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What is the length and width of the rectangle?
Three rectangles of different sizes make up a larger rectangle. The larger rectangle's length is labeled length. The larger rectangle's width is labeled width. The smaller rectangle on the left has fifteen k to the fourth power inside it. The smaller rectangle in the middle has thirty five k cubed inside it. The smaller rectangle on the right has twenty k squared inside it.



Three rectangles of different sizes make up a larger rectangle. The larger rectangle's length is labeled length. The larger rectangle's width is labeled width. The smaller rectangle on the left has fifteen k to the fourth power inside it. The smaller rectangle in the middle has thirty five k cubed inside it. The smaller rectangle on the right has twenty k squared inside it.
Width
=
Width=start text, W, i, d, t, h, end text, equals
Length
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Length=start text, L, e, n, g, t, h, end text, equals

The unit vector for n = (4, -3) is V = (4/5, -3/5)

An unit vector will be a vector that has the same direction than the given one, but a magnitude of 1 unit.

Then we can define the vector V = k*n

Where k > 0 is a real number, then the unit vector is:

V = (4k, -3k)

But notice that this must have a magnitude of 1, then:

1 = √( (4k)² + (-3k)²)

1 = √25k²

1 = 5k

1/5 = k

Then the unit vector is:

V = (4/5, -3/5)

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Answer:

length=12ft

width=6ft

Step-by-step explanation:

The volume formula is V=lwh.

Plug the values into the equation like this: 432=(x+6)(x)(6)

Divide both sides of the equation by 6: 72=(x+6)(x)

Distribute the x:  [tex]72=x^{2} +6x[/tex]

Subtract the 72:  [tex]0=x^{2} +6x-72[/tex]

Factor: 0=(x+12)(x-6)

x=-12

x=6

Now, plug in x into the original length and width equations.

length: (6+6)

length=12

width=6

Fred will pay $43.05 in sales tax if he buys the new refrigerator.

To calculate the sales tax Fred will pay for the new refrigerator, we first need to find the amount of the sales tax.

The cost of the new refrigerator is $615.

To calculate the sales tax, we multiply the cost by the tax rate of 7%:

So, Sales tax = 7% of $615

Sales tax = (7/100) x $615

Sales tax = $43.05

Therefore, Fred will pay $43.05 in sales tax if he buys the new refrigerator.

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To convert from degrees to radians, we use the conversion factor that 180 degrees is equal to π radians (or π/180 radians per degree).

Given that the angle is 45 degrees, we can calculate the radian measure as follows:

Radian measure = (45 degrees) * (π/180 radians per degree)

Radian measure = 45π/180

Simplifying further:

Radian measure = π/4

Therefore, the radian measure of a 45 degree angle is π/4.

The calculated inches from end to end on the bed is 72 inches

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

Length = 6 feet long

By conversion of units, we have

1 feet = 12 inches

using the above as a guide, we have the following:

Length = 6 * 12 inches long

Evaluate the products

Length = 72 inches long

Hence, the inches from end to end on the bed is 72

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A square and a traingle are present in a large rectangle with given dimensions in the figure.

[tex]\qquad\displaystyle \tt \dashrightarrow \: 12 \times 8[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 96 \: \: unit {}^{2} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 4 \times 4[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 16 \: \: unit {}^{2} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{1}{2} \times 4 \times 5[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{1}{2} \times 4 \times 5[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 2 \times 5[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 10 \: \: unit {}^{2} [/tex]

[ area of square / total area ]

[tex]\qquad\displaystyle \tt \dashrightarrow \: p(inside \: \: the \: \: square) = \frac{16}{96} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: p(inside \: \: the \: \: square) = \frac{1}{6} [/tex]

[ total area except area of triangle / total area ]

[tex]\qquad\displaystyle \tt \dashrightarrow \: p(outside \: the \: triangle) = \frac{96 - 10}{96} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: p(outside \: the \: triangle) = \frac{86 }{96} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: p(outside \: the \: triangle) = \frac{43}{48} [/tex]

The location of point A''' after the three transformations would be (-4, 1).

To determine the location of point A''', we need to apply the three transformations (reflection over the y-axis, reflection over the x-axis, and rotation of 180°) to point A.

When a point is reflected over the y-axis, the x-coordinate is negated while the y-coordinate remains the same.

So, the reflection of point A (-4, 1) over the y-axis would be (4, 1).

When a point is reflected over the x-axis, the y-coordinate is negated while the x-coordinate remains the same. So, the reflection of point (4, 1) over the x-axis would be (4, -1).

When a point is rotated 180°, the x-coordinate and y-coordinate are both negated. So, the rotation of point (4, -1) by 180° would be (-4, 1).

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Answer:The max volume of Purple berry paint is 85

Step-by-step explanation:

Purple = Red + Blue

P = 5 : 2

Simplify 5 : 2 which is 2.5 : 1

P = 30L : 10L

P = (30 x 2.5 ) + (10 x 1)

P = 75 + 10

P = 85 L

Answer:

A. 1.78cm².

B. 331.34 square meters.

Step-by-step explanation:

The area of the shaded region in a circle if the radius and central angle is given can be calculated using the following formula:

Area of shaded region = (θ/360) * πr²

Where:

A.

If the radius is 2 meters and the central angle is 51 degrees, then the area of the shaded region is:

Area of shaded region = (51/360)*π*2² = 0.357π m²

≈ 1.78 square meters

Therefore, the area of the shaded region is approximately 1.78square meters.

Therefore, the area of the shaded region is 1.78cm².

B.

If the radius is 12.5 meters and the central angle is 243 degrees, then the area of the shaded region is:

Area of shaded region = (243/360)*π*12.5² = 105.47π m²

≈ 105.47π square meters

Therefore, the area of the shaded region is approximately 331.34 square meters.

Length of JN = 10

x = 6

Given ,

S is the center of the circle.

JK = 20

LM = 3x + 2

SN = 12

SP = 12

Now ,

SN and SP are perpendicular to the chords JK and LM respectively .

Perpendiculars drawn from the center of circle to the chords bisect chords into two equal halves .

Thus,

JN = JK/2

JN = 10

Now join SJ,

In ΔSJN ,

Apply pythagoras theorem,

SN² + NJ² = SJ²

12² + 10² = SJ²

SJ = 14.52

SJ =Radius of the circle .

Now,

LP = LM/2

LP = 1.5x + 1

Now join  SL,

In ΔSLP

SP² + PL² = SL²

SL = SJ (radius of circle)

So,

12² + (1.5x + 1)² = 244

x = 6

Hence the value of x is 6 and JN is 10 .

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Answer:

The perimeter of the rectangle is P = 4x^2 + 16x - 4.

Step-by-step explanation:

1. L = 3x + 2, W = 2x^2 + 5x - 4

2. P = 2(L + W)

3. P = 2((3x + 2) + (2x^2 + 5x - 4))

4. P = 2(2x^2 + 8x - 2)

5. P = 4x^2 + 16x - 4

The length of y in the right triangle is 15 units.

A right angle triangle is a triangle that has one of its angles as 90 degrees.

The sum of angles in a triangle is 180 degrees.

The side y in the triangle XYZ can be found using trigonometric ratios as follows:

Therefore,

sin 45 = opposite / hypotenuse

opposite sides = y

hypotenuse side = 15√2

sin 45 = y / 15√2

cross multiply

y = 15√2 × sin 45

y = 15√2 × 1 / √2

y = 15 units

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The total cost of producing the additional units is $767.50.

In order to determine the total cost of producing 10 additional units assuming 2 units are currently being produced, we would have to integrate the marginal cost function for this handbag manufacturer with respect to x, and over the interval [10, 2].

Based on the information provided above, the marginal cost function for this handbag manufacturer is given by this function;

C'(x) = 0.046875x² − x + 100

₂∫¹⁰C'(x)dx = ₂∫¹⁰(0.046875x² − x + 100)dx

₂∫¹⁰C'(x)dx = ₂∫¹⁰(0.046875x²)dx − ₂∫¹⁰(x)dx + ₂∫¹⁰(100)dx

₂∫¹⁰C'(x)dx = 0.046875x³/3|¹⁰₂ - x²/2|¹⁰₂ + 100x|¹⁰₂

₂∫¹⁰C'(x)dx = 0.015625(10³ - 2³) - 1/2(10² - 2²) + 100(10 - 2)

₂∫¹⁰C'(x)dx = 0.015625(1000 - 8) - 0.5(100 - 4) + 100(8)

₂∫¹⁰C'(x)dx = 0.015625(992) - 0.5(96) + 800

₂∫¹⁰C'(x)dx = 15.5 - 48 + 800

₂∫¹⁰C'(x)dx = $767.50

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The area under the curve y = x² + 5x + 4 and the x-axis is [tex]1\frac{2}{3}[/tex] square units.

To find the area under the curve y = x² + 5x + 4 and the x-axis, we need to integrate the given function over a specific interval.

We need to find the definite integral of the function over a suitable interval.

Let's find the definite integral of the function from its roots (where the curve intersects the x-axis).

First, let's find the roots of the function by setting y = 0:

x² + 5x + 4 = 0

Factoring the quadratic equation:

(x + 1)(x + 4) = 0

Setting each factor equal to zero:

x + 1 = 0 => x = -1

x + 4 = 0 => x = -4

The roots of the function are x = -1 and x = -4.

To find the area under the curve, we integrate the function from x = -4 to x = -1:

∫[x=-4 to -1] (x² + 5x + 4) dx

Integrating the function:

∫[x=-4 to -1] (x² + 5x + 4) dx = [1/3x³ + (5/2)x² + 4x] from -4 to -1

Substituting the limits:

[1/3(-1)³ + (5/2)(-1)² + 4(-1)] - [1/3(-4)³ + (5/2)(-4)² + 4(-4)]

Simplifying:

[-1/3 + 5/2 - 4] - [-64/3 + 40/2 - 16]

[tex]1\frac{2}{3}[/tex]

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In the equation [tex]y = -2(0.5)^x[/tex], the initial amount (a) is -2, and the growth/decay factor (b) is 0.5.

In the given equation, [tex]y = -2(0.5)^x[/tex], we can identify the initial amount and the growth/decay factor.

The equation is in the form of exponential decay, as the base (0.5) is between 0 and 1, resulting in the function decreasing as x increases.

The initial amount, denoted as "a," is the coefficient in front of the exponential term. In this case, the initial amount is -2. This means that when x = 0, y = -2.

The growth/decay factor, denoted as "b," is the base of the exponential term. In this equation, the base is 0.5. The value of the base determines how quickly the function decreases or decays.

To summarize:

Initial amount (a) = -2

Growth/decay factor (b) = 0.5

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The solution is the point (0, 1/6) y = 1/6

Given the equation y = (-3/4)x + 1/6, which represents a linear equation, there is no "system" of equations involved since there is only one equation.

In this case, the equation is in slope-intercept form (y = mx + b),

where m represents the slope (-3/4) and b represents the y-intercept (1/6).

The slope-intercept form allows us to determine various properties of the equation.

Since there is only one equation, the solution to this equation is a single point on the Cartesian plane.

Each pair of x and y values that satisfy the equation represents a solution.

For example, if we choose x = 0, we can substitute it into the equation to find the corresponding y value:

y = (-3/4)(0) + 1/6

y = 1/6

Therefore, the solution is the point (0, 1/6).

In summary, the given equation has a unique solution, represented by a single point on the Cartesian plane.

Any value of x plugged into the equation will yield a corresponding y value, resulting in a unique point that satisfies the equation.

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[tex] \boxed{\rm{Similarity \: shape}}[/tex]

[tex]\begin{aligned} \frac{AB}{DE}&= \frac{BC}{EF}\\ \frac{36}{24}&=\frac{15}{x} \\ x &= \frac{\cancel{^{ \green{2}}24} \times 15}{\cancel{36_{ \green{3}}}} \\ x&= \frac{2 \times 15}{3} \\ x &= \bold{10} \\ \\\small{\blue{\mathfrak{That's \: it \: :)}}} \end{aligned}[/tex]

Answer:

Step-by-step explanation:

The system of equations with no solution is:

y + 3x = -7

4z - 2y = 10

The system of equations with exactly one solution is:

y = 6z+8

y = 6x-4

y = 3x + 2

2z-y = 5

y=-2z+8

The system of equations with infinitely many solutions is:

4z + y = 8

Answer: (4x-12) + ( 1/2x y -10) = 6

Step-by-step explanation:

First, input 4 for x and 6 for y into the equation so it looks like this:

(4(4)-12) + (1/2(4)(6)-10)

Now solve inside the parentheses starting with the first one. 4 * 4 = 16 so the inside of the first parentheses should look like (16 - 12) which equals 4.

For the second set of parentheses, 1/2 * 4 * 6 = 12, so the inside of that parentheses would look like (12 - 10), which equals 2.

At this point, the equation should look like this: (4) + (2). If you add those two together, your answer should be 6.

Answer:

To solve the inequality −4p − (5p − 4) ≤ 7p + 10 + 3p, we can simplify and isolate the variable p. Let's work through the steps:

Step 1: Distribute the negative sign (-) inside the parentheses:

-4p - 5p + 4 ≤ 7p + 10 + 3p

Simplifying further:

-9p + 4 ≤ 10p + 10

Step 2: Group like terms by adding 9p to both sides of the inequality:

-9p + 9p + 4 ≤ 10p + 9p + 10

Simplifying further:

4 ≤ 19p + 10

Step 3: Subtract 10 from both sides of the inequality:

4 - 10 ≤ 19p + 10 - 10

Simplifying further:

-6 ≤ 19p

Step 4: Divide both sides of the inequality by 19:

-6/19 ≤ 19p/19

Simplifying further:

-6/19 ≤ p

So the solution to the inequality is p ≥ -6/19.

Step-by-step explanation:

ln 54.60 = 4         e^x both sides

e ^ (ln 54.60) = e^4

         54.60 = e^4                 Done.

The value of x in the given figure is 15.

In the given figure

The length of section of chords are given

We have to find the value of x

In order to find the value of x

Apply the intersecting chord theorem,

The intersecting chords theorem, often known as the chord theorem, is a basic geometry statement that defines a relationship between the four line segments formed by two intersecting chords within a circle. It asserts that the products of the line segment lengths on each chord are equal.

Therefore,

From figure we get,

⇒ 10/x = 8/12

⇒ x = 120/8

⇒  x = 15  

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Answer:

B. 3188.5 cubic inches.

Step-by-step explanation:

The volume of a cone is calculated using the following formula:

Volume = (1/3) * π * r² * h

Where:

In this problem, we are given that r = 17 inches and S.h = 20 inches.

First we need to find height h.

py using Pythagorous theorem,we get

c²=a²+b²

here c= slight height and a is radius

20²=17²+b²

20²-17²=b²

111=b²

b=√(111)

Plugging these values into the formula, we get:

Volume = ⅓*π* 17² *√(111) = 3188.5 cubic inches

Therefore, the volume of the cone is 3188.5 cubic inches.

Answer:

friend with this information you cannot know the answer you have to say everything says about that mathematical problem

Answer:

(2x + 3)(x - 5)

Step-by-step explanation:

2x² - 7x - 15

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × - 15 = - 30 and sum = - 7

the factors are - 10 and + 3

use these factors to split the x- term

2x² - 10x + 3x - 15 ( factor the first/second and third/fourth terms )

= 2x(x - 5) + 3(x - 5) ← factor out (x - 5) from each term

= (2x + 3)(x - 5) ← in factored form

Blank 1 is 3

Blank 2 is 5

The difference between an observational study and an experiment is that  in an observational study, the researchers do not control treatment, and in an experiment, they do

In an observational study, it should be noted that the participants are measured or surveyed without any attempt to influence them. *

However the controlled experiment, participants or objects are divided into groups, and one group is given a treatment while the other is not.

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In this dataset, the mean is approximately 65.77, the median is 65, and the mode is 5 and 75.

Part A: Finding the mean of the data:

To find the mean, we need to calculate the average of all the data points.

Step 1: Identify the stems and their corresponding leaves:

3 | 5

4 | 4, 5

5 | 3, 6

6 | 2, 5

7 | 5, 5, 6

8 | 2, 5

9 | 2

Step 2: Assign numerical values to each stem-leaf combination:

3 | 5 = 35

4 | 4 = 44, 5 = 45

5 | 3 = 53, 6 = 56

6 | 2 = 62, 5 = 65

7 | 5 = 75, 5 = 75, 6 = 76

8 | 2 = 82, 5 = 85

9 | 2 = 92

Step 3: Calculate the sum of all the numerical values:

35 + 44 + 45 + 53 + 56 + 62 + 65 + 75 + 75 + 76 + 82 + 85 + 92 = 855

Step 4: Determine the count of all the data points:

The count is the total number of data points, which can be determined by adding up the frequencies of each stem-leaf combination:

1 (stem 3) + 2 (stem 4) + 2 (stem 5) + 2 (stem 6) + 3 (stem 7) + 2 (stem 8) + 1 (stem 9) = 13

Step 5: Calculate the mean by dividing the sum of all values by the count:

Mean = Sum of all values / Count = 855 / 13 = 65.77 (rounded to two decimal places)

The mean of the data is approximately 65.77.

Part B: Finding the median of the data:

To determine the median, we need to arrange the data in ascending order and find the middle value.

Arranging the data in ascending order: 35, 44, 45, 53, 56, 62, 65, 75, 75, 76, 82, 85, 92

There are 13 data points, the median will be the value in the middle. In this case, the middle value is the 7th value, which is 65.

The median of the data is 65.

Part C: Finding the mode of the data:

The mode represents the value(s) that occur with the highest frequency.

From the stem-leaf plot, we can see that the leaves with the highest frequency are 5 and 75. Both of these frequencies occur twice.

The mode of the data is 5 and 75.

Part D: Comparing the mean, median, and mode:

In this dataset, the mean is approximately 65.77, the median is 65, and the mode is 5 and 75.

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