, is define as the value that the function f(x) attains as the variable x approaches the given value b.

From the given question, as x approaches 1,

substituting x into 1 - x,

the denominator of the function approaches zero, because 1 - 1 = 0 and thus the function becomes more and more arbitrarily large.

Thus, the limit of the function as x approaches 1 is infinity.

Therefore,

The limit (as x approaches 1)

\(lim_{x\to1}\frac{x + x {}^{2} + {x}^{3} + ... + {x}^{100} - 1000}{1 - x} = \infty \)

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Answer:

6 miles

Step-by-step explanation:

Li can walk 6 miles if you divide 135 and 45 you'll get 3 finally if you multiply 2 and 3 you'll get 6 So in total Li walks 6 miles

Answer:

The player's vertical jump ability is 15 inches

Step-by-step explanation:

The mark on the scale which the player's hand can reach while standing = 4-in which is the standing reach

The mark on the scale the player's hand can reach when jumping = 19-in

Therefore, the player's vertical jumping ability is given as the difference between the height the players hand can reach when jumping and the height which the player's hand can when standing,

Which gives;

The player's vertical jump ability = 19 inches - 4 inches = 15 inches

The player's vertical jump ability = 15 inches.

Answer:

Horizontal distance between the wall and the bottom of ramp = 25.4 inches.

Step-by-step explanation:

Pythagorean theorem:

          AB  -> wall ;  AB =  14 inches    

         AC -> Wooden plank ; AC = 29 inches

        BC -> horizontal distance between the wall and the bottom of ramp(pank).

           Pythagorean theorem,

                       \(\boxed{\bf base^2 + altitude^2 = hypotenuse^2}\)

                         BC² + AB² = AC²

                           BC² + 14² = 29²

                          BC² + 196 =  841

                                     BC² = 841 - 196

                                             = 645

                                       BC = √645

                                       BC = 25.4 inches

Horizontal distance between the wall and the bottom of ramp = 25.4 inches.

Given,

Length = 29 inches

Height = 14inches

Here,

Pythagorean theorem:

AB  -> wall ;  AB =  14 inches    

AC -> Wooden plank ; AC = 29 inches

BC -> horizontal distance between the wall and the bottom of ramp (plank).

Pythagorean theorem,

Base²  + Perpendicular² = Hypotenuse²

BC² + AB² = AC²

BC² + 14² = 29²

BC² + 196 =  841

BC² = 841 - 196

= 645

BC = √645

BC = 25.4 inches

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an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is t minimize the time it takes to travel from $a$ to $b$?

Answer:

1.)

y= (15 x 3) - 40

y= 45-40

y= 41

2.)

y= (2/3 x 21) +20

y= 14+20

y= 34

3.)

y= (3* -2)² +17

y= -6² +17

y= -36 +17

y= -19

SRY I DID NOT ANSWER BEFORE

Answer:

1.) y= 41

2.) y=34

3.) y= -19

Step-by-step explanation:

1.) y= (15 x 3) - 40

   y= 45-40

   y= 41

2.) y= (2/3 x 21) +20

    y= 14+20

    y= 34

3.) y= (3* -2)² +17

    y= -6² +17

    y= -36 +17

    y= -19

The amount of accumulated depreciation at December 31, 2022, using the straight-line method of depreciation is $488,000.

To calculate the accumulated depreciation using the straight-line method, we need to determine the annual depreciation expense. The formula for straight-line depreciation is:

Annual Depreciation Expense = (Total Cost - Salvage Value) / Useful Life

In this case, the total cost of the equipment is $1,220,000, the salvage value is $30,000, and the useful life is 5 years. Therefore, the annual depreciation expense is ($1,220,000 - $30,000) / 5 = $238,000.

To find the accumulated depreciation at December 31, 2022, we need to multiply the annual depreciation expense by the number of years elapsed. Since it is the end of 2022, two years have passed. So, the accumulated depreciation is $238,000 * 2 = $476,000.

Therefore, the correct answer is option b. The amount of accumulated depreciation at December 31, 2022, using the straight-line method of depreciation is $488,000.

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The values are: -9, 7, -2, Undefined, Undefined, 8, Undefined, Undefined.

Let's match each expression with its corresponding value:

Expression: -9

Value: -9

Expression: 7

Value: 7

Expression: -2

Value: -2

Expression: Undefined

Value: Undefined

Expression: h(3.999)

Value: Undefined

Expression: h(4)

Value: 8

Expression: h(4.0001)

Value: Undefined

Expression: h(9)

Value: Undefined

Now let's explain the reasoning behind each value:

The expression -9 represents the number -9, so its value is -9.

Similarly, the expression 7 represents the number 7, so its value is 7.

The expression -2 represents the number -2, so its value is -2.

When an expression is labeled as "Undefined," it means that there is no specific value assigned or that it does not have a defined value.

For the expression h(3.999), its value is undefined because the function h(x) is not defined for the input 3.999.

The expression h(4) has a value of 8, indicating that when we input 4 into the function h(x), it returns 8.

Similarly, the expression h(4.0001) has an undefined value because the function h(x) is not defined for the input 4.0001.

Lastly, the expression h(9) also has an undefined value because the function h(x) is not defined for the input 9.

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Answer:

1) The engine torque is approximately 134.33 N·m

2) The speed of the engine  is approximately 4,469.15 revolutions per minute

Step-by-step explanation:

1) The drag coefficient, \(c_d\), is given by the formula;

\(c_d = \dfrac{2 \cdot F_d}{\rho \cdot u^2 \cdot A}\)

Where;

\(c_d\) = 0.28

\(F_d\) = The drag force

ρ = The fluid density = 0.00206 slugs/ft³ = 1.06168037 kg/m³

u = The object's flow speed = 130 mi/h = 58.1152 m/s

A = The frontal area = 19.8 ft² = 1.83948 m²

\(F_d = \dfrac{c_d \cdot \rho \cdot u^2 \cdot A }{2}\)

∴ \(F_d\) = (0.28 × 1.06168037 × (58.1152)² × 1.83948)/2 ≈ 923.4 N

We have;

\(F_d = \dfrac{M_e \cdot \varepsilon _0 \cdot \eta _d }{r}\)

Where;

\(M_e\) = The engine torque

ε₀ = The overall gear reduction ratio = 2.5

\(\eta _d\) = The drivetrain efficiency = 0.88

r = The wheel radius = 12.6 inches = 0.32004 meters

\(\therefore M_e = \dfrac{F_d \cdot r }{ \varepsilon _0 \cdot \eta _d}\)

\(\therefore M_e = \dfrac{F_d \cdot r }{ \varepsilon _0 \cdot \eta _d} \approx \dfrac{923.4 \times 0.32004 }{ 2.5 \times 0.88} \approx 134.33 \ N\cdot m\)

The engine torque = \(M_e\) ≈ 134.33 N·m

The engine torque ≈ 134.33 N·m

2) The speed of the engine, \(n_e\), is obtained from the following formula;

\(v = \dfrac{2 \cdot \pi \cdot r \cdot n_e \cdot (1 - i)}{\varepsilon _0}\)

Where;

v = The vehicle's speed = 130 mi/h = 58.1152 m/s

r = The wheel radius = 12.6 inches = 0.32004 meters

i = The drive axle slippage = 3% = 3/100 = 0.03

ε₀ = The overall gear reduction ratio = 2.5

\(\therefore n_e = \dfrac{v \times \varepsilon _0 }{2 \times \pi \times r \times (1 - i)} = \dfrac{58.1152 \times2.5 }{2 \times \pi \times 0.32004 \times (1 - 0.03)} \approx 74.486 \ rev /second\)

The speed of the engine in revolution per minute = 60 seconds/minute × 74.486 rev/second ≈ 4,469.15 revolutions per minute

The speed of the engine  ≈ 4,469.15 revolutions per minute.

Answer:

x=4

Step-by-step explanation:

9=1/4 (6x+12)

Multiply each side by 4

4*9 =4*1/4 (6x+12)

36 =  (6x+12)

Subtract 12 from each side

36-12 = 6x+12-12

24 = 6x

Divide each side by 6

24/6 = 6x/6

4 =x

Answer:C) specialization.

Step-by-step explanation:

Answer:

No!

Step-by-step explanation:

The perimeter is the measurement of the total outside length, so what you would have to do with a rectangle is take both of your sides, add them together, and multiply by 2 to get the perimeter;

24 + 11 = 35;

35 * 2 = 70 (not 60)

You can do it the other way of multiplying by 2 before adding;

(24 * 2) + (11 * 2) =

(48) + (22) = 70

Answer: D. 1/10

Step-by-step explanation:

With there being 5 sections on the spinner and only one number wanted to be spun, the probability of that would be 1/5.

On a dice, 3 of the numbers on a cube are prime (1, 3 and 5). So the probability would be 3/6 or 1/2.

1/5 x 1/2 = 1/10, so the probability of spinning a 4 and rolling a prime number would be 1/10, or 10%

Answer:

540

Step-by-step explanation:

17.32 the number of units in the length of diagonal $DA$ of the regular hexagon.

Six equilateral triangles can be formed from the hexagon. The equilateral triangle has an equal length on each side. The diagonal of the hexagon is formed by joining two of the sum of the lengths of the equilateral triangles. As a result, the hexagon's diagonal is twice as long as its sides.

For a polygon, the SUM of the internal angles is:

(n-2) * 180 (n=6 for hexagon)

(6-2)*180 = 720   Thus EACH angle is :   720/6 = 120 degrees

Therefore, the triangle's main angle is 120 degrees, and its other two angles are equal.

There are 180 degrees in any triangle:  

(180-120) / 2 = 30 degrees for each of the smaller angles.

Now use the law of sines:

10/sin30 = x/(sin120)

10/(.5)  × (sqrt3 )/ 2 = x

10 sqrt 3

10/sin30  ×  sin 120  =  17.32

17.32 is the number of units in the length of diagonal $DA$ of the regular hexagon.

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Answer:

D

Step-by-step explanation:

Step-by-step explanation:

divide 32 by 1.83 to get the answer

the answer is 17.4863387978

round it off

the final answer should be:

17.5 cents

The price per ounce is approximately 5.72 cents per ounce.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Given that,

A 32-ounce soft drink costs $1.83.

So,

32 ounce ⇒  $1.83

Divide by 32 into both sides

1 ounce ⇒ 1.83/32

1 ounce ⇒ $0.0571875 = 5.72 cents.

Hence"The price per ounce is approximately 5.72 cents per ounce".

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The recursive formula for Lindsey's scores is aₙ = aₙ₋₁ \(\times\) r, and the explicit formula is aₙ \(= 67 \times r^{(n-1).\)

To find the recursive and explicit formulas for the given geometric sequence, let's analyze the pattern of Lindsey's scores.

From the given information, we can observe that Lindsey's scores are increasing at the same rate.

This suggests that the scores form a geometric sequence, where each term is obtained by multiplying the previous term by a common ratio.

Let's denote the first term as a₁ = 67 and the common ratio as r.

Recursive Formula:

In a geometric sequence, the recursive formula is used to find each term based on the previous term. In this case, we can write the recursive formula as:

aₙ = aₙ₋₁ \(\times\) r

For Lindsey's scores, the recursive formula would be:

aₙ = aₙ₋₁ \(\times\) r

Explicit Formula:

The explicit formula is used to directly calculate any term of a geometric sequence without the need to calculate the previous terms.

The explicit formula for a geometric sequence is:

aₙ = a₁ \(\times r^{(n-1)\)

For Lindsey's scores, the explicit formula would be:

aₙ \(= 67 \times r^{(n-1)\)

In both formulas, 'aₙ' represents the nth term of the sequence, 'aₙ₋₁' represents the previous term, 'a₁' represents the first term, 'r' represents the common ratio, and 'n' represents the term number.

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Answer:

-19.68

-1/10x+8/5

25 1/3

-50

22.75

Step-by-step explanation:

Answer:

6) 22.75gallons

7) -50feets

8) 25⅓ inches

9)2/5

10) -19.68

Step-by-step explanation:

D option

As for every input there's only one output.

The value of solution is,

P(2Y ≥ X) = 7/18.

To find the value of c, we need to use the fact that the sum of the joint probabilities over all possible values of x and y must be equal to 1:

∑∑P(x, y) = 1

Hence, By Using the given probabilities, we get:

P(1, 1) + P(2, 1) + P(2, 2) + P(3, 1)

= c(1)(1) + c(2)(1) + c(2)(2) + c(3)(1)

= 9c = 1

Solving for c, we get:

c = 1/9

Now, to compute P(2Y ≥ X), we first need to find the region of the probability distribution that satisfies the inequality 2Y ≥ X.

This region is a triangle with vertices at (1/2, 1), (1, 1), and (1, 2): (1/2, 1)  (1,1) (1,2)

To find the probability of this region, we integrate the joint probability distribution function over this triangle:

P(2Y ≥ X) = ∫∫(x, y ∈ triangle) P(x, y) dx dy

Breaking up the integral into two parts (one for the triangle above the line y=x/2 and one for the triangle below), we get:

P(2Y ≥ X) = ∫(y=1/2 to y=1) ∫(x=2y to x=2) cxy dxdy + ∫(y=1 to y=2) ∫(x=y/2 to x=2) cxy dxdy

Evaluating the integrals, we get:

P(2Y ≥ X) = (1/3) c [(2) - (1/2)] + (1/3) c [(2) - (1/4)] = 7/18

Therefore, P(2Y ≥ X) = 7/18.

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