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Five less than 18 times the number x, is less than or equal to - 45. Write an inequality for this statement.

The ratio of angelfish to guppies is 5 to 2

In this question, we have the followng parameters

Fishes = 30

Goldfish = 9

Guppies = 6

The rest = angelfish

This means that

Angelfish = Fishes - Goldfish  -  Guppies

Substitute the known values in the above equation, so, we have the following representation

Angelfish = 30 - 9 - 6

Evaluate

Angelfish = 15

The ratio is then represented as

Ratio = Angelfish : Guppies

This gives

Ratio = 15 : 6

Evaluate

Ratio = 5 : 2

Hence, the ratio is 5 : 2

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Answer:

106 or 4x+18  

Step-by-step explanation:

Since Ray QR is a bisector you can determine that PRQ and QRS are equal angles (def. of a bisector). Then, what I chose to do is graph them and find where they intercept which was 22. We now know 22 is x so we can substitute it into the equation and solve to deterine that our answer is 106.

Answer:

the total of 14% of $500.00 is $70

so for 7yrs $70 X 7=$490

The amount I'll have in two years at the growth rate described is; $1.21x.

Since it follows that the savings grow by 10% each year, it can be concluded that the growth factor is; 110% = 1.1

Hence, in two years, we have;

= $x × (1.1)²

= $1.21x.

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Answer:

1.21x

Step-by-step explanation:

on rsm it says its correct

Given:

The ratio and rates:

1. 30 ft. To 60.Ft

2. 51 males to 21 females

3. 1,500 meters in 6 seconds

4. $36 for 4 rounds of shrimp

To find:

The fraction in simple terms for the given ratio and rates.

Solution:

1. 30 ft. To 60.Ft

\(\dfrac{30\text{ ft}}{60\text{ ft}}=\dfrac{1}{2}\)

2. 51 males to 21 females

\(\dfrac{51}{21}=\dfrac{17}{7}\)

3. 1,500 meters in 6 seconds

\(\dfrac{1500\text{ meters}}{6\text{ seconds}}=250\text{ meter/second}\)

4. $36 for 4 rounds of shrimp

\(\dfrac{\$ 36}{4}=\$ 9\text{ per round of shrimp}\)

Answer:

Step-by-step explanation:

Since VW = VX ; Two sides are equal, then it is an isosceles triangle.

An isosceles triangle is a triangle that has 2 equal sides and 2 equal angles.

Given: m∠V = 50° ;

Since interior angles must total 180° the remaining 2 unknown angles must have a sum of 130°.

180° - 50° = 130°

130° / 2 = 65°

m∠W = 65° and m∠X = 65°

Answer:

x=14°

SEE the IMAGE FOR SOLUTION

Answer:Child ticket sold = 30

Adult ticket sold = 50

Total ticket sold = 80

Step-by-step explanation:

The number of seconds after which the ball will hit the ground will be: 0.022 seconds when rounded to the nearest tenth.

To find the length of time, the question first requires that we obtain the values for g, Vo and H. We will proceed by using the kinematic equation that makes a relationship between the vertical displacement of an object, its initial velocity, acceleration due to gravity, and time:

y = Vo*t + (1/2)gt^2.

To obtain the value of g, we will use the value of acceleration due to gravity, which is approximately 32 ft/s^2.

Also, to find Vo, we use the initial velocity of the ball, which is 64 ft/s, and for the value of H, we use the initial vertical displacement of the ball, which is 12 ft.

When we substitute all of these figures into the first equaltion, we will have:

-12 = 64t + (1/2)gt^2

Multiplying both sides by 2 and rearranging, we get:

g*t^2 + 128t - 24 = 0

Using the quadratic formula, we get:

t = (-128 ± sqrt(128^2 - 4g(-24)))/(2*g)

t = (-128 ± sqrt(16384 + 384))/64

t = (-128 ± sqrt(16768))/64

t = (-128 ± 129.4)/64

So, t = 1.4/64 or t = -257.4/64

The negative root does not align with the value of time in reality. Therefore, the time it takes for the ball to hit the ground is: t = 1.4/64 = 0.022 seconds.

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Answer:

200

Step-by-step explanation:

Given:

0.482 x 61.2^2 ÷ √98.01

61.2^2 = 3745.44

√98.01 = 9.9

So,

0.482 × 3745.44 ÷ 9.9

= 1,805.30208 ÷ 9.9

= 182.35374545454

To one significant figure

= 200

One significant figure means only 1 non zero value and others are zero

The approximation to 1 significant figure of the result is 200

Given that:

To express     \(\dfrac{0.482 \times 61.2^2}{\sqrt{98.01}}\\\)      with approximation to 1 significant figure.

The calculations will go like this:

\(\dfrac{0.482 \times 3745.44}{\sqrt{98.01}}\\\\=\dfrac{1805.302}{9.9}\\\\\approx 182.35\\\)

Significant figure 1 means only 1 non zero digit should be present and rest places can be having zeros.

Rounding to 1 significant figure:

200

Thus, the result approximated to 1 significant figure is 200.

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Answer:

Step-by-step explanation:

90-28=62

62 is the answer

To find the total number of different routes from town A to town C, we can first find the number of different routes from A to B and then multiply it by the number of different routes from B to C. There are 7 different roads between A and B and 4 different roads between B and C. Therefore, the total number of different routes from A to C is 7 x 4 = 28.

(b) To find the total number of different routes from town A to town C and back, we can use the product rule. There are 28 different routes from A to C (as calculated in part a) and 28 different routes from C to A (since we can use any road once in each direction). Therefore, the total number of different routes from A to C and back is 28 x 28 = 784.

(c) To find the total number of different routes from town A to town C and back in part (b) that visit town B at least once, we can use the principle of inclusion-exclusion. There are 28 different routes from A to C and 28 different routes from C to A. However, we need to subtract the routes that do not visit B at all. To find this number, we can use the product rule again, since there are 5 different roads between A and C that do not go through B (2 from A to C and 3 from C to A). Therefore, the number of routes that do not visit B at all is 2 x 3 = 6. So, the total number of different routes from A to C and back in part (b) that visit B at least once is 28 x 28 - 6 = 784 - 6 = 778.

(d) To find the total number of different routes from town A to town C and back in part (b) that do not use any road twice, we can use the principle of permutations. Since we cannot use any road twice, we need to find the number of permutations of the roads. There are 7 roads between A and B, 4 roads between B and C, and 2 roads between A and C. Therefore, the total number of different routes from A to C and back in part (b) that do not use any road twice is 7P2 x 4P2 x 2P2 = 126 x 12 x 2 = 3024.

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The coordinates for H are (9,2)

What are the coordinates?

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

Here, we have

D(0, 0), E(3, 1), and F(3, 0) is similar to triangle EGH.

coordinates are (x,y) = (x+6,y+2)

F's coordinate is (3,0)

using the coordinates we get (9,2)

Hence, the coordinates of H are (9,2)

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The equation in vertex form is y = 2(x+3)² + 1. The vertex is (-3,1), the axis of symmetry is x = -3, and the direction of opening is upwards.

The vertex form of the equation is y = a(x-h)^2 + k, where (h, k) is the vertex. The axis of symmetry is x = h, and the direction of opening is determined by the value of a.

Using this formula, let us write each equation in vertex form and then identify the vertex, axis of symmetry, and direction of opening.

1. y = x² + 8x + 18

To write this equation in vertex form, we need to complete the square. y = x² + 8x + 18 is equivalent to y = (x+4)² - 2. Therefore, the equation in vertex form is y = (x+4)² - 2.

The vertex is (-4,-2), the axis of symmetry is x = -4, and the direction of opening is upwards.2

. y = -x² - 12x - 36To write this equation in vertex form, we need to complete the square. y = -x² - 12x - 36 is equivalent to y = -(x+6)² - 12. Therefore, the equation in vertex form is y = -(x+6)² - 12.

The vertex is (-6,-12), the axis of symmetry is x = -6, and the direction of opening is downwards.3. y = 2x² + 12x + 13To write this equation in vertex form, we need to complete the square. y = 2x² + 12x + 13 is equivalent to y = 2(x+3)² + 1.

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Answer:  20

Step-by-step explanation:

Answer:

The main aim of public participation is to encourage the public to have meaningful input into the decision-making process. Public participation thus provides the opportunity for communication between agencies making decisions and the public. Public participation can be time-consuming and sometimes expensive.

Step-by-step explanation:

The maximum rate of change of f at (0, 5) is 45, and it occurs in the direction of the vector ⟨1, 0⟩.

To find the maximum rate of change of a function, we need to calculate the gradient vector (∇f) and evaluate it at the given point. The gradient vector represents the direction of the steepest ascent of the function at that point, and its magnitude gives the rate of change.

First, we find the gradient vector of f(x, y) by taking the partial derivatives with respect to x and y:

∂f/∂x = 9y cos(xy)

∂f/∂y = 9x cos(xy)

Evaluating these partial derivatives at the point (0, 5), we get:

∂f/∂x(0, 5) = 9(5)cos(0) = 45

∂f/∂y(0, 5) = 9(0)cos(0) = 0

The maximum rate of change occurs in the direction of the gradient vector (∇f) at (0, 5), which is given by ⟨∂f/∂x, ∂f/∂y⟩. Therefore, the direction vector is ⟨1, 0⟩.

Hence, the maximum rate of change of f at (0, 5) is 45, and it occurs in the direction of the vector ⟨1, 0⟩.

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The correct answer is c. Inferential Statistics.

Inferential statistics is the branch of statistics that allows for drawing conclusions about a population based on the information collected from a sample. When conducting research or surveys, it is often impractical or impossible to collect data from an entire population.

Instead, a representative sample is chosen, and inferential statistics are used to make inferences or predictions about the larger population. By analyzing the characteristics and patterns observed within the sample, inferential statistics enable researchers to make generalizations or draw conclusions about the population as a whole.

This process involves applying various statistical techniques, such as hypothesis testing and confidence intervals, to estimate population parameters and assess the reliability of the conclusions. Magnitude statistics, central tendency, and effect size are important concepts in statistics, but they do not specifically address the ability to draw population-level conclusions from sample data.

Magnitude statistics focuses on the size of the effect or relationship between variables, central tendency measures summarize the central values of a dataset, and effect size quantifies the strength of an effect or relationship.

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Answer:

-4

Step-by-step explanation:

f(-1) = 2(-1) - 2 = -4

Answer: \(4a^4+4b^4-8a^3b+8ab^3-13a^2b^2\)

Step-by-step explanation:

\(4(a^2-b^2)^2-8ab(a^2-b^2)-5a^2b^2\)

First, solve the square binomial.

\(4((a^2)^2-2(a^2)(b^2)+(b^2)^2)-8ab(a^2-b^2)-5a^2b^2\)

\(4(a^4-2a^2b^2+b^4)-8ab(a^2-b^2)-5a^2b^2\)

Now, distribute the 4 and 8ab respectively.

\(4a^4-8a^2b^2+4b^4-8a^3b+8ab^3-5a^2b^2\)

Combine like terms. (I'll group them so that you can see them more clearly)

\(4a^4+4b^4-8a^3b+8ab^3+(-8a^2b^2-5a^2b^2)\)

\(4a^4+4b^4-8a^3b+8ab^3+(-13a^2b^2)\)

\(4a^4+4b^4-8a^3b+8ab^3-13a^2b^2\)

Answer:

(2a²-2b²+a²b²)(2a²-2b²-5a²b²)

Step-by-step explanation:

4(a²-b²)²-8ab(a²-b²)-5a²b²

Let's replace 2(a²-b²)= m and a²b²=n for simplicity

then we have

Now we can replace m and n with initial values:

The prove that BOC = 90° + A/2. is given below:

Note that, bisectors of angles B and C and that of a triangle ABC is one that pass across each other at the point O.

Hence: one need to to prove that ∠BOC = 90° + A/2

Since:

BO is said to be the bisector of angle B e.g. ∠OBC = (∠1)

CO is said to be the bisector of angle C e.g.  ∠OCB = (∠2)

Looking at the triangle BOC, to interpret  by the use of angle sum property, then:

∠OBC + ∠BOC + ∠OCB = 180°

∠1 + ∠BOC + ∠2 = 180° ---- ( equation 1)

Looking at triangle ABC and by the use of angle sum property, So;

∠A + ∠B + ∠C = 180°

∠A + 2(∠1) + 2(∠2) = 180°

Then we divide by 2 on the two sides, and it will be:

∠A/2 + ∠1 + ∠2 = 180°/2

∠A/2 + ∠1 + ∠2 = 90°

∠1 + ∠2 = 90° - ∠A/2 ---(equation 2)

Then one need to Substitute (2) in (1), So:

∠BOC + 90° - ∠A/2 = 180°

∠BOC - ∠A/2 = 180° - 90°

∠BOC - ∠A/2 = 90°

Hence , ∠BOC = 90° + ∠A/2

Therefore, from the above, we care able to prove that BOC = 90° + A/2.

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Mrs. Bernard can take her son to the trampoline park for up to 3.64 hours, as long as she spends no more than $20.

An equation is a mathematical statement that expresses two expressions using an equals sign (=). It is used to show the relationship between the two expressions, which can be numbers, variables, or a combination of both. An equation is often used to solve for a particular unknown value, such as the slope of a line or the solution to a problem. Equations can also be used to express an idea, such as the Laws of Motion in Physics.

To solve this equation, we need to rearrange the equation so that it reads 3x + 5.50 < 20. Once rearranged, we can solve for x, which equals 3.64. This means Mrs. Bernard can take her son to the trampoline park for 3.64 hours, as long as she spends no more than $20.

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Answer:

honest or no?

Step-by-step explanation:

To find the probability that a survey participant named another color, we need to calculate the percentage of women who named another color.

First, let's calculate the total percentage of women who named the given colors:

Blue: 18%

Red: 15%

Green: 15%

Yellow: 12%

Black: 13%

The sum of these percentages is: 18% + 15% + 15% + 12% + 13% = 73%

To find the percentage of women who named another color, we subtract this sum from 100% (the total):

100% - 73% = 27%Therefore, the probability that a survey participant named another color is 27%.

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Binding constraints directly influence the optimal solution in a linear Programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution.

binding constraints and positive slack in the context of linear programming. In a linear programming problem, we aim to find the optimal solution for an objective function, given a set of constraints. The terms "binding constraints" and "positive slack" are related to these constraints.

1. Binding constraints: These are constraints that directly impact the optimal solution of the problem. In other words, they "bind" the feasible region (the area where all the constraints are satisfied) and affect the maximum or minimum value of the objective function. Binding constraints are active constraints, as they influence the final solution.

2. Positive slack: Slack is the difference between the left-hand side and right-hand side of a constraint when the constraint is satisfied. If this difference is positive, it means that there is some "extra" or "unused" resource in that constraint. Positive slack indicates that the constraint is non-binding, meaning it does not directly impact the optimal solution. It shows that there is some room for the constraint to be further tightened without affecting the final outcome.

In summary, binding constraints directly influence the optimal solution in a linear programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution. Knowing the difference between these terms can help you better understand and analyze linear programming problems.

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Answer:

16

Step-by-step explanation:

3×6=18

12÷6=2

18-2=16

A) The correct features is,

⇒ a = 9000

⇒ r = 15%

B) The equation correctly models the context of the problem is,

⇒ y = 9000 (0.85)ˣ

We have to given that;

Tiffany’s mother bought a car for $9000 five years ago.

And, She wants to sell it to Tiffany based on a 15% annual rate of depreciation.

Now, We have;

the exponential growth formula is,

⇒ y = a(1 − r)ˣ

Here, We have;

⇒ a = 9000

⇒ r = 15%

Thus, We get;

The equation correctly models the context of the problem is,

⇒ y = a(1 − r)ˣ

⇒ y = 9000 (1 - 0.15)ˣ

⇒ y = 9000 (0.85)ˣ

Therefore, We get;

A) The correct features is,

⇒ a = 9000

⇒ r = 15%

B) The equation correctly models the context of the problem is,

⇒ y = 9000 (0.85)ˣ

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Answer: 18pi + 36 + (36-4.5pi)+4.5pi= 22.5pi + 36 + (36-4.5pi)

Step-by-step explanation:

CDEF is a square so all sides of CDEF are 6cm.

This tells us the area of CDEF which is 36cm squared

This tells us the radius of AE which is the side FE which we know is 6cm.

Area of a half circle= pi x r squared/2

Area of AE= pi x 36/2= 18pi

Now, look at the square with the half circle inside ABCF. If the half circle was part of the shaded square, the area would be 36cm squared. But since it isn't we need to minus the area of the half circle from 36cm square (area of ABCF)

Area of half circle BC= pi x 3 squared/2= pi x 9/2= 4.5pi.

So the area of ABCF is 36-4.5pi.

CD would also have an area of 4.5pi as it is the exact same half circle.

Area of AE=18pi cm squared

Area of CDEF= 36cm squared

Area of ABCF= 36-4.5pi

Area of CD= 4.5pi

18pi+36+(36-4.5pi)+4.5pi

simplified to:

22.5pi + 36 + (36-4.5pi)