Swimming Pool On a certain hot summer's day, 631 people used the public swimming pool. The daily prices are $1.25 for children and $2.00 for adults. The receipts for admission totaled $1013.00. How many children and how many adults swam at the public pool that day?​

They are intersecting

a) Not parallel because they share different slopes

b) Not perpendicular, they dont intersect creating a right angle. This is because neither of the slopes are a reciprocal of each other.

The angle measures are given as follows:

Two angles are called supplementary when the sum of their measures is of 180º.

On a trapezoid, consecutive interior angles are supplementary, hence the pairs of supplementary angles are given as follows:

Hence the value of y is obtained as follows:

y + 145 = 180

y = 35º.

(as the two angles are supplementary we know that the sum of their measures is of 180º).

The value of x is obtained as follows:

x + 62 = 180

x = 118º.

(as the two angles are supplementary we know that the sum of their measures is of 180º).

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Answer:

To find the efficiency of the ramp, we need to compare the work output to the work input. Work input is the force applied to the ramp multiplied by the distance over which the force is applied, and work output is the weight of the box multiplied by the distance it is lifted.

The force applied to the ramp is 600 N, and the distance over which it is applied is the length of the ramp, which is 2.5 m. So the work input is:

work input = force x distance = 600 N x 2.5 m = 1500 J

The weight of the box is 1200 N, and the distance it is lifted is 1.0 m (the height of the truck). So the work output is:

work output = weight x distance = 1200 N x 1.0 m = 1200 J

The efficiency of the ramp is the ratio of work output to work input:

efficiency = work output / work input = 1200 J / 1500 J = 0.8 = 80%

So the efficiency of the ramp is 80%.

To find the mechanical advantage of the ramp, we need to compare the output force to the input force. The output force is the weight of the box, which is 1200 N. The input force is the force applied to the ramp, which is 600 N.

So the mechanical advantage of the ramp is:

mechanical advantage = output force / input force = 1200 N / 600 N = 2

So the mechanical advantage of the ramp is 2.

Answer: The answer is the letter B

Step-by-step explanation:

Mean is the overall average of numbers or books and range is the length from greatest to least

Answer:

300.20

Step-by-step explanation:

because it was a nice guesss

Answer:

4 cats

Step-by-step explanation:

Let b represent birds and c represent cats

b = c + 3

c + b = 11

c + (c + 3) = 11

2c + 3 = 11

2c = 8

c = 4.

John has 4 cats

b = (4) + 3

b = 7

John has 7 birds

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Answer:

3.465 x 10⁸ hours

or

346,500,000 hours

Step-by-step explanation:

Distance to travel to star = 9.5 x 10¹² kilometers

1 kilometer = 0.62mile

Therefore

9.5 x 10¹² km = 9.5 x x 10¹ x 0.6 miles
= 5.89 x 10¹² miles

Speed of satellite = 17,000 mph

In scientific notation
17,000 = 17 x 10³ = 1.7 x 10⁴ mph

Time taken to reach star at distance of 5.89 x 10¹² miles

= 5.89 x 10¹² miles/1.7 x 10⁴ mph = 5.89/1.7  x 10¹²/10⁴

= 3.465 x 10¹²⁻⁴

= 3.465 x 10⁸ hours

= 346,500,000 hours

Answer: N′(−7, −2), M′(−4, −1), O′(−7, −5)

Step-by-step explanation:

im right and youre wromng

The correct statement regarding the limit of f(x) as x -> 1 is given as follows:

lim x -> 1 f(x) = -∞.

To obtain lateral limits, we need to take the limit of a function as it approaches a point from the left-hand side and the right-hand side separately.

If the two limits are equal, then this is the limit of the function, while if the lateral limits are different, then the limit of the function does not exist for the value of x.

From quadrant 2, the function approaches x = 1 on quadrant 4, hence the limit to the left is given as follows:

lim x -> 1^- f(x) = -∞.

A graph approaches x = 1 in quadrant 1, and curves down and approaches the x-axis in quadrant 1, hence the limit to the right is given as follows:

lim x -> 1^+ f(x) = -∞.

As the lateral limits are equal, the limit of the function is given as follows:

lim x -> 1 f(x) = -∞.

The problem describes the graph of the function.

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The monthly decay factor is 0.0733 of the four-wheeler, and the equation is x = P(D)ˣ.

Depreciation is an important subject in finance and economics since it is used to determine an asset's worth over time. For accounting and financial reporting needs, it enables people and businesses to monitor the fall in the value of their assets. Depreciation may be utilised to lower taxable income, which in turn lowers tax liabilities, hence it also plays a part in tax legislation.

The yearly decay factor is given as:

yearly decay factor = 1 - depreciation rate

yearly decay factor = 1 - 0.12

yearly decay factor = 0.88

Divide the yearly decay factor by 12:

monthly decay factor = yearly decay factor / 12

monthly decay factor = 0.88 / 12

monthly decay factor = 0.0733

n equivalent equation using the monthly decay factor as follows:

value after x months = initial value x (monthly decay factor)ˣ

x = P(D)ˣ

Hence, the monthly decay factor is 0.0733 of the four-wheeler, and the equation is x = P(D)ˣ

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72 items were checked to work correctly.

What is the solution of algebraic expression?

Finding the value of the variable is part of solving an algebraic statement. We must do certain algebraic operations to determine the value of one of the variables in the linear equations before we can substitute that value to get the value of another variable.

Then the percentage of defective items in the checked batch is x + 3%.

We know that out of 300 items, this percentage represents the number of defective items. So we can write:

(x + 3%) * 300 = number of defective items

Simplifying this equation, we get:

3x + 9 = number of defective items

number of items checked - number of defective items = number of items checked to work correctly

Substituting the equation we derived above for the number of defective items, we get:

300 - (3x + 9) = number of items checked to work correctly

Simplifying this equation, we get:

291 - 3x = number of items checked to work correctly

3x = number of defective items in a batch of 300 items with the normal percentage of defects

Substituting this expression for the number of defective items in our previous equation, we get:

291 - 3x = number of items checked to work correctly

Now we can solve for x:

3x = number of defective items in a batch of 300 items with the normal percentage of defects = x/100 * 300

3x = 3 * (300 - number of items checked to work correctly - number of defective items)

3x = 900 - 3(3x + 9)

3x = 900 - 9x - 27

12x = 873

x = 73

So the normal percentage of defective items is 73%.

Now we can find the number of items checked to work correctly:

291 - 3x = 291 - 3(73) = 72

Therefore, 72 items were checked to work correctly.

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The equation of the conic section shown below is x² + y² + 10x + 2y - 20 = 0

A circle is a two-dimensional geometric shape that consists of a set of points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius.

A circle can be defined by its center point and radius or by its circumference, which is the distance around the perimeter of the circle. The circumference of a circle can be calculated using the formula:

C = 2πr

where C is the circumference, r is the radius, and π (pi) is a mathematical constant approximately equal to 3.14.

The center of the circle is (-5,-1) and its radius is the distance from the center to any point on the circle. Using the distance formula, we can find the radius:

r = √((0 - (-1))² + (-10 - (-5))²) = √(1 + 25) = √(26)

So, the equation of the circle in standard form is:

(x + 5)² + (y + 1)² = 26

Alternatively, in general form, it can be written as:

x² + y² + 10x + 2y - 20 = 0

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Answer:

Let's denote the speed of the second car as x (in miles per hour). Then the speed of the first car is 12 miles per hour faster, which is x + 12.

We know that both cars traveled the same amount of time, so we can use the formula:

distance = speed × time

For the first car, we have:

234 = (x + 12) × time

For the second car, we have:

180 = x × time

We want to find the speeds of both cars, so we need to solve for x and x + 12. We can start by solving for time in both equations:

time = 234 / (x + 12)

time = 180 / x

Since both expressions are equal to time, we can set them equal to each other:

234 / (x + 12) = 180 / x

To solve for x, we can cross-multiply and simplify:

234x = 180(x + 12)

234x = 180x + 2160

54x = 2160

x = 40

Therefore, the speed of the second car is 40 miles per hour, and the speed of the first car is x + 12 = 52 miles per hour.

Step-by-step explanation:

Answer:

Let x = speed of first car x + 12 = speed of second

Step-by-step explanation:

Answer: :)

Step-by-step explanation:

To find the angle that the ramp makes with a horizontal line, we need to use trigonometry. The angle we are looking for is the angle between the ramp and the ground, which is the same as the angle between the hypotenuse of a right triangle (the ramp) and its adjacent side (the ground).

We can use the tangent function to find this angle:

tan(theta) = opposite/adjacent

In this case, the opposite side is the height of the ramp (4.1 feet) and the adjacent side is the length of the ramp along the ground (6 feet). So we have:

tan(theta) = 4.1/6

Using a calculator, we can solve for theta:

theta = tan^-1(4.1/6)

theta ≈ 34.3°

Therefore, to the nearest tenth of a degree, the measure of the angle that the ramp makes with a horizontal line is 34.3°.

Answer:

x = 5.5

Step-by-step explanation:

2x + 3 - 4 = 10

2x - 1 = 10

2x = 11

x = 5.5

Let's check

2(5.5) + 3 - 4 = 10

11 + 3 - 4  = 10

14 - 4 = 10

10 = 10

So, x = 5.5 is the correct answer.

Answer: x = 5.5

Step-by-step explanation:

To solve, we will isolate the variable x.

      Given:

             2x + 3 - 4 = 10

      Combine like terms on the left side:

             2x - 1 = 10

      Add 1 to both sides of the equation:

             2x = 11

      Divide both sides of the equation by 2:

             x = 5.5

If the bacteria in a dish that contains 2 bacteria quadruple every 16 minutes can be represented by the expression 2×4t/16, an equivalent expression for the number of bacteria in the dish for any time, t, in minutes is B. 8t/16.

An equivalent expression depicts two algebraic expressions that have the same value when the values for the variables are plugged in.

An algebraic expression is the combination of variables, values, constants, and numbers using mathematical operands without the equal symbol (=).

2×4t/16 = 8t/16

2×4t/16 ≠ 4t8

2×4t/16 ≠ 2×2t8

2×4t/16 ≠ 4×2t16

Thus, 2×4t/16 = 8t/16 as equivalent expressions.

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Therefore , the solution of the given problem of trigonometry comes out to be  it is roughly 5193 feet from pier A to the coral reef.

Relationships between mathematics but also cubic splines When the different fields were combined, astrophysics is thought to have been born in the third century BC. With the aid of exact angle mathematical techniques, many metric issues can be resolved or the outcomes of calculating them can be ascertained. The study of the six fundamental trigonometric formulas is known as trigonometry.

Here,

The north-south distance from pier A to the coral reef, x sin(31°37′), is the other side of the triangle (relative to angle ). The east-west path from dock A to the edge of the coral reef, which is equal to x cos(31°37′), forms the opposite side of the triangle. We're looking for x's number.

The Pythagorean theory allows us to write:

=> (x cos(31°37′) + 2599) + (x sin(61°37′)) = (x sin(31°37′))

By condensing and rearrangeing, we obtain:

=> x² - 5198x + 6790401 = 0

We can use the quadratic formula to answer the following quadratic equation:

=> x = (-(-5198) ± √(-5198)^2 - 4(1)(6790401))) / (2(1))

=> x = (5198 + √(26857604)) / 2

=> x = (5198 ± 5188) / 2

=> x = 5193 or x = 5

The negative answer x = 5 does not make logic in this situation because x is a measure of distance. Consequently, it is roughly 5193 feet from pier A to the coral reef.

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Answer:

Step-by-step explanation:

5*x+11=36

5*x=36-11

x=25/5

x=5

5 is the answer

Hey there!

Guide to follow

• Product = multiply/multiplication
• Sum = add/addition
• Quotient = divide/division
• Difference = subtract/subtraction

• Is = equal to/equivalent to

Question reads….
“The product of a 5 and a number plus 11 is 36”

We are not sure what the unknown number is, so we will label it as “w”

Your equation:

5 * w + 11 = 36

SOLVING for the answer to the equation:

5 * w + 11 = 36
5w + 11 = 36

SUBTRACT to both sides

5w + 11 - 11 = 36 - 11

SIMPLIFY it

5w = 25

DIVIDE 5 to BOTH SIDES

5w/5 = 25/5

SIMPLIFY it

w = 25/5

w = 5

Therefore, your unknown number should be: 5

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The required value of x for the given figure is 2√7 units.

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular edges. The foundation of geometry is the relationship between the sides and other angles of the right triangle.

In the given figure we have two triangle big and small triangle.

To find the value of x;

first we use Pythagoras theorem in big triangle.

So; let base of big triangle is b

9² = 7² + b²

b² = 81 - 49

b = √32

Now in small triangle;

(√32)² = x² + 2²

32 = x² + 4

x² = 28

x = √28

x = 2√7 units.

Thus, required value of x is 2√7 units.

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By similarity ratio of triangles, we have;

ΔPQR ∼ ΔPSR ∼ ΔRSQ

PS/PR = PR/PQ

PQ/RQ = RQ/SQ

Similar triangles are defined as triangles that have the same shape, but their sizes may vary. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Thus, applying the concept of similar triangle ratio we can say that;

ΔPQR ∼ ΔPSR ∼ ΔRSQ

Similarly, by similarity ratio of triangles, we have;

PS/PR = PR/PQ

We also have;

PQ/RQ = RQ/SQ

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The value of the ratio g(24)/g(21) is 729, and other solutions are shown below

The domain and the range of h(n)

Given that

h(n) is the number of houses

The possible values of n and h(n) are whole numbers

So, we have

The values of h(5) and h(11)

Based on the patterns in the sequence, we have

h(n) = n

So, we have

h(5) = 5

h(11) = 11

The explicit function of h(n)

In (b), we have

h(n) = n

The values of s(4) and s(7)

Given that

s(n) is the number of segments

Based on the patterns in the sequence, we have

s(n) = 2n

So, we have

s(4) = 8

s(7) = 14

The growth pattern of s(n)

Above, we have

s(n) = 2n

The above equation is a proportional equation

This means that

The growth pattern of s(n) is linear, with a constant rate of change

The explicit function of s(n)

Above, we have

s(n) = 2n

Complete the table for f(5) and f(7)

From the table, we can see that

As n increases, the value of f(n) is divided by 2 to get the next term

So, we have

f(5) = 2/2 = 1

f(7) = 1/2/2 = 1/4

The domain of f(n)

The possible values of n are real numbers

So, we have

Domain: All set of real numbers

The observation of the function

Above, we have

As n increases, the value of f(n) is divided by 2 to get the next term

This means that

As n gets larger and larger, the value of f(n) get halved

The value of g(4)

From the question, we have

First term, a = 9

Common ratio, r = 2

This means that

g(n) = 2(9)^n-1

So, we have

g(4) = 2(9)^3

g(4) = 1458

Completing the statements

Based on the function definitions, the statements when completed are

Recall that

g(n) = 2(9)^n-1

So, we have

g(24) = 2(9)^23

g(21) = 2(9)^20

Divide the equations

g(24) = 2(9)^23

-------     ----------

g(21) = 2(9)^20

Evaluate

g(24)/g(21) = 729

Hence, the value of the ratio is 729

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Answer:

See below.

Step-by-step explanation:

We are asked to simplify the expression provided.

An easy way to simplify this expression is by Combining Like Terms.

Combining Like Terms means adding terms that are similar, whether that's natural numbers, or variables.

For example, 8x + 9x are like terms since they both have the same variables. There's no exponents or any other variables that make these terms different from each other.

Using what we've learned, let's combine like terms for our problem now.

Combine Like Terms:

[tex]7h+6.3d-15+4d-3.4h[/tex]

[tex]7h - 3.4h = 3.6h[/tex]

[tex]6.3d + 4d = 10.3d[/tex]

-15 has no like terms.

We should have;

[tex]10.3d-15+3.6h[/tex]

This will be our final answer. There's no more like terms to combine and we can't simplify this expression further.

(5[tex]\sqrt{3}[/tex])^2

= (25 x 3)

= 75

(2[tex]\sqrt{5}[/tex])^2

= (4 x 5)

= 20

Answer:

Percent rate of change per unit, t ≈ 10.99%

Step-by-step explanation:

The percent rate of change per unit, t, for a function is equal to the derivative of the function with respect to t, divided by the function value at t.

For the given function g(t) = 200(1.12)^t, the derivative with respect to t is:

g'(t) = ln(1.12) * 200(1.12)^t

The function value at t is:

g(t) = 200(1.12)^t

Therefore, the percent rate of change per unit, t, is:

g'(t) / g(t) = [ln(1.12) * 200(1.12)^t] / [200(1.12)^t] = ln(1.12) ≈ 0.1099

Multiplying by 100 to express the answer as a percentage, rounded to the nearest tenth of a percent, we get:

Percent rate of change per unit, t ≈ 10.99%

The value of a discriminant determines the kind of roots in a quadratic equation, and the sign of a discriminant indicates whether the roots were real or complex, unique or recurring.

Definitions: x ax2 + bx + c = 0 is a quadratic equation, which is a 2nd quadratic formula in a single variable. a 0. It has at most one solution since it is a 2nd quadratic problem, which is guaranteed by the algebraic basic theorem. The solution could be straightforward or difficult.

To put it another way, if a twice the square of a expression that comes after b plus b times the same expression never squared plus c equals 0.

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the solutions are x = -13 and x = -5. So, the correct answer is (A) x = -5, x = -13.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given an algebraic expression:

5 - 3|x + 8| = 20

First, we can begin by adding 3|x+8| to both sides of the equation, giving us:

5-20 = 3|x+8|

Simplifying the left-hand side, we get:

-15 = 3|x+8|

Next, we can divide both sides by 3, giving us:

-5 = |x+8|

Now we have an absolute value equation, which has two possible solutions depending on whether x+8 is positive or negative.

If x+8 is positive, then we have:

-5 = x+8

Solving for x, we get:

x = -13

If x+8 is negative, then we have:

-5 = -(x+8)

Solving for x, we get:

x = -5

Therefore, the solutions are x = -13 and x = -5. So, the correct answer is (A) x = -5, x = -13.

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The expression when evaluated is 4√2x

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

√32x

Express 32 as the product of 16 and 2

So, we have

√32x = √(16 * 2x)

Take the LCM of 16

So, we have the following representation

√32x = 4√2x

Hence, the solution is 4√2x

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Based on the four options, Brianna should choose to invest her summer earnings in the Account 4 (compounded continuously) because interest is at highest in the account after like 3 years.

Interest is higher in compounded continuously because it is calculated more frequently than in other compounding methods, such as annually or semi-annually. In continuous compounding, interest is calculated and added to the principal an infinite number of times over a given period, which results in a higher effective interest rate than other compounding methods.

This means that the amount of interest earned on an investment or loan increases more rapidly, which can result in greater returns for investors or higher costs for borrowers. Continuous compounding is often used in financial markets where small changes in interest rates can have significant impacts on returns, such as in the case of short-term bonds or options trading.

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a) The altitude οf the plane is apprοximately 10,780 meters.

b) The pilοt will have apprοximately 14.4 minutes befοre he has tο land if the plane descends suddenly at a rate οf 750 meters per minute.

Trigοnοmetric functiοns are mathematical fοrmulas that cοnnect a triangle's angles and side ratiοs. Sine, cοsine, and tangent are the three fundamental trigοnοmetric functiοns; they are alsο knοwn as sin, cοs, and tan, respectively. These functiοns are emplοyed in the study οf physics, engineering, and οther branches οf science as well as in the study οf geοmetry, trigοnοmetry, and οther branches οf mathematics. They can be used tο sοlve issues invοlving angles and distances, such as determining a building's height, the separatiοn between twο οbjects, οr the speed οf a mοving οbject.

a) The Pythagοrean theοrem, which relates the three sides οf a right triangle, can be used tο determine the plane's altitude. In this instance, the slant range serves as the hypοtenuse οf a right triangle, with the grοund range serving as οne οf the legs and the height serving as the οther leg. As a result, we have:

altitude² + grοund range² = slant range²

Substituting the given values, we get:

altitude² + (10.15 km)² = (14.5 km)²

Simplifying and sοlving fοr altitude, we get:

altitude² = (14.5 km)² - (10.15 km)²

altitude² = 116.205 km²

altitude = √116.205 km² ≈ 10.78 km ≈ 10,780 m

Therefοre, the altitude οf the plane is apprοximately 10,780 meters.

b) If the plane descends suddenly at a rate οf 750 meters per minute, its altitude will decrease by 750 meters every minute. Tο find hοw much time the pilοt has befοre he has tο land, we can divide the initial altitude by the rate οf descent. Therefοre, we have:

time = initial altitude/rate οf descent

Substituting the initial altitude and rate οf descent, we get:

time = 10,780 m / 750 m/min

Simplifying, we get:

time = 14.3733 min ≈ 14.4 min

Therefοre, the pilοt will have apprοximately 14.4 minutes befοre he has tο land if the plane descends suddenly at a rate οf 750 meters per minute.

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Answer:

x = 3

y = -10

Step-by-step explanation:

  5x + y = 5                                                                    y = 3x - 19

  5x + 3x - 19 = 5

  8x - 19 = 5

  8x = 24

   x = 3

Now put x in to solve for y

y = 3(3) - 19

y = 9 - 19

y = -10

Let's check

5(3) - 10 = 5

15 - 10 = 5

5 = 5

So, x = 3 and y = -10 is the correct answer.