Which expression is equivalent to 65x0.15

Answer:

---------------------

The scale of the map is 3 cm : 1 km.

The distance of 6 cm is twice the 3 cm, so the actual distance is:

Answer:618.014

Step-by-step explanation: It may look like hundredths which is where must people mess up but it is instead thousandths.

20.25 square units are enclosed between the two curves.

To find the area enclosed between the two curves, find their intersection points first.

Setting the equations equal to each other:

8x² - x³ + x = x² + 13x

Simplifying and rearranging:

x³ - 7x² - 12x = 0

Factoring out x:

x(x² - 7x - 12) = 0

Solving for x using the quadratic formula:

x = 0, x = 3, x = -4

The two curves intersect at x = 0, x = 3, and x = -4.

Next, determine which curve is on top of the other between these intersection points. We can do this by comparing their y-values for each x:

At x = -4, y = 128

At x = 0, y = 0

At x = 3, y = 27

So, the curve y = 8x² - x³ + x is on top of y = x² + 13x for x in the range -4 ≤ x ≤ 0, and y = x² + 13x is on top of y = 8x² - x³ + x for x in the range 0 ≤ x ≤ 3.

Now find the area between the curves using integration:

∫[from -4 to 0] [(8x² - x³ + x) - (x² + 13x)] dx + ∫[from 0 to 3] [(x² + 13x) - (8x² - x³ + x)] dx

Simplifying:

∫[from -4 to 0] (-x³ + 7x² - 12x) dx + ∫[from 0 to 3] (x³ - 7x² + 12x) dx

Integrating:

[-(1/4)x⁴ + (7/3)x³ - 6x²] from -4 to 0 + [(1/4)x⁴ - (7/3)x³ + 6x²] from 0 to 3

Simplifying:

(64/3) + (81/4) - (27/3) - (64/3) = 20.25

Therefore, the area enclosed between the two curves is 20.25 square units.

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Image transcribed:

(1 point) Find the area of the region that is enclosed between y = 8x² - x³ + x and y = x² + 13x.

The area is

It will take 21/2 tiles to cover the length of the floor and it will take 13/2 tiles to cover the width of the floor.

What is width?

Width is a term used to describe the measurement of the shortest side or dimension of an object or space.

To determine the number of tiles needed to cover the length of the bathroom floor, we need to divide the length of the floor by the length of each tile. Similarly, to determine the number of tiles needed to cover the width of the floor, we need to divide the width of the floor by the width of each tile.

First, we need to convert the mixed numbers of the length and width to improper fractions:

Length = 10 1/2 feet = (2 x 10 + 1)/2 = 21/2 feet

Width = 6 1/2 feet = (2 x 6 + 1)/2 = 13/2 feet

Now, let's assume that each tile is 1 foot by 1 foot. Since each tile covers an area of 1 square foot, the number of tiles needed to cover a rectangular area can be calculated by dividing the total area of the rectangle by the area of each tile.

To determine the number of tiles needed to cover the length of the floor, we divide the length of the floor by the length of each tile:

Number of tiles to cover length = Length / Length of each tile

= (21/2) / 1

= 21/2

Therefore, it will take 21/2 tiles to cover the length of the floor.

To determine the number of tiles needed to cover the width of the floor, we divide the width of the floor by the width of each tile:

Number of tiles to cover width = Width / Width of each tile

= (13/2) / 1

= 13/2

Therefore, it will take 13/2 tiles to cover the width of the floor.

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Answer:

29.9

JUST PLUG BOTH POINTS INTO THE DISTANCE FORMULA TO GET YOUR ANSWER!!

Answer: The components of 3r-s are (-9, 7).

Step-by-step explanation:

To find 3r-s, we need to first find 3r and then subtract s from it:

3r = 3<-2, 2> = <-6, 6>

3r - s = <-6, 6> - <3,-1>

Now we can subtract the components of s from the corresponding components of 3r:

= <-6-3, 6-(-1)>

= <-9, 7>

Therefore, the components of 3r-s are (-9, 7).

[tex]\begin{cases} x = -7 &\implies x +7=0\\ x = 1 &\implies x -1=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +7 )( x -1 ) = \stackrel{0}{y}}\hspace{5em}\textit{we also know that } \begin{cases} x=-3\\ y=16 \end{cases} \\\\\\ a ( -3 +7 )( -3 -1 ) = 16\implies a(4)(-4)=16\implies -16a=16 \\\\\\ a=\cfrac{16}{-16}\implies a=-1 \\\\[-0.35em] ~\dotfill\\\\ -1( x +7 )( x -1 ) =y\implies -(x^2+6x-7)=y\implies \boxed{-x^2-6x+7=y}[/tex]

Check the picture below.

Answer:

x = 66.46

Step-by-step explanation:

To find the numerical limits for a D grade, we need to find the scores that fall below the top 84% and above the bottom 5%.

Step 1: Find the z-scores corresponding to the top 84% and bottom 5% of scores.

   The top 84% of scores corresponds to a z-score of approximately 1.04. (This can be found using a standard normal distribution table or calculator.)

   The bottom 5% of scores corresponds to a z-score of approximately -1.64.

Step 2: Use the z-score formula to find the corresponding scores.

For the top 84% of scores:

z = (x - μ) / σ

1.04 = (x - 81.1) / 8.9

x - 81.1 = 9.25

x = 90.35

For the bottom 5% of scores:

z = (x - μ) / σ

-1.64 = (x - 81.1) / 8.9

x - 81.1 = -14.64

x = 66.46

Therefore, the numerical limits for a D grade are between 66 and 90 (rounded to the nearest whole number).

An equivalent expression using the distributive property is:

0.005d³ - 0.015d² + 0.15d + 19.5.

What is distributive property?

In mathematics, the distributive property is a property of operations that states how multiplication or addition of two or more numbers works with respect to each other.

Using the distributive property, we can rewrite the given expression as:

20 + 0.005d³ - 0.15d² + 1.5d - 5

Distributing 0.005 to the terms inside the parentheses, we get:

20 + 0.005d³ - 0.015d² + 0.15d - 0.5

Combining like terms, we get:

0.005d³ - 0.015d² + 0.15d + 19.5

Therefore, an equivalent expression using the distributive property is:

0.005d³ - 0.015d² + 0.15d + 19.5.

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It's not possible to directly convert a numerical line plot into a categorical line plot.

Without specific examples of the data displays in question, it's difficult to provide a detailed answer. However, in general, a numerical line plot displays the relationship between two numerical variables, usually showing how one variable changes over time or some other continuous scale. On the other hand, a categorical line plot shows the relationship between a numerical variable and a categorical variable, where the categories are displayed on the x-axis.

One similarity between the two displays is that they both use lines to represent the data. However, in a numerical line plot, the lines are used to connect data points in a continuous manner, while in a categorical line plot, the lines connect the means or medians of each category.

One difference between the two displays is that a numerical line plot can show the exact values of the data points, while a categorical line plot only shows the mean or median for each category. Additionally, a categorical line plot is often used when the categories are unordered, while a numerical line plot is used when the x-axis represents a continuous scale.

In general, it's not possible to directly convert a numerical line plot into a categorical line plot. However, if the numerical variable in the original plot is binned into categories, a categorical line plot can be created using the mean or median value for each bin.

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The 3 transformed functions are:

1)  g(x) = -|x + 3| + 7

2)   g(x) = |x + 7| - 7

3)   g(x) = |x + 4| - 10

The function f(x) is:

f(x) = |x + 3| - 7

Now let's define the transformations:

A reflection across the x-axis is:

g(x) = -f(x)

A Horizontal shift of N units is written as:

g(x) = f(x + N)

A Vertical shift of N units is written as:

g(x) = f(x) + N

Then we have:

1) g(x) = -f(x) = -( |x + 3| - 7)

g(x) = -|x + 3| + 7

2) g(x) = f(x + 4) =  |x + 4 + 3| - 7

   g(x) = |x + 7| - 7

3) g(x) = f(x) - 3

           =  |x + 4| - 7 - 3

   g(x) = |x + 4| - 10

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Answer:

Step-by-step explanation:

Let x be the amount Ms. Walsh invested in the account yielding 8% interest, and let y be the amount she invested in the account yielding 10% interest.

According to the problem, the total amount invested is $18,000, so we have:

x + y = 18,000

The interest earned from the account yielding 8% interest is 0.08x, and the interest earned from the account yielding 10% interest is 0.10y. The total interest earned is $1,600, so we have:

0.08x + 0.10y = 1,600

We now have two equations with two unknowns. We can solve for one of the unknowns and then use that value to find the other unknown.

Solving the first equation for y, we get:

y = 18,000 - x

Substituting this expression for y into the second equation, we get:

0.08x + 0.10(18,000 - x) = 1,600

Simplifying and solving for x, we get:

0.08x + 1,800 - 0.10x = 1,600

-0.02x = -200

x = 10,000

Therefore, Ms. Walsh invested $10,000 in the account yielding 8% interest. To find the amount she invested in the account yielding 10% interest, we can substitute x = 10,000 into the equation y = 18,000 - x:

y = 18,000 - 10,000

y = 8,000

Therefore, Ms. Walsh invested $8,000 in the account yielding 10% interest.

The tangent of the angle θ is approximately 0.5774.

In trigonometry, the tangent (commonly abbreviated as tan) is a trigonometric function that describes the relationship between the lengths of the sides of a right triangle that are near to acute angles and their opposite sides.

We can use the reciprocal identity of the tangent and cotangent functions to solve this problem:

tangent(θ) = 1 / cotangent(θ)

Substituting the given value of the cotangent of angle θ, we get:

tangent(θ) = 1 / 1.7321

Evaluating the right-hand side of the equation, we obtain:

tangent(θ) ≈ 0.5774

Therefore, the tangent of the angle θ is approximately 0.5774.

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Answer:

The proportion is:

$0.25 / 5$ inches $= x / $ inches bought for $1.80

Simplifying the left-hand side:

$0.25 / 5 = 0.05$

The equation to find x becomes:

$0.05 = x / 1.80$

To solve for x, we can multiply both sides by 1.80:

$0.05 \cdot 1.80 = x$

$x = 0.09$

Therefore, the length of rope candy that can be bought for $1.80 is 0.09 inches.

Answer: 36

Step-by-step explanation:

.25/5 = .05

1.80/.05 = 36

Answer:    It's not entirely clear what is being asked for in the given question, as it is not clear what the numbers represent or what operation is being performed. If you could provide more information or context, I would be happy to try and help you.

Step-by-step explanation:

Answer:35 or 115

Step-by-step explanation

combine like terms

Answer:222222.333

Step-by-step explanation:

easy just divide

10) Total revenue is 0.1x¹ + 4.3x³ - 34.2x² + 295.7x - 137.7. 11) Profit for this year minus profit for last year equals 0.3x⁴ - 7.8x³ + 66.6x² - 211.4x + 185.9.

Profit is the financial gain that is achieved when the revenue from sales or business activities exceeds the expenses, costs, and taxes associated with running the business or conducting those activities.

10) To find the polynomial that models the total profit for both last year and this year, we add the two given profit equations:

Last year's profit: -0.3x¹ + 843 - 70.3x² + 247.5x - 137.7

This year's anticipated profit: 0.243 - 3.7x² + 36.1x + 48.2

Total profit = Last year's profit + This year's anticipated profit:

Total profit = (-0.3x¹ + 843 - 70.3x² + 247.5x - 137.7) + (0.243 - 3.7x² + 36.1x + 48.2)

Simplifying and combining like terms, we get:

Total profit = -0.3x¹ + 36.1x - 74x² + 295.7

Therefore, the polynomial that models the total profit for both last year and this year is:

A. 0.1x¹ + 4.3x³ - 34.2x² + 295.7x - 137.7

11) To find the polynomial that models how much more profit Helena anticipates this year compared to what she made last year, we can subtract the equation for last year's profit from the equation for this year's anticipated profit:

This year's anticipated profit: 0.243 - 3.7x² + 36.1x + 48.2

Last year's profit: -0.3x + 843 - 70.3x² + 247.5x - 137.7

Difference in profit = This year's anticipated profit - Last year's profit:

Difference in profit = (0.243 - 3.7x² + 36.1x + 48.2) - (-0.3x¹ + 843 - 70.3x² + 247.5x - 137.7)

Simplifying and combining like terms, we get:

Difference in profit = 0.3x¹ - 3.7x² + 36.1x - 595.5

Therefore, the polynomial that models how much more profit Helena anticipates this year compared to what she made last year is:

D. 0.3x⁴ - 7.8x³ + 66.6x² - 211.4x + 185.9

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Answer:

Step-by-step explanation:

To find the zeros of the function f(x) = -3x² + 75, we need to solve the equation -3x² + 75 = 0 for x. We can start by factoring out a common factor of -3:

-3x² + 75 = 0

-3(x² - 25) = 0

Now we can use the difference of squares formula to factor the expression inside the parentheses:

-3(x - 5)(x + 5) = 0

This equation is satisfied when one of the factors is equal to zero, so we can set each factor equal to zero and solve for x:

x - 5 = 0 --> x = 5

x + 5 = 0 --> x = -5

Therefore, the zeros of the function are x = -5 and x = 5, and we can write them in order from least to greatest as:

lesser x = -5

greater x = 5

Calculator solution:

To verify these results using a calculator, you can graph the function y = -3x² + 75 and look for where the graph intersects the x-axis. Here's how you can do that on a TI-84 calculator:

1) Press the "Y=" button to enter the function.

2) Enter "-3x^2 + 75" after "Y1=".

3) Press the "GRAPH" button to see the graph.

4) Press the "2nd" button followed by the "CALC" button (which is the "TRACE" button).

5) Select option 2: "zero" by pressing the number 2 on the calculator or using the arrow keys to highlight it and pressing "ENTER".

6) Move the cursor to the left of the zero on the left side of the graph and press "ENTER".

7) Move the cursor to the right of the zero on the right side of the graph and press "ENTER".

8) The calculator will display the zeros and ask if you want to store them to a variable. You can simply write down the values and press "ENTER" twice to exit the calculator's calculation.

The calculator will confirm that the zeros are x = -5 and x = 5, as we found above.

Step-by-step explanation:

See image:

The local minimum are at

b and r

There is neither minimum or maximum at

a, d, and s

In calculus, a local minimum is a point on a graph where the function has the lowest value in a specific region (usually a small interval around the point) compared to all other nearby points on the graph.

Similarly, a local maximum is a point on a graph where the function has the highest value in a specific region compared to all other nearby points.

To determine if a point is a local minimum or maximum on a graph, we need to examine the behavior of the function around that point. Specifically, we need to check the slope of the graph near that point.

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Answer:

The local minimum are at b and rThere is neither minimum or maximum at a, d, and s

Step-by-step explanation:

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Cost of cleaning and pressing x shirts = 6x

Cost of whole order with discount = y = 6x - 7

It's always worth taking advantage of the discount, so there is no minimum number of shirts required to make the discount worthwhile.

Assuming that the dry cleaner's special offer of $6 per shirt for cleaning and pressing applies to all shirts,

the total cost of cleaning and pressing n shirts would be 6n dollars.

Additionally, the special offer includes a discount of $7 off the entire order.

Therefore, the total cost C of cleaning and pressing n shirts after the discount would be:

C = 6n - 7

For example,

if you have 5 shirts to be cleaned,

the total cost before the discount would be $30 (5 x $6), and after the discount,

the total cost would be $23 (6 x 5 - 7).

Note that this assumes that the discount is applied after the cost of cleaning and pressing the shirts is calculated. If the discount is applied to each shirt individually, the total cost would be different.

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Answer:

  45 units²

Step-by-step explanation:

You want the area of the figure comprised of a triangle atop a rectangle.

The area of the whole will be the sum of the areas of the parts. Here, we can decompose the figure into a rectangle of width 5 -(-4) = 9 units and height -2 -(-4) = 2 units.

The triangle above the rectangle has the same base width, and height 4 -(-2) = 6 units.

The total area is ...

  [tex]A = bh_r +\dfrac{1}{2}bh_t\qquad\text{$h_r$=rectangle height; $h_t_$=triangle height}\\\\A=b(h_r+\dfrac{1}{2}h_t)= 9(2+\dfrac{6}{2})=9\cdot5=45[/tex]

The area of the polygon is 45 units².

__

Additional comment

When finding the area of composite figures, we often find it useful to treat the area of a triangle as equal to the area of a rectangle of the same width and half the height, or the same height and half the width.

You can figure the area other ways, too. You can subtract the triangle corner areas from the 9 wide by 8 high enclosing rectangle. You can draw a vertical line through N and divide the figure into two trapezoids with bases 2 and 8. Or, you can simply add the areas of rectangle and triangle after computing them separately.

1. The expression 2/3 (3/4 x - 3/2) is equivalent to x - 1/2. not equivalent to 1/2x - 1 and the third option. 2. The expression (2x + 1) - (x + 3/2) is equivalent to x - 1/2, not equivalent to 1/2x - 1 and the third option.

An expression is a mathematical sentence that may or may not have an equal sign, whereas an equation is a declaration that two expressions are equal. The equal sign in an equation indicates whether the result is true or false, depending on the values of the variables. On the other hand, while expressions can be assessed or sped up, they cannot be true or untrue. Expressions are used to represent quantities or operations, whereas equations are used to find the values of variables that the equation requires.

For the given expressions simplifying we get:

1. 2/3 (3/4 x - 3/2)

= 1/2 x - 1

This expression is equivalent to x - 1/2.

2. (2x + 1) - (x + 3/2)

= x - 1/2

This expression is equivalent to x - 1/2.

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there are 24 different 4-digit numbers that can be created using two 1's, a 2, and a 3.

what are  4-digit numbers ?

A 4-digit number is a number that has exactly four digits or places in its representation. The digits can be any of the ten digits from 0 to 9. The first digit of a 4-digit number can be any digit from 1 to 9, except 0. The remaining three digits can be any digit from 0 to 9.

In the given question,

To find the number of different 4-digit numbers that can be created using two 1's, a 2, and a 3, we can use the permutation formula.

The number of permutations of n objects taken r at a time is given by:

P(n, r) = n! / (n - r)!

where n! means n factorial, which is the product of all positive integers up to n.

In this case, we have 4 objects (two 1's, a 2, and a 3) and we want to arrange them in a 4-digit number, which means we need to take all 4 objects at a time. Therefore, the number of different 4-digit numbers we can create is:

P(4, 4) = 4! / (4 - 4)!

= 4! / 0!

= 4 x 3 x 2 x 1 / 1

= 24

So there are 24 different 4-digit numbers that can be created using two 1's, a 2, and a 3.

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Answer:

[tex]\frac{2}{\frac{1}{24} }[/tex]

Step-by-step explanation:

2/x = 48

48x = 2

x = (2)/ (1/24)

[tex]\frac{2}{\frac{1}{24} }[/tex] = 48

The longer dimension of the new garden will be approximately 20.19 meters.

Area is a measure of the amount of space inside a two-dimensional flat surface or shape. It is usually measured in square units, such as square meters, square feet, or square inches. The area of a shape is calculated by multiplying its length by its width. For example, the area of a rectangle can be calculated by multiplying its length and width.

In the given question,

The area of the original garden is:

Area = length x width = 13m x 10m = 130 m²

To increase the area of the garden to 208 m², we need to find the amount by which both the length and width must be increased. Let's call this amount "x".

The new area of the garden will be:

New area = (length + x) x (width + x) = 208 m²

Expanding the brackets, we get:

New area = length x width + length x x + width x x + x²

Substituting the values we know, we get:

208 m² = 130 m² + 13 m x x + 10 m x x + x²

Simplifying, we get:

208 m² = 130 m² + 23 m x x + x²

Rearranging, we get:

0 = x² + 23 m x - 78 m²

Now we can use the quadratic formula to solve for x:

x = (-b ± √(b² - 4ac)) / 2a

Where a = 1, b = 23 m, and c = -78 m². Plugging in these values, we get:

x = (-23 m ± √(23² - 4(1)(-78))) / 2(1)

x = (-23 m ± √(1025)) / 2

We can ignore the negative solution, since x must be a positive length. Simplifying the positive solution, we get:

x = (-23 m + √(1025)) / 2

Therefore, the length (longer dimension) of the new garden will be:

Length = 13 m + x

Length = 13 m + (-23 m + √(1025)) / 2

Length = 3 m + √(1025) / 2

Length = 20.19 m (rounded to two decimal places)

So the longer dimension of the new garden will be approximately 20.19 meters.

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Out of the given options, option C is a rational function because it can be expressed as the ratio of two polynomial functions:

F(x) = (x² + 5x - 6) / 3x

A function that is the ratio of polynomials is referred to as rational. When a function of one variable, x, can be written as f (x) = p (x)/q (x), where p (x) and q (x) are polynomials with q (x) 0, the function is said to be rational.

A rational function is a function that can be expressed as the ratio of two polynomial functions, where the denominator is not equal to zero.

Out of the given options, option C is a rational function because it can be expressed as the ratio of two polynomial functions:

F(x) = (x² + 5x - 6) / 3x

The numerator of the function is a polynomial of degree 2 and the denominator is a polynomial of degree 1, so it satisfies the definition of a rational function.

Option A and B are not rational functions because they cannot be expressed as the ratio of two polynomial functions.

Option D is also not a rational function because it contains a square root function, which is not a polynomial function.

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Dante will need 30 album pages to hold all of his baseball cards.

What is meant by pages?

Pages refer to the individual sheets of paper within a document or book, typically numbered consecutively, that are used to present information, text, images, or illustrations.

What is meant by cards?

Cards typically refer to rectangular pieces of stiff paper, plastic, or similar material used for playing games, collecting information, or providing details about a product or service, such as business cards or trading cards.

According to given information

Dante has 10 cards for each of the 24 teams, for a total of 10 x 24 = 240 cards.

To determine the number of album pages he will need, we can divide the total number of cards by the number of cards each page can hold:

240 cards ÷ 8 cards/page = 30 pages

Therefore, Dante will need 30 album pages to hold all of his baseball cards.

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