A cyclist rides her bike at a rate of 5 miles per hour. What is this rate in kilometers per hour? How many kilometers will the cyclist travel in 5 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answer.

Answer:

Step-by-step explanation:

Since she will use 4 groups or class intervals, the the class width would be 20/4 = 5 hours

The class groups would be

1 to 5

5 to 10

10 to 15

15 to 20

The class mark for each class is the average of the minimum and maximum value of each class. Therefore, the class marks are

(1 + 5)/2 = 3

(5 + 10)/2 = 7.5

(10 + 15)/2 = 12.5

(15 + 20)/2 = 17.5

The frequency table would be

Class group Frequency

1 - 5 4

5 - 10 8

10 - 15 6

15 - 20 2

The total frequency is 4 + 8 + 6 + 2 = 20

Answer:

All three answers are correct, but they represent different algebraic expressions that are equivalent to x + 8.

Step-by-step explanation:

i) 1/4(x + 8) is equivalent to x/4 + 2. This expression distributes the 1/4 coefficient to both terms inside the parentheses.

ii) x + 2 is equivalent to 1x + 2. This expression simplifies x + 8 by subtracting 6 from the constant term.

iii) 1/4x + 2 is equivalent to 2 + 1/4x. This expression rearranges the terms in x + 8 to separate x from the constant term.

Therefore, the students who provided any of these answers demonstrated a correct understanding of algebraic expressions.

A total of 7 Cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

A line plot is drawn with the cyclists' names plotted on the x-axis and their corresponding distances covered plotted on the y-axis.

The dots are then joined to form a line, revealing the relationship between the cyclist's names and their corresponding distance traveled. The cyclist names and their corresponding distances are given in the table below.

Name Distance (in miles) Gina 40 1/2 Rey 50 Faye 35 3/4 Mark 60 John 45 1/2 James 40 1/2 Albert 40 1/4 William 54 1/4 Nathan 40 Kate 40 1/4 Mary 60 Risa 40 Abi 35 3/4 Joan 50 1/2 1. The number of cyclists is 14. 2. The longest distance covered by a cyclist is 60 miles.

Mary and Mark both covered this distance.3. A total of 7 cyclists traveled less than 50 miles. 4. The most common distance traveled by cyclists is 40 1/2 miles. Gina, James, and Albert covered this distance. 5. 2 more cyclists traveled 45 miles than 55 1/4 miles. Only William traveled 55 1/4 miles, while John and James both traveled 45 1/2 miles.6.

A total of 7 cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

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The property used in step 1 was distributive property

The property used in step 2 was subtraction property of equality

The property used in step 3 was division property of equality .

Given :

we are given with steps to solve linear equation

The steps are

\(\frac{1}{3} (12x+15)=7\\Step 1 : 4x+5=7\\Step 2 : 4x=2\\Step 3 : x= \frac{1}{2}\)

Lets analyze each step

In step 1. 1/3 is multiplied inside the parenthesis part

Fraction is distributed inside the parenthesis

The property used in step 1 was distributive property

In step 2, 5 is subtracted from both sides

The property used in step 2 was subtraction property of equality

In step 3: 4 is divided on both sides

The property used in step 3 was division property of equality .

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The solution to the linear equation is x = 1/2. The properties used were the Distributive Property, Property of Equality, and Multiplicative Property of Equality.

Let's analyze the steps used to solve the linear equation 1/3(12x + 15) = 7:

Step 1: Distributive Property

The property used in Step 1 is the Distributive Property, which states that when you have a number (or variable) multiplied by a sum or difference inside parentheses, you need to distribute the multiplication across all terms inside the parentheses. In this case, we distribute 1/3 to both terms (12x and 15):

1/3 * 12x + 1/3 * 15 = 7

This simplifies to:

4x + 5 = 7

Step 2: Solving for x

The property used in Step 2 is the Property of Equality. We want to isolate the variable x on one side of the equation, so we subtract 5 from both sides to get rid of the constant term:

4x + 5 - 5 = 7 - 5

This simplifies to:

4x = 2

Step 3: Isolating x

The property used in Step 3 is the Multiplicative Property of Equality. To solve for x, we divide both sides of the equation by the coefficient of x (which is 4):

4x / 4 = 2 / 4

This simplifies to:

x = 1/2

Therefore, the solution to the linear equation is x = 1/2. The properties used were the Distributive Property, Property of Equality, and Multiplicative Property of Equality.

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Answer:

all real numbers

Step-by-step explanation:

if you subtract x from both sides, you get x=x. This is true for basically any number

The marginal frequency of students who chose dancing is 37.

The correct answer to the given question is option 3.

The marginal frequency of students who chose dancing can be calculated by adding up the number of students who chose dancing in each row or column. In this case, we need to add up the number of art students who chose dancing (22) and the number of music students who chose dancing (15), which gives us a total of 37. This is the marginal frequency of students who chose dancing.

Based on the survey results, it appears that a slightly higher percentage of art students prefer dancing (41.5%) compared to music students (31.9%). However, both groups of students seem to be fairly evenly split between dancing and playing sports, with a slight preference for playing sports overall.

It's worth noting that cardiovascular activity is important for overall health and well-being, and both dancing and playing sports can provide great opportunities for exercise and physical activity. Additionally, both activities can also be enjoyable and provide a sense of community and social connection, which is important for middle school students who are still developing their social skills and relationships. Ultimately, the choice between dancing and playing sports will depend on individual interests, preferences, and abilities.

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Answer:

\(\huge\boxed{\sf Option \ 4}\)

Step-by-step explanation:

When the figure is cut along the dotted line, it makes two shapes.

1) Triangle:

Since, one shape has three sides, it is a triangle.

2) Parallelogram:

The other shape has both oppsoite sides parallel to eachother, so it is a parallelogram.

\(\rule[225]{225}{2}\)

9a^2 - 9

Uejdjeujdksjdndkdkdk

The value of x is 1.75 and y is 5. The solution is obtained using properties of congruent triangles.

What is a congruent triangle?

Two triangles that are congruent will have precisely the same three sides and three angles.

The dimensions of the triangles' sides and angles determine whether two or more triangles are congruent. A triangle's size is determined by its three sides, and its shape by its three angles. Pairs of corresponding sides and corresponding angles in two triangles are said to be equal if they are congruent. They share a similar size and shape. In triangles, there are numerous congruence conditions.

The triangles are congruent by SAS congruency because

AC = CD (Given)

∠ACB = ∠DCE ( Vertically opposite angles)

BC = CE  (Given)

Thus, Triangle ABC ≅ Triangle DEC

Since, the triangles are congruent, therefore

⇒AC = CD

⇒4y-6 = 2x+6   ...(1)

Also, BC = CE

⇒3y+1 = 4x

⇒(3y+1)/4 = x    ...(2)

Now, substituting the value of x in (1), we get,

⇒4y-6 = 2(3y+1)/4+(6)

⇒4y-6 = (6y+2 +24)/4

⇒16y-24 = 6y+2 +24

⇒10y = 50

⇒y = 5

Now putting the value of y in (2), we get

⇒(3(2)+1)/4 = x

⇒7/4 = x

⇒ x = 1.75

Hence, the value of x is 1.75 and y is 5.

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Answer:

x ≈ 41.6°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan x = \(\frac{opposite}{adjacent}\) = \(\frac{JK}{KL}\) = \(\frac{80}{90}\) = \(\frac{8}{9}\) , then

x = \(tan^{-1}\) ( \(\frac{8}{9}\) ) ≈ 41.6° ( to the nearest tenth )

Step-by-step explanation:

I'm sorry I can't answer that but I know something so you can answer that. search Chrome quickmath all your problems, equations and more can be solved

Answer:

c = 3/2x + −3/2

Step-by-step explanation:

Let's solve for c

-3x+2c=-3

Step 1: Add 3x to both sides.

2c −3x + 3x = −3 + 3x

2c = 3x −3

Step 2: Divide both sides by 2.

2c = 3x−3

2        2

c = 3/2x + −3/2

Answer:

c = 3/2x + −3/2

Step-by-step explanation:

The function f was shifted 8 units to the right to obtain g.

Answer:

\( \frac{3( {5}^{8} - 1) }{5 - 1} = 292968\)

Answer:

14)  m∠WYZ = 23°

15)  m∠ACB = 87°

Step-by-step explanation:

If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

According to the SAS Similarity Theorem, triangle VWX and triangle YWV are similar triangles.

If two triangles are similar their corresponding angles are congruent.

Therefore, m∠WYZ is the same as m∠WVX.

Angles on a straight line sum to 180°:

\(\implies m \angle WYZ + m \angle VYZ = 180^{\circ}\)

\(\implies (3x-7)^{\circ} + (16x-3)^{\circ} = 180^{\circ}\)

\(\implies (3x-7) + (16x-3) = 180\)

\(\implies 3x-7+ 16x-3 = 180\)

\(\implies 19x-10= 180\)

\(\implies 19x= 190\)

\(\implies x=10\)

To find the measure of angle WYZ, substitute the found value of x into the expression for the angle:

\(\begin{aligned}\implies m \angle WYZ &=(3x-7)^{\circ}\\&=(3(10)-7)^{\circ}\\&=(30-7)^{\circ}\\&=23^{\circ}\end{aligned}\)

Therefore, the measure of angle WYZ is 23°.

According to the SAS Similarity Theorem, triangle ABC and triangle AED are similar triangles.

If two triangles are similar their corresponding angles are congruent.

Therefore, m∠ABC is equal to m∠AED:

\(\implies m \angle AED=m \angle ABC\)

\(\implies (11x-2)^{\circ}=(6x+13)^{\circ}\)

\(\implies 11x-2=6x+13\)

\(\implies 5x=15\)

\(\implies x = 3\)

To find the measure of angle ABC, substitute the found value of x into the expression for the angle:

\(\begin{aligned}\implies m \angle ABC&=(6x+13)^{\circ}\\&=(6(3)+13)^{\circ}\\&=(18+13)^{\circ}\\&=31^{\circ}\end{aligned}\)

Interior angles of a triangle sum to 180°:

\(\implies m \angle ACB + m \angle ABC + m \angle BAC = 180^{\circ}\)

\(\implies m \angle ACB + 31^{\circ}+ 62^{\circ} = 180^{\circ}\)

\(\implies m \angle ACB + 93^{\circ} = 180^{\circ}\)

\(\implies m \angle ACB =87^{\circ}\)

Therefore, the measure of angle ACB is 87°.

Step by step:

Perimeter = Summation of all sides = AB+BC+CD+DA = 2x+2+x+2x+2+x=(6x+4)

⇒6x+4=154

⇒6x=154−4

⇒\(\frac{150}{6x}\)

⇒25=x

The breadth is x=25

The length of the rectangular pool = (2×25+2)=50+2=52m

breadth is 25 and the length is 52

Hope it helps!

\(\blue\star \rm\pink{ Question:}\)

The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and the breadth of the pool?

\( \\ \\ \)

\(\blue\star \rm\pink{ Given :}\)

\( \\ \\ \)

\(\blue\star \rm\pink{ To ~Find :}\)

\( \\ \\ \)

\(\blue\star \rm\pink{Let :}\)

\( \\ \\ \)

We know:-

\( \bigstar \boxed{ \rm perimeter \: of \: rextangle = 2(length +breadth)}\)

So:-

\( \\ \\ \)

\( \dashrightarrow\sf perimeter \: of \: rextangle = 2(length +breadth) \\ \)

\( \\ \\ \)

\( \dashrightarrow\sf 154 = 2( 2 + 2x +x) \\ \)

\( \\ \\ \)

\( \dashrightarrow\sf 154 = 2( 2 + 3x) \\ \)

\( \\ \\ \)

\( \dashrightarrow\sf 154 = 2( 2 )+ 2(3x) \\ \)

\( \\ \\ \)

\( \dashrightarrow\sf 154 = 4+ 2(3x) \\ \)

\( \\ \\ \)

\( \dashrightarrow\sf 154 = 4+ 6x\)

\( \\ \\ \)

\( \dashrightarrow\sf 154 - 4 =6x\)

\( \\ \\ \)

\( \dashrightarrow\sf 150 =6x\)

\( \\ \\ \)

\( \dashrightarrow\sf 6x = 150\)

\( \\ \\ \)

\( \dashrightarrow\sf x = \dfrac{150}{6} \)

\( \\ \\ \)

\( \dashrightarrow\sf x = \cancel \dfrac{150}{6} \)

\( \\ \\ \)

\( \dashrightarrow\bf x =25\)

\( \\ \\ \)

Let's Verify value of x:-

\( \\ \\ \)

\( \dashrightarrow\sf 154 = 2( 2 + 2x +x) \\ \)

put value of x in equation

\( \\ \\ \)

\( \dashrightarrow\sf 154 = 2( 2 + \{2 \times 25 \} +25) \\ \)

\( \\ \\ \)

\( \dashrightarrow\sf 154 = 2( 2 + 50+25) \\ \)

\( \\ \\ \)

\( \dashrightarrow\sf 154 = 2( 2 + 75) \\ \)

\( \\ \\ \)

\( \dashrightarrow\sf 154 = 2(77) \\ \)

\( \\ \\ \)

\( \dashrightarrow\bf 154 =154\)

\( \\ \\ \)

\(\Large \bf\dag LHS = RHS \dag\)

Hence proved

\( \\ \\ \)

Finally Let's find length and breadth of pool:-

\( \\ \\ \)

To find breadth

➙ Breadth = x

➙ Breadth = 25 m

\( \\ \)

To find length

➙ Length = 2 + 2x

➙ Length = 2 + 2(25)

➙ Length = 2 + 50

➙ Length = 52 m

____________________________________☆~

Cheers! all done. :)

Answer:

217 ft

Step-by-step explanation:

Sea level is 0 height.

217 ft below sea level is -217 ft.

The opposite of -217 ft is 217 ft.

|-217 ft| = 217 ft

Answer:

P + S / P [(r - 1) P - S] dP

Step-by-step explanation:

If r = 0.10 and S = 900 then,

P + 900 /  P [(0.10 - 1) P - 900] dP

Solving the equation we get,

P + 900 = (B - 0.9A)P - 900A

If A = -1,

B = 0.10

t = 0 and P = 10,000

ln 10000 - 1 /9 ln (0.9 * 10000 + 900) + C

C = 10.2326.

Answer:

I

Step-by-step explanation:

owing a lot of money bc it hurts your credit score

Answer:

it is 4.6 sorry girl

Step-by-step explanation:

Answer:

Step-by-step explanation:

4.6=4 3/5=23/5

Answer:

B

Step-by-step explanation:

The points with these coordinates form a triangle with a side 5 units and height 4 units. It' area is equal to 5*4÷2=10units^2

The value of the Integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

The length of the curve described by the function f(x) = 1 + 3x^2 + 2x^3 is to be found. The formula used to find the length of a curve is:

L = ∫(sqrt(1 + [f'(x)]^2))dx where f'(x) is the derivative of f(x)We have to first find f'(x):f(x) = 1 + 3x^2 + 2x^3f'(x) = 6x + 6x^2

The integral becomes:L = ∫(sqrt(1 + [6x + 6x^2]^2))dx = ∫(sqrt(1 + 36x^2 + 72x^3 + 36x^4))dx The integral appears to be difficult to evaluate by hand.

Therefore, we use software like Mathematica or Wolfram Alpha to solve the problem. Integrating the expression using Wolfram Alpha gives:

L = 1/54(9sqrt(10)arcsinh(3xsqrt(2/5)) + 2sqrt(5)(2x^2 + 3x)sqrt(9x^2 + 4))The limits of integration are not given. Therefore, the definite integral  be solved.

We can, however, find a general solution. We use the above formula and substitute the limits of integration.

Then, we subtract the value of the integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

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Every three candy bars cost a dollar.

Divide 25 by three.  

$8.33

Answer:

x ≈ 30,37

y ≈ 29,00

Step-by-step explanation:

Use trigonometry:

\( \sin(38°) = \frac{9}{x} \)

Now, use the property of the proportion to find x:

\(x = \frac{9}{ \sin(38°) } ≈30.37\)

Do the same thing to find y:

\( \tan(38°) = \frac{9}{y} \)

\(y = \frac{9}{ \tan(38°) } ≈29.00\)

An axiom of predicate calculus is the foundation of predicate calculus that is based on a fundamental and obvious principle or statement

The foundation of predicate calculus is based on a fundamental and obvious principle or statement known as an axiom.

The aforementioned axioms act as a foundation for deducing rational conclusions and evidence within the domain of predicate calculus.

Universally accurate and accepted without the need for additional reasoning is how they are commonly perceived.

The fundamental regulations and connections that oversee quantifiers, predicates, and logical operations, including conjunction, disjunction, and implication, are determined by the axioms of predicate calculus. They offer a sturdy groundwork for rationalizing statements that involve variables, quantification, and logical connectors in formal systems of logic.

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The total savings that the couple Puan Yani and her husband have now is A) RM126,000.

The total savings of the couple can be determined by addition.

Addition is one of the four basic mathematical operations, including subtraction, divsion, and multiplication.

Let the amount that Puan Yani has in her savings account, a = RM24,700

Let the amount that her husband has than Puan Yani = RM75,300

The total amount that her husband has = a + 75,300

= RM100,000 (R24,700 + RM75,300)

The additional amount that Puan Yani deposited at the end of May = RM1,300

The total amount that Puan Yani has in her savings account at the end of May = RM26,000 (RM24,700 + RM1,300)

The total savings in the couple's accounts = RM126,000 (RM100,000 + RM26,000)

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\(\left(15^{1/5} \right)^5 = 15^{(5/5)} = 15^1 = 15\)

Answer:

\(0.40 * 6 = 2.4\\)

So if one pound costs 2.4$, you will be able to buy 2 pounds with 6$