City worker drain a community pool that contains 403,920 gallons of water. The pump they use removes water at a rate of 40 cubic feet per minute. One cubic foot of water contains 7.48 gallons how long in hours will it take to remove all the water from the pool

The fields in which Trigonometry is well applied and their explanations are as explained below.

The three fields that trigonometry is useful are as described below;

1) In construction;

Trigonometry is useful in Construction field because it can be used in measurement of walls parallel and perpendicular; Installing ceramic tiles; Roof inclination; the height of the building, the width length e.t.c. It is also useful in finding roof slopes, ground surfaces, sun shading and light angles.

2) In marine biology;

Marine biologists utilize trigonometry to establish measurements. For instance, when trying to find out the manner in which light levels at different depths affect the ability of algae to photosynthesize. Trigonometry is used in finding the distance between celestial bodies. Marine biologists also use it to create mathematical models to measure and understand sea animals and their behavior.

3) In criminology:

In criminology, trigonometry is useful in calculating a projectile’s trajectory in order to estimate the possible cause of a collision in a car accident or the manner in which an object fall down or in which angle a bullet was shot etc.

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Answer:

Where is the formula

Step-by-step explanation:

Answer:

D. 115

Step-by-step explanation:

because if Angle 6 is 115 then so is Angle is 4 due to AIA (alternate Interior Angles)

Answer: 8

Step-by-step explanation:

We know that scale factor = (image)/(preimage).

Substituting in what we have,

[tex]5=\frac{R'S'}{RS}\\\\5=\frac{40}{RS}\\\\RS=\boxed{8}[/tex]

Answer:

Step-by-step explanation:

We know that r's't' was formed by a scale factor of 5.

This means rst was multiplied by 5 to create r's't'.

Dividing the sides of r's't' by 5 will give us the sides of the

pre-image.  If r's' = 40 - dividing 40 by 5 = 8.

So rs is 8.

Answer:

25 minutes

150 gallons

Step-by-step explanation:

Definition of variables

Let t = time in minutes

Let V = volume in gallons

Create two equations with the given information:

Pool A

⇒ V = 300 - 6t

Pool B

⇒ V = 400 - 10t

To find after how many minutes the two pools will have the same amount of water, substitute the equation for pool A into the equation for pool B and solve for t:

⇒ 300 - 6t = 400 - 10t

⇒ 300 - 6t + 10t = 400 - 10t + 10t

⇒ 300 + 4t = 400

⇒ 300 + 4t - 300 = 400 - 300

⇒ 4t = 100

⇒ 4t ÷ 4 = 100 ÷ 4

⇒ t = 25

Therefore, the two pools will have the same amount of water after 25 minutes.

To find how much water will be in the pools at that time, substitute the found value of t into one of the equations and solve for V:

⇒ V = 400 - 10t

⇒ V = 400 - 10(25)

⇒ V = 400 - 250

⇒ V = 150

Therefore, the amount of water in the pools at the time when they have the same amount of water is 150 gallons.

If time be x and volume be y

The equations are

Equate and solve

Now

Answer:

m∠1 = 50°

m∠2 = 130°

Step-by-step explanation:

There is a formula:

[tex]\text{angle} = \frac{1}{2} (\text{intercepted arc}_1 + \text{intercepted arc}_2)[/tex]

[tex]\text{m} \angle 1 = \frac{1}{2} (53^\circ + 47^\circ)[/tex]

[tex]\text{m} \angle 1 = \frac{1}{2} (100^\circ)[/tex]

[tex]\text{m} \angle 1 = 50^\circ[/tex]

Angle 1 and angle 2 together form a straight angle, which measures 180°. Angle 1 and angle 2 are suplementary angles.

[tex]\text{m} \angle 1 + \text{m} \angle 2 = 180^\circ[/tex]

[tex]50^\circ + \text{m} \angle 2 = 180^\circ[/tex]

[tex]\text{m} \angle 2 = 180^\circ - 50^\circ[/tex]

[tex]\text{m} \angle 2 = 130^\circ[/tex]

Answer: B

Step-by-step explanation:

[tex]P(x) Q(x)=R(x) \implies Q(x)=\frac{R(x)}{P(x)}\\\\Q(x)=\frac{2x^{3}+2x^{2}+3x+3}{x+1}={2x^{2}(x+1)+3(x+1)}{x+1}=\boxed{2x^{2}+3}[/tex]

After transferring $450 from the savings account to the checking account, the updated balance in :

All of that is based on the notion that Sarah's savings and checking accounts are distinct from one another.

Assume that, Sarah's savings account balance was 'x' and checking account balance was 'y'.

She transferred $450 from the savings to the checking account.

∴Updated savings account balance= x-450 units

∴Updated checking account balance= y+ 450 units.

Therefore, it can be concluded that the current value of Sarah's savings account would be the amount >$450, and the updated value of her checking account would be the balance <$450 if she transferred $450 from her savings account to her checking account.

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The best-fitting regression model for the scatter plot is exponential curve , Option C is the right answer.

The missing graph is attached with the answer.

An exponential graph is given by y = aˣ , the graph for an exponential growth is also attached with the answer,

From the graph given in the question it can be concluded that it is not linear , not quadratic and it is not true that it doesn't have a pattern , It is an exponential growth graph, Therefore Option C is the right answer.

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Step-by-step explanation:

-10-2x = 3x+15

5x = -25

x= -5

Answer:

B.

Step-by-step explanation:

The product of means that you're multiplying, which means that you need to use parentheses. That narrows it down to B or D. Since the question asks you to provide a number first (x) and then 11, that means that 11 will be subtracted from the number.

Answer:

the answer is L

Step-by-step explanation:

that's just how u round

[tex]\textsf {21 cm}[/tex]

[tex]\textsf {If it is correct to the nearest centimeter, then the least side length}\\\textsf {would be 8 - 1 = 7 cm. }[/tex]

[tex]\textsf {Then, the least possible perimeter would be :}[/tex]

[tex]\mathsf {7 \times 3}[/tex]

[tex]\textsf {21 cm}[/tex]

[tex] \sf \underline{Answer:}

[/tex]

Pick any value for x, like x = 0, plug it into the equation, and get the value for y. For x = 0,

2(0) + y = 5

y = 5

The ordered pair is (0,5). Find other ordered pairs using the same reasoning.

[tex]2(0) + y = 5[/tex]

[tex]y = 5[/tex]

The value of (abscissa of P) -(abscissa of Q) is -1.

The given coordinates are P(4,6) and Q(5,-7).

We need to find (abscissa of P) -(abscissa of Q).

The horizontal coordinate of a point in a planar Cartesian coordinate system that is determined by measuring parallel to the x-axis is what abscissa stands for.

Now, (abscissa of P) -(abscissa of Q)=4-5=-1

Hence, the value of (abscissa of P) -(abscissa of Q) is -1.

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(-5, 2) is the only point which we plot in given graph then it still represent a function.

A function is a special type of relation in which each and every element of set A have a unique image in its codomain set B.

Here, Given points on graph

{(-4, 2), (-2, -3), (2, 3), (3, -1)}

2 and -2 are already available in given ordered pair.

so only (-5, 2) is the only option which satisfies the definition of function.

Thus, (-5, 2) is the only point which we plot in given graph then it still represent a function.

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The central tendency of the given data will be 22.79.

Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.

There are 3 ways in which we can express the centre of the data given: (1) mean or average, (2) mode, (3) median

For the mean, we sum up all the given and divide them by the number of data

mean = 433 / 19 = 22.79

For the mode, we just determine which among the given data appears more frequently and in this given that is 23.

For the median, we arrange the numbers from highest to lowest and determine which number will appear in the centre. Since there are 19 data, we need to find which among them will appear to be the 10th. That is also 23.

So, the value that would best describe the central tendency is 23. Since the values to the left of 23 are more scattered than those to its right, the distribution exhibits negative.

Therefore central tendency of the given data will be 22.79.

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The simplified radical for the given equation is 2√3.

The given equation is [tex]\frac{3}{x} =\frac{x}{4}[/tex].

Radical of any number is the same as the root of the number. The root can be a square root, cube root, or in general, it is nth root. Thus, any expression or number that uses a root is known as a radical.

To compute for the values of x given the proportion, we can cross-multiply both sides of the equation as follows:

[tex]\frac{3}{x} =\frac{x}{4}[/tex]

⇒x×x=3×4

⇒x²=12

⇒x=±√12

From this, we can see that the solutions for the equation are the positive and negative roots of 12.

By simplifying the radical, we get √12 = √(2² x 3) = 2√3

Therefore, the simplified radical for the given equation is 2√3.

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Answer:

if a line is parallel they have the same slope

so the slope is 5

Hope This Helps!!!

Answer:

y = 2x - 1

Step-by-step explanation:

gradient is defined as rise over run.

we need coordinates that are both whole numbers. from looking at the graph, I have (0, -1) and (1, 1)

for the run, 1 - 0 = 1

for the rise, 1 - -1 = 2

2 / 1 = 2

it crosses the y-axis at -1

therefore in the form y = mx + b, the equation is y = 2x - 1

Answer:

t= 31/175 ≈ 5.64516129

​

Step-by-step explanation:

Refer Pic For Steps....

Hope it Helps!!!

3 packages of bread would produce more utility than 2 jars of jam

The marginal utility function of jam is given as:

f(x) = 55 - 4x

Integrate the above function to determine the total utility function

f'(x) = 55x - 2x^2

Hence, the total utility function of the jam is f'(x) = 55x - 2x^2

The marginal utility function of bread is given as:

g(x) = 37 - x

Integrate the above function to determine the total utility function

g'(x) = 37x - 0.5x^2

Hence, the total utility function of the bread is g'(x) = 37x - 0.5x^2

We have:

Jam = 2 jars

Bread = 3 packages

Substitute 2 for x in f'(x) = 55x - 2x^2

f'(2) = 55 * 2 - 2 * 2^2

f'(2) = 102

Substitute 3 for x in g'(x) = 37x - 0.5x^2

g'(3) = 37 * 3 - 0.5 * 3^2

g'(3) = 106.5

106.2 is greater than 102

Hence, 3 packages of bread would produce more utility

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Answer:

Discount=$8.7

Selling price=$49.3

Step-by-step explanation:

First you need to write that in an equation form-

a/58=15/100

Then you need to do cross multiplication-

100a=58(15)

100a=870

Now divide 100 from both sides-

100a/100=870/100

a=8.7

Thats the discount rate

Now subtract that from the original price

58-8.7=49.3

Thats the price after the discount

Hope this helped :)

Answer:

A

Step-by-step explanation:

y = - 2x + 5 → (1)

y = x² + 3x + 9 → (2)

substitute y = x² + 3x + 9 into (1)

x² + 3x + 9 = - 2x + 5 ( subtract - 2x + 5 from both sides )

x² + 5x + 4 = 0 ← in standard form

(x + 1)(x + 4) = 0 ← in factored form

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x + 4 = 0 ⇒ x = - 4

substitute these values into (1) for corresponding values of y

x = - 1 : y = - 2(- 1) + 5 = 2 + 5 = 7 ⇒ (- 1, 7 )

x = - 4 : y = - 2(- 4) + 5 = 8 + 5 = 13 ⇒ (- 4, 13 )

The boat's travel from when it was first noticed until it stopped is 554.89 ft.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly.

From the given information we can draw a right-angle triangle.

14°52' = 14 + 0.86 = 14.86 degree

45°10' = 45 + 0.16 = 45.16 degree

In the right-angle triangle ACD

tan14.86 = 200/AC

AC = 753.772 ft

In the right-angle triangle DBC:

tan45.16 = 200/CB

CB = 198.886 ft

AB = AC - CB

AB =  753.772 ft - 198.886 ft

AB = 554.886 ≈ 554.89 ft

Thus, the boat's travel from when it was first noticed until it stopped is 554.89 ft.

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There are 5 students who are 65 inches or taller. Option C is correct.

Height is defined as the vertical distance between an object's top and bottom. It is measured in centimeters, millimeters, meters, and other units.

The term "height" is frequently used to describe someone's or something's height.

The height of the student in the Spanish class in the data set;

65, 63, 67, 59, 73, 60, 68, 61, 64, 60, 69

Student's heights are 65 inches or taller from the data set are;

65,67,73,68,69

There are 5 students who are 65 inches or taller.

Hence, option C is correct.

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Step-by-step explanation:

x | y

-2.| 13

-1. | 15

0. | 17

1. | 19

2. | 21

just start with the y-intercept and then add 2 or subtract two depending on whether your increasing x or decreasing x. as x increases 1 y increases 2.

Answer:

Vertical angles are always congruent

Step-by-step explanation:

Answer:

Statement

Measure of angle 2 and 3 are a linear pair and

Reason

Definition of linear pair

Step-by-step explanation:

Hook me up with a 5 star and a Thanks :)

Answer:

2 1/4

Step-by-step explanation:

Half of 4 is 2 and half of 1/2 is 1/4 so half of 4 1/2 is 2 1/4

The value of h is -1.5 if the graph shows the function f(x)= |x-h| + K or f(x) = |x + 1.5| - 3.5.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a function:

f(x) = |x - h| + k is shown in the graph.

The above function is a transformation of a parent function:

F(x) = |x|

After applying transformation we get:

f(x) = |x + 1.5| - 3.5

On comparing:

h = -1.5

k = -3.5

Thus, the value of h is -1.5 if the graph shows the function f(x)= |x-h| + K or f(x) = |x + 1.5| - 3.5.

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