A cat runs 3/5 of a mile in 2/10 of an hour. How many miles did the cat run in 1 hour?

The answer in fraction form is in the picture

Answer:

4.84

Step-by-step explanation:

4+2/5+2/5+1/25

The factored form of the expression x^2 - 8x + 9 is (x - 9)(x - 1). We can use the concept of factoring quadratic expressions. The given expression is a quadratic trinomial in the form of ax^2 + bx + c, where a = 1, b = -8, and c = 9.

To factor the expression, we need to find two binomials whose product is equal to the original expression. In this case, we're looking for two binomials in the form of (x - p) and (x - q), where p and q are numbers.

To find the values of p and q, we need to consider their sum and product. The sum of p and q should be equal to the coefficient of the x term, which is -8 in this case. The product of p and q should be equal to the constant term, which is 9 in this case.

By examining the factors of 9, we can see that the only combination that satisfies these conditions is p = 9 and q = 1. Therefore, we can factor the expression as (x - 9)(x - 1).

The factored form of x^2 - 8x + 9 is (x - 9)(x - 1). This means that if we multiply (x - 9) and (x - 1) together, we will obtain the original expression x^2 - 8x + 9.

Additionally, it's worth noting that (x - 9)(x - 1) is a prime factorization of the expression. This means that the factors (x - 9) and (x - 1) cannot be further factored into linear binomials.

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We can restricted domain of the quadratic(y=x^2 +4) is {-∞,0} or {0,∞}.

What is Quadratic Equation?

Having the form ax^2 + bx + c = 0, quadratic equations are second-degree algebraic expressions. From the term "quad," which meaning square, comes the word "quadratic." A quadratic equation is a "equation of degree 2," to put it another way. A quadratic equation is employed in numerous situations.  In addition, there are many uses for quadratic equations in physics, engineering, astronomy, etc.

There are a maximum of two solutions for x in the second-degree quadratic equations. These two solutions for x are denoted as (, ) and are also known as the roots of the quadratic equations.

What is Domain?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

It cannot have an inverse function because the largest exponent is even (2), unless the domain is constrained.

We know that the vertex is at x = 0 since our equation is already in vertex form;

a(x - h)^2 + k, or 1(x - 0) + 4

In order to limit the domain to only one side of x = 0

either  {-∞,0} or {0,∞}

Therefore, We can restricted domain of the quadratic(y=x^2 +4) is {-∞,0} or {0,∞}.

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The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

depends

Step-by-step explanation:

depends on how many units are on each side of the triangular prism

the area base of triangular prism is 1/2bh

The maximum possible volume of the box is 4.5 cubic meters and this is achieved by having a square bottom of the box with a  side length of 3 cm and a height of 1/2 cm.

Volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube,  cuboid,  cone,  cylinder or  sphere. Different shapes have different volume. The formula for volume is: volume = length x width x height.

 Let the side of the base of the square  be x cm. Then the area of ​​the base would be x² square cm.

 The material needed to make the box would be the sum of the areas of the bottom and  four sides. Since the bottom of the box is square  and the sides are perpendicular to the base, the area of ​​each side is x times the height.

 So the total  area of ​​the box would be:

x² + 4 (x times height)

We know that the total  area is 16 square cm, so we can write:

x² + 4 (x times the height) = 16

We want to maximize the volume of the box. The volume of a square box  is obtained as follows:

V = x² times height

We can solve the first height equation with x:

height = (16 - x²)/(4x)

Substituting this height expression  into the volume formula, we get:

V = x² times (16 - x²)/(4x)

Simplifying this expression, we get:

V = (4x³ -\(x^4\))/16

We want to find the maximum value of V. To do this, we take the derivative of V with respect to x and set it  to zero:

dV/dx = (12x² - 4x³)/16 = 0

This gives us two solutions: x = 0 and x = 3.

 Since x represents the side of the square root, it must be positive. Therefore we choose x = 3.

 Substituting this value into the height expression, we get:

height = (16 - 3²)/(4 times 3) = 1/2

So the maximum volume of the box is:

V = 3² times 1/2 = 4.5 cubic meters

Therefore, the maximum possible volume of the box is 4.5 cubic meters and this is achieved by having a square bottom of the box with a  side length of 3 cm and a height of 1/2 cm.

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Answer:

5,260,000

Step-by-step explanation:

I don't know if this is right - you can try it!!

Answer:

opposite operation

Step-by-step explanation:

divide 35 by 5 so x=7

The value of x = 2.

Three points of collinear are A, B, and C. Here point B is between A and C.

The properties of collinear point are,

a>The slope of AB is equal to the slope of BC,

b>Line AB + BC = AC

c>The area is equal to 0.

As the three points are collinear, and from the second property we have

AB + BC= AC

Where, AB = 4x + 3

            BC = 3x + 2

So we have,

(4x + 3) + (3x + 2) =19

7x + 5=19

7x = 14

x=2

Therefore we get the value of x =2.

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The width of the rectangle is 0.9 cm to 1 d.p.

A triangle is a three-sided polygon or a three-dimensional object composed of three flat surfaces that intersect at three vertices. Triangles can be classified based on their sides and angles. Equilateral triangles have all three sides equal, isosceles triangles have two sides equal, and scalene triangles have all three sides of different lengths. Triangles can also be classified based on their angles. Right triangles have one 90-degree angle, obtuse triangles have one angle greater than 90-degrees, and acute triangles have all angles less than 90-degrees.

The circumference of the shaded face can be calculated using the formula for circumference of a circle, C = 2πr, where r is the radius of the circle. The radius of the shaded face can be found by subtracting the height of the net (h) from the radius of the cylinder (R). Therefore, the circumference of the shaded face can be calculated as follows:

C = 2π(R-h)
= 2π(2-1)
= 2π
= 6.28

The circumference of the shaded face is 6.28 cm to 1 d.p.

b) To calculate the width, w, of the rectangle, we can use the formula for area of a rectangle, A = lw, where l is the length of the rectangle. The area of the rectangle can be found by adding the area of the two semicircles (πr2) and subtracting the area of the triangular part (½bh). Therefore, the width of the rectangle can be calculated as follows:

A = lw
w = A/l
w = (2πr2+2πr2-½bh)/2(2πr)
w = (4πr2-½bh)/(4πr)
w = (8-1)/(8)
w = 7/8

The width of the rectangle is 0.9 cm to 1 d.p.

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My age is 2 years from the given condition.

Given that, if you square my age and subtract 28 times my age, the result is 60.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let x be my age.

Now, square my age is x²

28 times my age =28x

The square of my age and subtract 28 times my age, the result is 60.

x²-28x=60

⇒ x²-28x-60=0

⇒ x²+30-2x-60=0

⇒ x(x+30)-2(x+30)=0

⇒ (x+30)(x-2)=0

⇒ x=2

Hence, my age is 2 years from the given condition.

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Answer:

169 / 14

Step-by-step explanation:

7/1 + 71/14 = 7/1 * 14/14 + 71/14

= 98/14 + 71/14

= (98 + 71) / 14

= 169 / 14

So, the answer is 169 / 14

a. X follows a normal distribution (X ~ N).

b. To find the proportion of novels between 48,956 and 66,089 words, we need to calculate the z-scores for these values and find the corresponding proportions using a standard normal distribution table or calculator.

c. The 70th percentile for novels is approximately 68,467 words.

d. The middle 50% of romance novels have a word count range from approximately 46,618 to 82,134 words.

a. The distribution of X, the number of words in a randomly selected romance novel, is approximately normal (X ~ N(64376, 17133)).

b. To find the proportion of novels that are between 48,956 and 66,089 words, we need to calculate the z-scores for these values and then find the corresponding probabilities using the standard normal distribution table. Let's denote the z-scores as z1 and z2, respectively:

z1 = (48956 - 64376) / 17133

z2 = (66089 - 64376) / 17133

Using the z-scores, we can find the probabilities P(Z < z1) and P(Z < z2) from the standard normal distribution table. Then, the proportion of novels between 48,956 and 66,089 words is given by:

P(z1 < Z < z2) = P(Z < z2) - P(Z < z1)

c. The 70th percentile for novels corresponds to the value below which 70% of novels fall. To find this value, we need to find the z-score corresponding to the 70th percentile using the standard normal distribution table. Let's denote this z-score as z70. Then, we can calculate the number of words using the z-score:

Number of words = Mean + (z70 * Standard deviation)

d. The middle 50% of romance novels corresponds to the interval between the 25th and 75th percentiles. To find these values, we need to find the z-scores corresponding to the 25th and 75th percentiles using the standard normal distribution table. Let's denote these z-scores as z25 and z75. Then, we can calculate the number of words using these z-scores:

Number of words (lower bound) = Mean + (z25 * Standard deviation)

Number of words (upper bound) = Mean + (z75 * Standard deviation)

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Question isn't well formatted, however. From what can be gathered form the question :

Options are given

Answer:

4(1.5 * 16.50) + (1.5 * 9.60)

$113.40

Step-by-step explanation:

Last year:

Cost of full page ad = $16.50

Cost of half page ad = $9.60

50% increase in ad price this year :

Price, this year :

Full page = 1.50 * 16. 50 = $24.75

Half page = 1.50 * $9.60 = $14.4

Expression :

4(1.5 * 16.50) + (1.5 * 9.60)

Cost of a 4 and 1/2 page ad :

Full page = 4 * $24.75 = $99

Half page = 1 * $14.4 = $14.40

Total cost = $(99 + 14.40) = $113.40

Answer:

You cannot

Step-by-step explanation:

You cannot multiply a 2×3 matrix by a 2×2 matrix. The number of columns in the first matrix ( 3 ) is not the same as the number of rows in the second matrix ( 2 ).

Answer:

x² + 34x + 104 = 0

x² + 34x = -104

x² + 34x + ((1/2)(34))² = -104 + ((1/2)(34))²

x² + 34x + 17² = -104 + 17²

x² + 34x + 289 = 185

(x + 17)² = 185

x + 17 = +√185

x = -17 + √185

The domain will be D:{x ∈ R| x ≠ 4} and the range will be R:{y ∈ R| y ≠ 11}. Then the correct option is A.

The domain means all the possible values of x and the range means all the possible values of y.

The function is given below.

f(x) = (x² - 3x - 28) / (x + 4)

Simplify the function, then we have

f(x) = (x² - 7x + 4x - 28) / (x + 4)

f(x) = [x(x - 7) + 4(x - 7)] / (x + 4)

f(x) = [(x + 4)(x - 7)] / (x + 4)

f(x) = x - 7

The Domain of the function is all real numbers except 4. And the range of the function is all real numbers except 11.

The domain will be D:{x ∈ R| x ≠ 4} and the range will be R:{y ∈ R| y ≠ 11}. Then the correct option is A.

The diagram is given below.

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Bill enjoys collecting coins and is a member of a club for coin collectors. This club for coin collectors is an illustration of a(n) membership group.

Given that,

Bill enjoys collecting coins and is a member of a club for coin collectors, which grants him access to events and a monthly magazine. This club for coin collectors is an illustration of a(n) ________ group.

We have to fill the blank.

We know that,

Option- C is correct .

Bill enjoys collecting coins and is a member of a club for coin collectors, which grants him access to events and a monthly magazine. This club for coin collectors is an illustration of a(n) membership group.

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The relation "r" defined on the set of people, where xry if x is older than y, is not a partial ordering. The first paragraph will provide a summary of the answer, and the second paragraph will explain why the relation fails to satisfy the properties of a partial ordering.

Reflexivity: For every person x, x must be older than or equal to themselves. In this case, the relation holds true since a person is always older than or equal to themselves.

Antisymmetry: If x is older than y and y is older than x, then x and y must be the same person. However, in this case, the relation does not satisfy antisymmetry because two different people can have different ages. For example, person A can be older than person B, and person B can be older than person C, but person A and person C can still be different individuals.

Transitivity: If x is older than y and y is older than z, then x must be older than z. In this case, the relation satisfies transitivity since if person A is older than person B and person B is older than person C, then person A is older than person C.

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The MP curve initially rises to its maximum value because of the specialized nature of the fixed capital, where each additional worker's productivity rises due to the marginal product of the fixed capital.

Production Function: q = f(L,K) = 20L + 25K + 5KL - 0.03L² - 0.02K²

Given, K = 5, i.e., capital is fixed. Therefore, the total product of labor, average product of labor, and marginal product of labor are:

TPL = f(L, K = 5) = 20L + 25 × 5 + 5L × 5 - 0.03L² - 0.02(5)²

= 20L + 125 + 25L - 0.03L² - 5

= -0.03L² + 45L + 120

APL = TPL / L, or APL = 20 + 125/L + 5K - 0.03L - 0.02K² / L

= 20 + 25 + 5 × 5 - 0.03L - 0.02(5)² / L

= 50 - 0.03L - 0.5 / L

= 49.5 - 0.03L / L

MP = ∂TPL / ∂L

= 20 + 25 - 0.06L - 0.02K²

= 45 - 0.06L

The following diagram illustrates the TP, MP, and AP curves:

Figure: Total Product (TP), Marginal Product (MP), and Average Product (AP) curves

The production function demonstrates increasing marginal returns due to specialization when L is low enough, i.e., when L ≤ 750. The marginal product curve initially increases and reaches a maximum value of 45 units of output when L = 416.67 units. When L > 416.67, MP decreases, and when L = 750 units, MP becomes zero.

The MP curve's initial increase demonstrates that the production function displays increasing marginal returns due to specialization when L is low enough. This is because when the capital is fixed, an additional unit of labor will benefit from the fixed capital and will increase production more than the previous one.

In other words, Because of the specialised nature of the fixed capital, the MP curve first climbs to its maximum value, where each additional worker's productivity rises due to the marginal product of the fixed capital.

The APL curve initially rises due to the MP curve's increase and then decreases when MP falls because of the diminishing marginal returns.

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We were given a function with the following expression:

And we need to calculate the value of this function for a pair of inputs. In this case a = 4 and b = 5. So we have:

Answer:

Reciprocal

Step-by-step explanation:

That's it right there

Answer:

G. y = -\(\frac{1}{9}\)(x - 2)² -3

Step-by-step explanation:

There's this website called Desmos it has graphing calculators that will help you on these type of questions. This is not a random website so please trust me.

Answer:

  9.80 m

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationship between sides of a right triangle and its angles.

__

The geometry of this problem can be modeled by a right triangle, so these relations apply. We are given an angle and adjacent side, and asked for the opposite side, so the relation of interest is ...

  Tan = Opposite/Adjacent

Using the given values, we have ...

  tan(24°) = AC/AB = (tree height)/(distance from tree)

  tan(24°) = AC/(22 m)

Multiplying by 22 m gives ...

  tree height = AC = (22 m)·tan(24°) ≈ 9.79503 m

The height of the tree is about 9.80 meters.

Answer:

4/6 is the answer

Step-by-step explanation:

You'll make equivalent fractions by multiplying or dividing both top and bottom by the same amount. You only multiply or divide, never add or subtract, to get an equivalent fraction. Only divide when the top and bottom stay as whole numbers.

Answer:

C

Step-by-step explanation:

sorry cant really explain it i had it on a test and thats what i remeber.

The system of inequalities is 6.50x + 10y ≥ 1100 and x + y ≤ 140.

The graph is attached below

To plot the system of equations, we can first plot the lines for each equation on the same coordinate plane.

The first inequality is 6.50x + 10y ≥ 1100.

We can rewrite this in slope-intercept form as

y = (-6.50/10)x + (1100/10).

The slope of the line is -6.50/10 = -0.65

And the y-intercept is (1100/10) = 110.

The second inequality is x + y ≤ 140.

We can rewrite this in slope-intercept form as y = (-1/1)x + (140/1).

The slope of the line is -1/1 = -1

And the y-intercept is (140/1) = 140.

We can now plot these lines on the same coordinate plane.

The points of intersection are the solutions to the system of equations.

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The symmetric difference of two sets is the set of elements that are in either of the sets, but not in their intersection. In this case, the intersection of {1, 3, 5} and {1, 2, 3} is {1, 3}, so the symmetric difference is the set of elements that are in either {1, 3, 5} or {1, 2, 3}, but not in {1, 3}. This set is {2, 5}, since 2 is in {1, 2, 3} but not in {1, 3, 5}, and 5 is in {1, 3, 5} but not in {1, 2, 3}. Therefore, the symmetric difference of {1, 3, 5} and {1, 2, 3} is {2, 5}.

Step 1: Identify the two sets.
Set A = {1, 3, 5}
Set B = {1, 2, 3}

Step 2: Find the difference between the two sets.
A - B = {5} (elements in A that are not in B)
B - A = {2} (elements in B that are not in A)

Step 3: Combine the two differences to find the symmetric difference.
Symmetric Difference = A - B ∪ B - A

Your answer: The symmetric difference of {1, 3, 5} and {1, 2, 3} is {2, 5}.

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The standard deviation of customer visits yesterday for this sample of mall kiosk vendors is 1.95.

To find the standard deviation of customer visits yesterday for the sample of mall kiosk vendors, we first need to calculate the mean.

We can then use this value along with the number of customers each vendor had to calculate the standard deviation.

The mean for this sample can be calculated as follows:

Mean = (Sten + Terrance + Ulysses + Val)/4

= (9 + 8 + 13 + 9)/4 = 9.75

Now, we need to calculate the variance, which is the average of the squared differences between each data point and the mean.

The variance can be calculated using the following formula:

Variance = [(Sten - Mean)² + (Terrance - Mean)² + (Ulysses - Mean)² + (Val - Mean)²]/4

= [(9 - 9.75)² + (8 - 9.75)² + (13 - 9.75)² + (9 - 9.75)²]/4

= [0.5625 + 2.0625 + 12.0625 + 0.5625]/4

= 3.8125

Finally, the standard deviation can be calculated by taking the square root of the variance:

Standard deviation = √(Variance) = √(3.8125) = 1.95 (rounded to two decimal places)

Therefore, the standard deviation of customer visits yesterday for this sample of mall kiosk vendors is 1.95.

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