What was the distance of the first part of yuna's swim? round to the nearest tenth as needed. the distance in the first part of her swim was miles.

The rational equation is equivalent to the polynomial 27 · x² - 36 · x + 12.

In this case we find a rational equation whose numerator and denominator are polynomials, which must be simplified by using algebra properties. The complete procedure is now shown:

(9 · x - 6)² / (2 · x⁴ + 4 - 2 · x⁴ - 1)                  Given

(81 · x² - 108 · x + 36) / (3)                             Perfect square binomial / Associative, commutative and modulative properties / Existence of additive inverse /Definition of subtraction

27 · x² - 36 · x + 12                                        Addition and subtraction of fractions with same denominator / Associative and commutative properties / Definition of division

The rational equation is equivalent to the polynomial 27 · x² - 36 · x + 12.

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Given:

Numbers in the container: All integers from 10 to 50

Let's find P(Prime numbers| numbers between 11 and 30).

Here, we are to find the conditional probability.

Apply the formula:

P(Prime|between 11 and 30) = P(prime numbers and between 11 and 30) ÷ P(numbers between 11 and 30).

Where:

• Prime numbers between 11 and 30 = 11 , 13 , 17 , 19 , 23 , 29 =6 numbers

• Intergers from 10 to 50 = 41 integers.

To find the probability, we have:

Therefore, we have:

P(Prime|between 11 and 30) = 3/10.

ANSWER:

D. 3/10

P

OQ = 4S - 10

OP = 23

PQ = 1

Equation

OQ = OP + PQ

Substitution

4S - 10 = 23 - 1

Simplification

4S = 22 + 10

4S = 32

S = 32/4

S = 8

Determine OP

OQ = 4(8) - 10

OQ = 32 - 10

OQ = 22

150 - 5.5n= 95 equation to model when the balloon will reach an altitude of 95 meters above the ground.

Two or more expressions with an Equal sign is called as Equation.

Given that,

A hot air balloon is cruising at an altitude of 150 meters above the ground when it begins its descent.

The balloon descends at a rate of 5.5 meters per minute.

We need to write an equation to model when the balloon will reach an altitude of 95 meters above the ground.

The equation is 150 - 5.5n= 95

Hence 150 - 5.5n= 95 equation to model when the balloon will reach an altitude of 95 meters above the ground.

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Formula to work out the Total surface area of half-cylinder = [tex]\pi rh + \pi r^{2} + 2rh[/tex]

To find:

Formula to work out the surface area of half a cylinder

Solution:

The surface area of ​​a semi-cylinder can be calculated by adding half the curved area of ​​the cylinder to the area of ​​the two semi-circles and the area of ​​the rectangular section below. The formula for the surface area of ​​a semi-cylinder is given by: Total surface area of ​​

Total surface area of a half-cylinder = (1/2) × curved area of ​​cylinder + 2 × area of ​​semi-circle + area of ​​base of cylinder.

total surface area of a half-cylinder = [tex]\pi rh+\pi r^{2} +2rh[/tex]

where r = radius of cylinder

[tex]\pi[/tex] = 3.14 or 22.7 cm

h = height of cylinder

(Or)  We can find Total surface area of half cylinder as, Total surface area of half cylinder ÷ 2

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If equation of the height is h = -16[tex]t^2[/tex]+150, then the time taken for the object to be 6 feet above the valley floor is 4.28 seconds

The equation of the height h = -16[tex]t^2[/tex]+150

Where h is the height

t is the time taken

We have to find the time taken for the object to be 6 feet above the valley floor

The height = -150+6

= -144

Substitute the values in the equation

-16[tex]t^2[/tex]+150 = -144

-16[tex]t^2[/tex] = -144-150

-16[tex]t^2[/tex] = -294

[tex]t^{2}[/tex] = 18.375

t = 4.28 seconds

Hence, if equation of the height is h = -16[tex]t^2[/tex]+150, then the time taken for the object to be 6 feet above the valley floor is 4.28 seconds

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Given:

Required:

To find the domain of the given function.

Explanation:

Now consider

Answer:

6.50 × 65 tickets.

Answer = $422.5

The theater sells 43 adult tickets and 22 child tickets.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let us assume,

The number of adult tickets sold is x

The number of tickets sold for children is y

Since the total number of tickets sold is 65,

x + y = 65 .....(i)

Charge per adult ticket=$10.50,

So the amount collected by selling adult tickets is 10.50×x

Charge per child ticket=$6.50,

So the amount collected by selling tickets for children is 6.50×y

We know that the total amount earned by the theater is $594.50

So, 10.5x +6.5y = 594.50  ......(ii)

After solving equations (i) and (ii), we get the values of x and y as

x = 43 and y = 22

Therefore, the theater sells 43 adult tickets and 22 child tickets.

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The volume of the glass is 454.16cm² and the number of glasses filled upto a horizontal line of 2 cm from top is 4

A cylindrical drinking glass has radius 3 cm and height 8 cm.

The volume of a cylinder is 2πr²h

= 2 (3.14) 3² x 8

= 452.16cm³

The jug contains 1.5 litres of water

1 litre = 1000cm³

1.5 litre = 1500cm³

The volume of glass if it is filled upto a horizontal line 2 cm from the top.

volume =  2πr²h

= 2 (3.14) 3² x 6

= 339.12cm³

Number of glasses filled = 1500/339.12 = 4.42

4 glasses can be filled up to the line from the jug

Therefore, the volume of the glass is 454.16cm² and the number of glasses filled upto a horizontal line of 2 cm from top is 4

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Let x be the minimum number of cars Ken has to wash to reach his goal, then we can set the following linear equation:

Solving the above equation for x, we get:

Rounding up to the nearest whole number we get:

121670000 different license plates are possible.

A license plate consists of 7 characters.

The first 4 characters are numerals from 0 to 9.

each character can be in 10 ways

so possible ways = 10 * 10 * 10 * 10  = 10000

The last 3 characters are letters excluding I, O, and X.

                    Each character can be in 26 - 3 = 23 Ways

                         Possible ways = 23 *23 * 23  = 12167

Number of possible different license plates  = 10000 * 12167

                                                                          = 121670000

Motor vehicle registration is the registration of a motor vehicle with a public authority, whether compulsory or otherwise. The purpose of registering a motor vehicle  is to establish a link between the vehicle and the owner or user of the vehicle. This link may be used for taxation or criminal investigations.

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EXPLANATION

The equation of the function can be represented as shown as follows:

-This function is discrete.

-If we have 20 gallons, we can obtain the number of miles by plugging in the value into the equation, as shown as follows:

Dividing both sides by 12:

Simplifying:

We can make 1.67 miles with 20 gallons.

-The domain of the function are all the Real Numbers and the Range are also the Real numbers.

-Finally, drawing the graph of the function:

The points of the table are the following:

Gallons Miles

2 24

4 48

6 72

8 96

-We can get the number of gallons needed to, make 500 miles by plugging the value 500 into the equation, as shown as follows:

Isolating m:

Simplifying:

The number of gallons to make 500 miles is equal to 41.7 gallons

Finally, labeling the graph:

Answer: 65$

Step-by-step explanation:

1. 40% of 150 is 60 so 60$ off of 150 is 90

2. total amount off is 85$. 60 is the 40% off and additional 25 for the rebate

3. final price will be 65$. 90-25=65

Answer:

1. Fact that all individuals are created equal and are endowed by their creator with certain unalienable rights is a clear statement in the Declaration of Independence.

2. Aim of having a government is to safeguard these rights,  the people have the right and the duty to alter, abolish, or over through that government.

3. The Decoration of Independence lists the grievances that the government has failed to resolve and reconcile with the colonies.

4. The decree was made to become an autonomous nation and the motives for asserting independence are listed in the grievances.

Answer:

It has reflectional symmetry with four lines of symmetry.

Step-by-step explanation:

======================================================

Explanation:

Choice A is false since it does have rotational symmetry. See choice B.

Choice B is close, but the "90 degrees" needs to be "45 degrees". Each 45 degree rotation of the figure has the "before" and "after" be the same.

Choice C is one of the answers. There's a vertical line of symmetry, and a horizontal one as well.  Then there are two diagonal lines of symmetry. Each goes through the center. A line of symmetry is a mirror line to allow us to reflect one half over this line to get the other half.

Choice D is another answer. It has point symmetry since we can pick any point on the figure and reflect it over the center point, to land on a corresponding image point on the opposite side of the figure. For example, the northern most point reflects over the center to land on the southern most point.

Given:

a.) A person had 14,000 infested in two accounts.

b.) One paying 9% simple interest.

c.) One paying 10% simple interest.

Let,

x = the amount invested at 9% simple interest

y = the amount invested at 10% simple interest

1.) We know the total amount of money invested is $14,000. We get,

x + y = 14,000

2.) We know that the total interest for the year for the two accounts is $1432. We get,

0.09*x + 0.1*y = 1,339

Let's equate the two equations,

x = 14,000 - y (Substitute for x)

0.09*(14,000 - y) + 0.1*y = 1,339

1,260 - 0.09y + 0.1y = 1,339

0.1y - 0.09y = 1,339 - 1,260

0.01y = 79

0.01y/0.01 = 79/0.01

y = 7,900

Therefore, $7,900 was invested at the rate of 10% simple interest.

Let's determine x, substituting y = 7,900 in x + y = 14,000.

x + y = 14,000

x + 7,900 = 14,000

x = 14,000 - 7,900

x = 6,100

Therefore, $6,100 was invested at the rate of 9% simple interest.

Answer

Part A

(g o h)(x) = x - 1

Part B

Domain of (g o h) = (-∞, ∞)

Explanation

Part A

We are given that

g(x) = x² + 3

h(x) = √(x - 4)

We are then asked to find (g o h)(x)

To do that, we need to note that (g o h)(x) means we write g(x), but instead of x, we write h(x). That is,

(g o h)(x)

= g(h(x))

= [h(x)]² + 3

= [√(x - 4)]² + 3

= x - 4 + 3

= x - 1

Part B

To find the domain

The domain of a function refers to the values of the independent variable (x), where the dependent variable [y or f(x)] or the function has a corresponding real value. The domain is simply the values of x for which the output also exists.

And for (g o h)(x) = x - 1, we know there will be an answer for all real number values of x. Hence,

Domain = (-∞, ∞)

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The option that is not a statistical question is D. how tall are the corn plants?

A statistical question is one that may be answered by gathering data and for which the data will vary. Questions answered with a single data point are not statistical questions since the data utilized to answer the question is not variable.

A statistical question is one that can be answered by gathering varying amounts of data. A statistical inquiry is one that yields varying responses and outcomes (data). It must be collected on more than one person and there must be room for the facts to vary.

Therefore, based on the information illustrated, the correct option is D. It was too general and not specific

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Answer:

90%

Step-by-step explanation:

To find the percent of increase in the height of the tree, we need the change of the height and the original height (40 feet)

The change of height = 76 - 40 = 36 feet

Now, we need to divide the change by the original height to find the percent of increase.

36/40 = 9/10

9/10, which is then 90%.

1) How many ways can 4 candy bars be chosen from a store that sells 30 candy bars?

In this case we can combine 30 types of candy bars in a set of 4 bars.

This can be calculated as a combination of 30 in 4 with no repetition:

Answer: 27,405 possible combinations (C).

2) How many ways can 13 students line up for lunch?

In this case we have a permutation of 13 in 13 with no repetition.

We can calculate this as:

Answer: 6,227,020,85)00 possible permutations (P).

3) How many ways can you make a 3-letter arrangements out of the letters in the word TRAPEZOID.

In the word we have 9 letters with no repetition, so we have to calculate a permutation (as order matters) of 9 letters in 3 places.

We can calculate this as:

Answer: 504 possible permutations (P).

4) How many ways can you choose 2 books from a shelf of 40 books.

In this case, the order does not matter, so it is a combination of 40 in 2.

This can be calculated as:

Answer: 780 possible combinations (C)

5) How many ways can 12 swimmers finish in first, second, and third place?

In this case, the order does matter, so we have a permutation of 12 in 3:

Answer: 1320 permutations (P)

6) How many ways can Mrs. Sullivan choose two students from 27 to help put away calculators at the end of class?

The order does not matter between the two students, so it is a combination of 27 in 2:

Answer: 351 combinations (C)

Answer: √141

Step-by-step explanation:

a^2=c^2-b^2

The hypotenuse is larger in this question so we subtract them.

25^2-22^2=625-484=141

√141

Answer:

x = √141  

or

x = 11.87

Step-by-step explanation:

is a right triangle, we solve it with the Pythagorean theorem ("In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides".)

x² = 25² - 22²

x² = 625 - 484

x² = 141

x = √141  

or

x = 11.87

slope = -1/2

y-intercept = (0, -1)

Given:

To find:

the slope and the y-intercept

To determine the slope we will use the linear function formula:

We need to rewrite the given equation in the form above so as to get the slope

From the above, m = -1/2

Hence, the slope is -1/2

The y-intercept is the value of y when x = 0

To get the y-intercept, we will substitute x with 0:

The percentage of students that like rap that are also in grades 9–10 = 32%.

A frequency table is the type of table that shows the number of occurrence of different types of variables of an experiment.

From the frequency table given;

In grade 9 - 10;

Rap students = 40 students

Rock students = 30 students

Country students = 55 students

The total students in grade 9 - 10 = 125

Therefore, the percentage of rap students in grade 9 - 10;

= 40/125×100/1

= 4000/125

= 32%

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The number of each type of coins are as follows:

q = 15 quarters.

d = 30 dimes.

n = 25 nickels.

In order to solve this word problem, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:

Let d represent the number of dimes.

Let q represent number of quarters.

Let n represent number of nickels.

Let T represent total number of coins.

Note: 1 quarter is equal to 0.25 dollar, 1 nickel is equal to 0.5 dollar, and 1 dime is equal to 0.1 dollar.

Translating the word problem into an algebraic equation, we have;

Dimes; d = 2q     .....equation 1.

Nickels; (70 - (q + 2q)) = (70 - 3q)     .....equation 2.

Total coins; T = n + d + q

0.5(70 - 3q) + 2q(0.1) + q(0.25) = 8.00

Multiplying all through by 100, we have:

5(70 - 3q) + 2q(10) + q(25) = 800

350 - 15q + 20q + 25q = 800

350 + 30q = 800

30q = 800 - 350

30q = 450

q = 450/30

q = 15 quarters.

For the number of dimes, we have:

Dimes, d = 2q

Dimes, d = 2(15)

Dimes, d = 30 dimes.

For the number of nickels, we have:

Nickels, n = (70 - 3q)

Nickels, n = (70 - 3(15))

Nickels, n = (70 - 45)

Nickels, n = 25 nickels.

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We have to indicate the steps to follow in order to evaluate:

(12.9-3.1) x 6.2-2 + 43

So FIRST: we solve for the operation indicated inside the parenthesis

12.9 - 3.1 = 9.8 (we subtract 3.1 from 12.9)

This is the answer you need to select.

[tex]\frac{dx}{dy} = \frac{5}{3}. 4\frac{ft}{s} = \frac{20}{3}\frac{ft}{s}[/tex] is moving at the speed of the shadow

x is the distance from the man to the pole, and y is the distance from the tip of the man's shadow to the pole. I assume the man and pole are standing straight up, which means the two cases are similar.

[tex]\frac{y-x}{y} = \frac{6}{15}[/tex]

15(y-x) = 6y

9y = 15x

[tex]\frac{5}{3}x\\[/tex] = y

differentiate both sides with respect to t or time.

[tex]\frac{dx}d{y} = \frac{5}{3}\frac{dx}{dt}[/tex]

you know [tex]\frac{dx}{dy} = 4\frac{ft}{s}[/tex] because the man is walking that speed away from the pole. you want to find [tex]\frac{dx}{dy}[/tex] , how fast the tip of the shadow is moving.

that means

[tex]\frac{dx}{dy} = \frac{5}{3}. 4\frac{ft}{s} = \frac{20}{3}\frac{ft}{s}[/tex]

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SOLUTION

Consider the image given below.

From the image above,

To find the measures of each angle, we need to obtain the value of small x in the diagram.

Applying the rule: Sum of angle in a triangle is 180 degrees

Then substitute the given expression, we have

Collect like terms and add

Divide both sides by 6, we have

hence, x=30

Then substitute the value of x to obtain the measure of each angles.

Since the triangle is an issoceles triangle, then

Hence

Therefore

Answer : ∠V= 28°, ∠W=28°, ∠X=124°

Answer:

[tex] \csc(θ) = \frac{1}{ \sin(θ) } [/tex]

The unknown angle in the triangle is as follows;

The angle H can be found using the exterior angle theorem.

The exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.

In other words,  an exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Hence,

∠DFG = ∠G + ∠H

∠DFG = 14x + 1

∠G  = 89°

∠H = 5x - 7

14x + 1 = 89 + 5x - 7

14x + 1 = 89 - 7 + 5x

14x - 5x = 89 - 7 - 1

9x = 81

divide both sides by 9

x = 81 / 9

x = 9

Therefore,

∠H = 5(9) - 7 = 45 - 7 = 38 degrees.

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The time taken for Montraie to travel a distance of 88 miles is 2 hours.

Speed is simply referred to as distance traveled per unit time.

It expressed mathematically as;

Speed = Distance ÷ time.

Given the data in the question;

First, we determine the speed of Montraie.

Speed = Distance ÷ time.

Speed =  220 miles ÷ 5 hours

Speed = 44 miles per hour.

Now, time spent in traveling a distance of 88 miles will be;

Speed = Distance ÷ time

Time = Distance / Speed

Time = 88 miles / 44 miles per hour

Time = 2 hours

Therefore, the elapsed time is 2 hours.

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If Montraie drove 220 miles in 5 hours. If he continued at the same rate, then it takes 2 hours to travel 88 miles.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that,

Montraie drove 220 miles in 5 hours.

We need to find how long it would take to reach 88 miles.

Let us form a equation based on given data.

Let x be the time to reach 88 miles.

We need to find value of x.

220/5=88/x

Apply cross multiplication

220x=440

x=440/220

x=2

Hence it takes 2 hours to travel 88 miles with same rate.

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