Word problem example but want to see step by step.


A thief steals a number of rare plants from a nursery. On the way​ out, the thief meets three security​ guards, one after another. To each security​ guard, the thief is forced to give​ one-half the plants that he still​ has, plus 3 more.​ Finally, the thief leaves the nursery with 4 plants. How many plants were originally​ stolen?

Answer:

A(3) = 13

A(4) = 18

A(10) = 48

Step-by-step explanation:

This seems like a plug and play.

Starting with A(3). Everywhere you see an n, you'll replace it with a 3, as follows;

3 + (3-1)(5) = ?

We'll solve it step by step. First is 3-1. That's 2, bringing it to

3 + (2)(5).

2 times 5 is 10, bringing it to

3 + 10.

3 + 10 = 13, which concludes

A(3) = 13.

Now doing it for the remaining 2.

3 + (4-1)(5)

3 + (3)(5)

3 + 15

A(4) = 18

Last one...

3 + (10-1)(5)

3 + (9)(5)

3 + 45

A(10) = 48

The sum of the angles formed on the same side of the transversal which are inside the two parallel lines is always equal to 180°

What exactly is the degree formula?

Yes, we can use the radian-to-degree formula to convert a negative radian to a degree. Degrees = Radians 180 / is the formula, and it may be used for both positive and negative values. Parallel lines are lines that are always the same distance apart in a plane. Parallel lines never cross. Perpendicular lines are those that connect at a straight angle (90 degrees).

These are referred to as parallels. A circle of latitude is an imaginary ring that connects all places that share a parallel. The Equator is the 0 degree latitude line. Each parallel is one degree north or south of the Equator, with 90 degrees north and 90 degrees south respectively.

Hence, The sum of the angles formed on the same side of the transversal which are inside the two parallel lines is always equal to 180°

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If Anthonia and Zahra compete at the same event, the probability that Anthonia will successfully land her jump and Zahra will not land hers is 18.33%.

We describe probability as the chance or likelihood that an expected event occurs when there are many possible outcomes.

Probability lies between one and zero when it is not 100% certain or uncertain.

The probability that Anthonia lands her triple axel jump = 33.33%

The chance that Anthonia does not land her jump = 66.67% (1 - 33.33%)

The likelihood of Zahra landing her jump successfully = 45%

The odds that Zahra will not successfully land her jump = 55% (1 - 45%)

The probability that Anthonia lands successfully while Zahra does not = 18.33% (33.33% x 55%)

Thus, Anthonia has the chance of winning Zahra at 18.33%.

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We can conclude that -

        Q = 5(280 - P)

Given is a story of Dr. Leona Williams who is a well-known plastic surgeon.

{ 1 } -

Dr. Williams estimated demand for her work is -

Q = 280 - 0.2P

Inverse of a function can be calculated by following the steps mentioned below -

So, we can write -

P = 280 - 0.2Q

P - 280 = - 0.2Q

- (280 - P) = - 0.2Q

(280 - P) = 0.2Q

Q = (280 - P)/0.2

Q = 5(280 - P)

{ 2 } -

The average variable cost function for reconstructive nose surgery is -

AVC = 2Q² – 15Q + 400

Let AVC = A{Q}

For maximum profit -

d/dQ (A{Q}) = 0

d/dQ (2Q² – 15Q + 400) = 0

d/dQ (2Q²) - d/dQ (15Q) + d/dQ (400) = 0

4Q - 15 = 0

4Q = 15

4Q = 15

Q = 3.7

Q = 4 {approx.}

Therefore, we can conclude that -

        Q = 5(280 - P)

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In a plane, intersecting lines are any two or more lines that cross each other. The point of intersection is the common point shared by all intersecting lines.

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Answer:

y = (-5/4)x - 19

Step-by-step explanation:

Given information,

→ Slope(m) = -5/4

→ Point = (-8, -9)

→ y-intercept = b

The slope-intercept form is,

→ y = mx + b

Now the y-intercept will be,

→ y = mx + b

→ -9 = (-5/4)(-8) + b

→ -9 = 10 + b

→ b = -9 - 10

→ [ b = -19 ]

Then the required equation is,

→ y = mx + b

→ [ y = (-5/4)x - 19 ]

Hence, this is the equation.

c=170/30 is the equation that represents the number of calories,c, burned per min.

A division is a process of splitting a specific amount into equal parts.

Given that Tarmu run 30 min and burned 170 calories

We need to find the equation that represents the number of calories, c, burned per min.

To find the calories burned in each minute we have to divide one hundred seventy by thirty.

c=170/30

c=5.66 cal/min

Hence, c=170/30 is the equation that represents the number of calories,c, burned per min.

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The area under the normal curve with a mean of 20 and a standard deviation of 5 is 0.8413 when x = 25.

The area under the normal distribution curve is calculated using the z-score, which is the number of standard deviations a value is from the mean. To calculate the area under the normal curve for a given mean and standard deviation, one must use the formula:

Area = ½[1 + erf(z)]

Where erf is the Gaussian error function, and z is the z-score.

To calculate the area under the curve given a boundary x, the z-score must be calculated first. This is done using the formula:

z = (x - mean) / standard deviation

Substituting this into the formula above gives:

Area = ½[1 + erf((x - mean) / standard deviation)]

For example, if the mean is 20 and the standard deviation is 5, and the boundary value is x = 25, the area under the normal curve is calculated as follows:

z = (25 - 20) / 5 = 1

Area = ½[1 + erf(1)] = 0.8413

Therefore, the area under the normal curve with a mean of 20 and a standard deviation of 5 is 0.8413 when x = 25.

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The Numerical Expressions answers are shown below:

Integers come in three types:

Given:

1. 7-6+ 5

= 7 -1

= 6

So, the value of 7-6+ 5 is 6.

2. 31 +19 -8

= 31 + 11

= 42

So, the value of 31 +19 -8 is 42.

3. 64-8+21

= 56 + 21

= 77

So, the value of 64-8+21 is 77.

4. 17+34-2

= 51-2

= 49

So, the value of 17+34-2 is 49.

5. 28+ 89 -67

= 117-67

= 50

So, the value of 28+ 89 -67 is 50.

6. (8+1) x 12- 13

= 9 x 12 -13

= 108 - 13

= 95

So, the value of (8+1) x 12- 13 is 95.

7. 63/9 +8

= 7 +8

= 18

So, the value of 63/9 +8  is 18.

8. 5 x 6 -(9-4)

= 5x 6 - 5

= 30- 5

= 25

So, the value of 5 x 6 -(9-4)  is 25.

9. 13x 4 -72 /8

= 13 x 4 - 9

= 52- 9

= 43

So, the value of 13x 4 -72 /8  is 43.

10. 16/2 + 8 x 3

= 8 + 8 x 3

= 8+24

= 32

So, the value of 16/2 + 8 x 3  is 32.

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Kimiyo would make $987 in a work week if she sold $4,800 worth of merchandise.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Kimiyo earns a weekly salary of $675 plus a 6.5% commission on sales at a gift shop.

She sold $4,800 worth of merchandise.

That means,

the commissioned amount = 4800 x 6.5 /100

The commissioned amount = $312

In a week,

Kimiyo's total earning is,

= $675 + $312

= $987

Therefore, $987 is the total salary.

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The required number is 42 which gives a result of −4 when 11 is subtracted from the quotient of the number and 5.

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

Let n be the number in question; then, we can write the word problem as an equation like this:

⇒ (n/6) - 11 = -4

Add 11 on both sides of the equation,

⇒ (n/6) - 11 + 11 = 11 - 4

⇒ (n/6) = 7

Multiply by 6 on both sides of the above equation, and we get

⇒ n = 42

Hence, the number is 42.

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They move off together with a speed of 1/3 v,The mass of the boxcar is m/3 (V₁ - V₂)².

A body's mass is an inherent quality. Prior to the discovery of the atom and particle physics, it was widely considered to be tied to the amount of matter in a physical body.

in Kinetic energy 4 system, the

K = Kf-Ki

K = 1 (Mcar + Mtruck) Vp ² + mcarv₁_ J 2 2 + Mtruck V2 2 2

K = +(m+2m) (V₁+2√2)² +mv₁² - 1 x 2m v₂ ² 2 2 9

K m (v, ² + 4 √₂ ² + AV₁ V2 ) - { mv, ² - tn v₂ 2 2 6

K = m (V₁²+ 4V₂² + 4 V₁ V2 -1/3V, ² - 6V, ²) /6.

K = m/6 (4V₁V2.-2V₁2-2√22)

k = + m/3 (V₁ - V₂)²

They move off together with a speed of 1/3 v, The mass of the boxcar is m/3 (V₁ - V₂)².

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728 kilograms of sugar is used in this month.

percentage, a relative value indicating hundredth parts of any quantity.

Given that a bakery used 30% more sugar this month than last month.

Let us convert 30% to decimal.

Divide 30 by 100

30/100=0.3

the bakery used 560 kilograms of sugar last month we have to find the amount of sugar used this month.

Now multiply 30% of 560

0.3×560

168.

So now 560+168=728 is the amount of sugar used this month.

Hence, 728 kilograms of sugar is used in this month.

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Answer:

59.036

Step-by-step explanation:

tanΘ = opposite/adjacent

Θ =tan⁻¹(opposite/adjacent)

tan⁻¹(10/6) - 59.03624347

The equation of the line passing through the point (8, 4) and having a slope of 0 is y = 4.

What is the slope intercept?

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

The line passing through the point (8, 4) and having a slope of 0 is a horizontal line which is parallel to the x-axis. The slope (m) of this line is 0.

The point-slope form of this line would be:

(y - 4) = 0(x - 8)

Simplifying this, we get:

y = 4

Hence, the equation of the line passing through the point (8, 4) and having a slope of 0 is y = 4.

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the opposite sides of the quadrilateral PQRS are equal and parallel and so PQRS is a PARALLELOGRAM.

Option (C) is CORRECT.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given, that the coordinates of the vertices of a  quadrilateral composed in the first quadrant of the coordinate plane are (0,0) (a, b), (a + c, b), and (c, 0).

We are to select the most accurate classification of the quadrilateral.

Let the coordinates of the vertices of the quadrilateral be P(0,0), Q(a, b), R(a + c, b), and S(c, 0).

The lengths of the sides are calculated using the distance formula as follows :

PQ = √(a² + b²)

QR = √(a +c -a)² + (b-b)² = √c² = c

RS =  √(a² + b²)

SP = c

So, the opposite sides are equal in length.

And, the slopes of the sides are calculated as follows :

The slope of PQ(m₁) = (b-0)/(a-0)

The slope of QR(m₂) = (b-b)/(c-a-c) = 0

The slope of RS(m₃) = 0-b/(c-a-c) = 0

The slope of SP(m₄) = (0-0)/(0-c) = 0

So, the slopes of the opposite sides are equal but:

m₁ *m₂ = 0 ≠ -1

m₃ *m₄ = 0 ≠ -1

Therefore, the opposite sides of the quadrilateral PQRS are equal and parallel and so PQRS is a PARALLELOGRAM.

Option (C) is CORRECT.

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Answer:

0.55 times 20.1 is equal to 11.055

Step-by-step explanation:

To show work, we can simply multiply 0.55 by 20.1 using long multiplication.

0.55

20.1

0.55

+11.05

11.055

So 0.55 times 20.1 is equal to 11.055

So, the possible fourth corners are (4,4) and (-2,2).

Given the three vertices of a parallelogram (1,1), (4,2), and (1,3), we can use vector algebra to find the fourth corner. We know that opposite sides of a parallelogram are parallel, and therefore have the same vector direction. We can use this property to find the vector pointing from one corner to another and then use this vector to find the fourth corner.

One possible method is:

Another possible method is:

So, the possible fourth corners are (4,4) and (-2,2).

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The movie theater will have 50 shows in 6 days

To find the total number of shows in 6 days, we need to calculate the number of shows for each type of day (4 days per week with 7 shows per day and 2 days per week with 11 shows per day) and then add them together.

First, let's calculate the number of shows for the 4 days per week with 7 shows per day:

4 days per week x 7 shows per day = 28 shows per week

Next, let's calculate the number of shows for the 2 days per week with 11 shows per day:

2 days per week x 11 shows per day = 22 shows per week

Now, we can add the number of shows for each type of day together to find the total number of shows in 6 days:

28 shows per week + 22 shows per week = 50 shows in 6 days

We used multiplication to calculate the number of shows per week for each type of day (by multiplying the number of days by the number of shows per day) and then added the two results together to find the total number of shows in 6 days.

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Since it has no impact on the result or solution of the problem, assuming that a > d does not reduce the generality of the statement. If a > d, the issue can be solved by simply swapping the values of a and d.

It makes no difference to the problem whether an is more or less than d because we are presuming that each integer is distinct. Furthermore, by supposing that a > d, the problem's variables can be arranged consistently, making it simpler to comprehend and resolve. As a result, making the assumption that a > d does not reduce the generality of the solution because the problem remains the same and the assumption may be readily changed if necessary.

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Answer:

As a whole, the piece first measured 38 inches. No matter how many times you cut it, all of the pieces will still add up to 38 inches. You know that 19 inches is the length of one of the two pieces, so all you need to find is the other unknown piece. Add the two together, with m being the unknown length.

19+m=38

If you want to solve the equation, just subtract 19 from both sides.

19+m=38

m=19

a) The z-score for a structure costing $2,300 is given as follows: -0.67.

b) The z-score for a structure costing $4,900 is given as follows: 1.5.

c) The interpretation of each z-score is given as follows:

d) The structure would have an unusual price, as the z-score has an absolute value greater than 2.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 3100, \sigma = 1200[/tex]

For item a, the z-score is then given as follows:

Z = (2300 - 3100)/1200

Z = -0.67.

For item b, the z-score is then given as follows:

Z = (4900 - 3100)/1200

Z = 1.5.

For the price of $13,000, the z-score is given as follows:

Z = (13000 - 3100)/1200

Z = 8.25.

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Answer:

7/12 of salt.

1/4 + 1/3 =

1/3 + 1/4 =

4/12 + 3/12 = 7/12.

Step-by-step explanation:

Hope it helps! =D

Answer: Match each equation with an equivalent equation. Some of the answer choices are

not used.

A. 3x + 6 = 4x+7

B. 3(x + 6) = 4x+7

C. 4x + 3x = 7-6

1.9x = 4x +7

2. 3x + 18 = 4x+7

3.3x = 4x + 7

4. 3x1 = 4x

5.7x = 1

A. 3x + 6 = 4x+7 = 3

B. 3(x + 6) = 4x+7 = 2

C. 4x + 3x = 7-6 = 5

1.9x = 4x +7 = 3

3x + 18 = 4x+7 = 2

3.3x = 4x + 7 = 1

3x1 = 4x = not used

5.7x = 1 = not used

So,

3x + 6 = 4x+7 matches with 3

3(x + 6) = 4x+7 matches with 2

4x + 3x = 7-6 matches with 5

1.9x = 4x +7 matches with 3

3x + 18 = 4x+7 matches with 2

3x = 4x + 7 matches with 1

3x1 = 4x is not used

7x = 1 is not used

Step-by-step explanation:

Answer:

A. 881

C. 353

Step-by-step explanation:

In order to form 8 lines with each line having equal length, the total number of members has to be divisible by 8:

440/8 = 55, so 440 isn't the answer

224/8 = 28, so 224 isn't the answer

881/8 = 110.125. In addition, even numbers can't be divided evenly by odd numbers like 881, so A. 881 is the answer.

Same goes to 353 since 353 is also an odd number that can't evenly divide the even number 8. Hence, C. 353 is the answer as well.

There are 2187 combinations to select 7 cookies from a bakery that sells cookies of 3 different flavors (oatmeal, chocolate chip, almond).

When selecting 7 cookies from a bakery that sells 3 different flavors, each cookie selected can be one of the 3 different flavors. This means that for the first cookie, there are 3 choices, for the second cookie, there are also 3 choices, and so on for the 7th cookie. This is known as the combinations formula and it can be represented as 3 x 3 x 3 x ... x 3 (3 being repeated 7 times).

Using the 3⁷ formula, we can calculate that there are 2187 ways to select 7 cookies from a bakery that sells cookies of 3 different flavors. This means that there are 2187 unique combinations of cookies that can be selected, assuming that more than 7 cookies are available for each flavor.

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Your question seems incomplete, but I assume the question was:

"How many ways can you select 7 cookies to buy from a bakery that sells cookies of 3 different flavors (oatmeal, chocolate chip, almond)? We assume that more than 7 cookies are displayed for each flavor. For example, one way is to choose 7 chocolate chip cookies."

The quadratic function y = 7(x + 1)² + 1 in standard form is y = 7x² + 14x + 2.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The given quadratic function is -

y = 7(x + 1)² + 1

Solve the equation to get the standard form.

First solve using the formula (a + b)² = (a² + 2ab + b²) -

y = 7(x + 1)² + 1

y = 7(x² + 2x + 1) + 1

Now, open the brackets -

y = 7x² + 14x + 1 + 1

Now, add the like terms -

y = 7x² + 14x + 2

Therefore, the value is obtained as 7x² + 14x + 2.

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