When full, one of the pools at Sapphire Island will hold 43,000 gallons of water. The pool currently holds 20,000 gallons of water and is being filled at a rate of 130 gallons per minute. Write an equation that can be used to find h, the number of hours it will take to fill the pool from its current level. Explain the steps you used to write your equation.

The fraction of the tiled floor is made of darker tiles is = [tex]\frac{4}{9}[/tex]

Now, According to the question:

Let's know:

What is a fraction in math?

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

The given data is;

A corner of a tiled floor is shown.

If the entire floor is tiled in this way and each of the four corners looks like this one.

To find fraction of the tiled floor is made of darker tiles.

Take the total darker portion is 16

All is = 6 x 6 = 36

The fraction of the tiled floor is made of darker tiles will be:

[tex]\frac{16}{36}=\frac{4}{9}[/tex]

The answer is:

= [tex]\frac{4}{9}[/tex]

Hence, The fraction of the tiled floor is made of darker tiles is = [tex]\frac{4}{9}[/tex]

The probability of a randomly selected student having at least two siblings is 0.160, which is equal to 0.160 when rounded to the thousandths place.

The probability of a randomly selected student having at least two siblings can be calculated by adding the probabilities of having two and three or more siblings.

Using the given probabilities, the calculation is as follows:

P(at least 2 siblings) = P(2 siblings) + P(3 or more siblings)

= 0.121 + 0.039

= 0.160

Therefore, the probability of a randomly selected student having at least two siblings is 0.160, which is equal to 0.160 when rounded to the thousandths place.

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Answer:

see below

Step-by-step explanation:

1. -2/3x [tex]\geq[/tex] 7

first, we need to divide -2/3 from x and 7 to get x alone, we also need to flip the inequality sign since we are dividing by a negative

x [tex]\leq[/tex] 21/2

or x [tex]\leq[/tex] 10 1/2

2. 32 > 23 - x

first, rearrange the inequality

32 + x > 23

subtract 32 from both sides

x > -9

3. 2 (x + 6) < 10

divide both sides by 2

x + 6 < 5

subtract 6 from both sides

x < -1

4. 15 - 4x [tex]\leq[/tex] 3x - 6

rearrange the equation

-4x + 3x [tex]\leq[/tex] - 15 - 6

-7x [tex]\leq[/tex] - 21

multiply both sides by -1 and reverse the inequality sign

7x [tex]\geq[/tex] 21

divide both by 7

x [tex]\geq[/tex] 3

im super sorry but im not sure how to help you with the graphing :(

Answer: A, [tex]\frac{-6}{17}[/tex]

Step-by-step explanation:

g(3) = 2([tex]3^{2}[/tex]) - 3(3) + 1 = 18 - 9 + 1 =10

f(10) = [tex]\frac{4-10}{7+10}[/tex] = [tex]\frac{-6}{17}[/tex]

Make a linear function that, after t minutes, returns the circle's radius in inches. The circle's radius will have increased by inches, hence the radius increases by inches [3 points]. Create a linear function that returns the circle's radius.

The slope-intercept form of a linear function equation. As a result, it is written as f(x) = mx + b, where m is the slope & b is the y-intercept of a line.

Therefore, the distance to the safe zone is 24 * 4 + 70, which is 166.

The formula should be D=166-24t. She needs to go 166 meters, and since she is approaching the safe place at 24 meters per second, her distance to the safe zone is decreasing by 24 meters per second, making the calculation -24 meters per second rather than 24 meters per second.

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The correct expression that represents the distance between the friends is 4 steps.

To calculate this

Joy walked 12 steps forward and Shaunte walked 8 steps backward. To find the distance between the two friends, we can add the number of steps they each took, so the expression would be:

12 + (-8) = 12 - 8 = 4

So the correct expression that represents the distance between the friends is 4 steps.

Note that the negative sign in front of Shaunte's steps indicates that she walked backward, and the positive sign in front of Joy's steps indicates that she walked forwards.

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Answer:

125 miles per week

Step-by-step explanation:

He is running: 100 x (100 + 20)% = 100 x 120% = 100 x 6/5 = 125 miles
He is running 125 miles per week

=> r = 125 miles

The 95% confidence interval for the standard deviation of the lengths of pipes is (10.2, 25.6)

given that

95% confidence interval for the standard deviation of the lengths of pipes

a sample of 21 pipes

standard deviation of 14.6 inches

chi-squared(1 - a/2) < or = (n-1)s^2/(std. dev.)^2 < or = chi-squared(a/2)

in the above

a is alpha

std is standard deviation

a = (1-95/100) = 1 - 0.95 = 0.05

then, degree of freedom = 21 - 1 = 20

chi-squared(0.975) = 20.5

chi-squared(0.025) = 3.25

chi-squared for 20.5 = (21-1)×[tex](14.6)^{2}[/tex] / 20.5 = 103.98

chi - squared for 3.25 = (21-1)×[tex](14.6)^{2}[/tex] / 3.25 = 655.8

we need to square-root of the above values

chi-squared for 20.5 = [tex]\sqrt{103.98}[/tex] = 10.2

chi - squared for 3.25 = [tex]\sqrt{655.8}[/tex] = 25.6

the 95% confidence interval for the standard deviation of the lengths of pipes is (10.2, 25.6)

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Answer:

Step-by-step explanation:

52.2 : 1 = x : 1.5

x = 52.2 × 1.5 : 1

78.3 miles

Answer: it is 0.05 m

Answer:

see below  : -0.0492

Step-by-step explanation:

-6*-6-3/10*-67=-33/670 = -0.0492

The information presented states that perhaps the sculpture is 21 feet in height.

A closed, two-dimensional triangle has three sides, three angles, and three vertices. A polygon also includes a triangle. Triangle ABC is shown in the image above. A triangle through one obtuse angle (more than 90°) and several acute angles is known as an obtuse trio (or obtuse-angled triangle). No Riemann triangle can contain more than one obscure angle because in Euclidean geometry, a rectangle angles must add up to 180°.

AB/DE = BC/EF

f/6 = 28.7/8.2

=> f/6 = 3.5

=> f = 3.5 *6 = 21 ft

Consequently, the memorial is 21 feet tall.

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The complete question is-

A monument casts a shadow 28. 7 feet long. A man who is 6 feet tall casts a shadow 8. 2 feet long. The triangle drawn with the monument and its shadow is similar to the triangle drawn with the man and his shadow. How tall is the monument? Complete the statement by providing the correct answer in number form.

The value of x is 19.

What is the slope intercept?

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of a linear equation is y=mx + b.

We can start by using the information given in the problem to set up an equation. We know that:

m < 1 = 6x + 3

m < 2 = 117

We are also given that m < 1 and m < 2 represent different values.

Now we can substitute the second equation into the first equation:

6x + 3 = 117

To solve for x, we can subtract 3 from both sides:

6x = 114

Finally, we can divide both sides by 6:

x = 19

Hence, the value of x is 19.

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A = 1.5x + 1400 is the equation for how much money was raised.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation.

The "=" sign and terms on both sides must always be present when writing an equation. both parties.

According to our question-

Let's stand in for

Adults = x, number of them

children = y is the number.

The total amount raised equals A

In the query, it is stated that:

400 people were fed during a pancake breakfast fundraiser that cost $5 for adults and $3.50 for kids.

Consequently, x + y = 400. Formula 1: y = 400 - x

Hence:

A is equal to $5 x and $3.50 y.

Where A = 5x + 3.50 and y = 400 - x (400 - x)

A = 5x + 1400 - 3.50x A = 1.5x + 1400

The formula for calculating how much money was raised is as follows:

A = 1.5x + 1400

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Answer:

Its 24ft

Step-by-step explanation:

Coordinates of the given endpoints of the line segments ( 1, -3) and (5,-4) after translation of 3 units to the right and reflected over x-axis is given by :

a. Coordinates ( 4,3) and (8,4) , length of the given line segment does not get affected.

As given in the question,

Line segment of xy with endpoints (1, -3) and ( 5,-4).

Distance between endpoints are:

√( 5 -1)² + ( -4 + 3)²

= √17

Conditions given:

Line segment reflected over x-axis.

After reflection y-coordinates become positive.

Endpoints become : ( 1, 3 ) and ( 5, 4)

Translation of 3 units to the right.

New coordinates after translation:

(1 +3, 3) and ( 5+3 , 4)

= ( 4,3) and (8,4)

Distance between new endpoints are:

√( 8 -4)² + ( 4 - 3)²

= √17

Therefore, for the given endpoints of the line segment after reflection and translation as per given condition new coordinates are given by:

Option a. Coordinates ( 4,3) and (8,4) , length of the given line segment does not get affected.

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Answer:

45 miles per hour is the answer. The unit rate (r) is calculated by dividing the number of miles (d) by the number of hours (t): r = d/t. We know that d equals 135 miles and t equals 3 hours. The unit rate is thus r = 135 miles/3 hours. r is equal to 135/3 miles per hour. r equals 45 miles per hour. 45 miles per hour is the unit rate. I hope this was helpful. Please let me know if you require any extra assistance!

Step-by-step explanation:

assuming a year is 365 days

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$19211.34\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily, thus 365} \end{array}\dotfill &365\\ t=years\dotfill &3 \end{cases}[/tex]

[tex]A = 19211.34\left(1+\frac{0.04}{365}\right)^{365\cdot 3} \implies \stackrel{balance}{\boxed{A \approx 21660.58}}~\hfill \underset{interest}{\stackrel{21660.58~~ - ~~19211.34}{\boxed{\approx 2449.24}}}[/tex]

The formula distance = speed x time must be used to calculate the duration of a marathon as a function of the runner's average speed.

 1: List the known data. For example, a marathon is 13.1 miles long, and an average runner moves at s miles per hour.

2 :Rearrange the equation to solve for time in Step 2: Time = Speed/Distance

3: Enter the known numbers for distance and speed into the equation: time = 13.1 miles per second.

4: If necessary, simplify the equation. The units of miles will cancel out because the time is measured in hours and the speed in miles per hour, therefore the ultimate unit of time will be hours.

  The final answer  is t = 13.1/s, which expresses the duration of a marathon (in hours) as a function of the runner's average speed (in miles per hour).

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Answer: 14 mg

Step-by-step explanation:

5 mg/2.5 mL = 2 mg per mL

2 mg * 7 mL = 14 mg

Answer:

there are 14 milligrams in 7 mL.

Step-by-step explanation:

to find the number of milligrams in 7 mL, you can use the proportion:

(5 mg) / (2.5 mL) = (x mg) / (7 mL)

Where x is the number of milligrams in 7 mL. To solve for x, you can cross-multiply and divide:

(5 mg) * (7 mL) = (2.5 mL) * (x mg)

x = (5 mg) * (7 mL) / (2.5 mL)

x = 14 mg

The curves r1(t) = t, 2 − t, 35 + t2 and r2(s) = 7 − s, s − 5, s2 intersect at the point (2.5, -2.5).

An equation is a mathematical statement that asserts the equality of two expressions. It is usually written with an equals sign (=) and expresses the relationships between different variables and constants. Equations are often used to model or describe physical, biological, and chemical phenomena and relationships.

This can be seen by solving the system of equations formed by equating the two curves:

t = 7 − s
2 − t = s − 5
35 + t2 = s2

Solving the first two equations for t and s yields t = 7 − s and s = 2 − t. Plugging these equations into the third equation yields:

35 + (7 − s)2 = s2

By rearranging terms and solving, this equation can be solved for s, which yields s = 2.5. Plugging this value back into the first two equations yields t = 7 − 2.5 = 4.5 and s = 2 − 4.5 = -2.5. Thus, the two curves intersect at the point (2.5, -2.5).

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Answer:

3 = 1 + 1/2 + 2/2 + 1/2

The blank number is:

1

Step-by-step explanation:

2/2 = 1

1/2 + 1/2 = 2/2

3 = a + 1/2 + 2/2 + 1/2

3 = a + 1 + 1

3 = a + 2

3 - 2 = a

a = 1

The probability that the chosen coin is the two-headed one will be 1/16.

It should be noted that probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events.

In this situation, one coin in a collection of 16 coins has two heads, the rest being fair coins with a head and a tail each.

When a coin is chosen at random from the collection and tossed four times, coming up with a head on each of the four tosses, the probability that the chosen coin is the two-headed one will be:

= Number of two headed coins / Total coins

= 1/16

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1000 kg of limestone is subjected to intense heat and high pressure to form marble. So, the statement "about 1000 kg of marble is produced" is applies to the formation of the marble. Hence, option b is correct.

When limestone is subjected to the heat and pressure of metamorphism, marble is created as a metamorphic rock. Calcite (CaCO3) makes up the majority of its composition, but it also frequently includes other minerals such clay, mica, quartz, pyrite, iron oxides, and graphite.

When limestone undergoes a process known as metamorphism, which involves heat and tremendous pressure, marble is created. The marble's interconnecting calcite crystals are created when the calcite limestone recrystallizes after metamorphism.

Hence, 1000 kg of limestone is subjected to intense heat and high pressure to form marble. So, the statement "about 1000 kg of marble is produced" is applies to the formation of the marble. Hence, option b is correct.

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Answer:

$17.08

Step-by-step explanation:

Ok, so we know it takes 61-23 = 38 minutes of call to change the credit from $22.24 to $17.68.

Basically, it takes 43 minutes to lose 22.24 - 17.68 = $4.56

38 minutes - $4.56

5 minutes - $4.56 x 5 /38 = 0.6

I took 5 minutes because 5 + 61 = 66

Now, we know it takes 61 minutes for the person to have $17.68 remaining.

So, if we had 5 minutes, it becomes 17.68 - 0.6 = $17.08 remaining.

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Therefore ,as a result, the answer to the given circle problem is  

√ 1996/(√ 62)3 =0.0915, which is the curvature.

A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is rotationally symmetric the about center at every angle. Every pair of endpoints in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally equal about the center at every angle.

Here,

Given: (7, 2t, 3t2) r'(t)

r''(t)= (0, 2, 6t) (0, 2, 6t)

r(t) x r(t) = (6t2, -42t, 14)

(36t4 + 1764t2 + 196) = sqrt (r'(t) x r"(t)

|r'(t)|= sqrt (49 + 4 T 2 + 9 T 4)

We know that t = 1 at (7,1,1), therefore sqrt (36 + 1764 + 196) = sqrt 1996 |r'(t)| = √ (49 + 4 + 9) = √ 62.

The curvature is then equal as√ 1996/(√ 62)3 =0.0915

Therefore ,as a result, the answer to the given circle problem is  √ 1996/(√ 62)3 =0.0915, which is the curvature.

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By using the logarithmic properties we can probe that,

(a) [tex]$\log _b \frac{x}{y}=\log _b x+\log _b y^{-1}$[/tex]

(b) [tex]$\log _b \frac{x}{y}=\log _b x-\log _b y$[/tex]

The logarithm is exponentiation's opposite function In mathematics. This means that the exponent which [tex]$b$[/tex] must be realized To produce a number [tex]$x$[/tex] is the logarithm of [tex]$x$[/tex] the base [tex]$b$[/tex]. For Instance, because[tex]$1000=10^{\wedge} 3$, Its logarlthm In base 10 is 3 , or $\log 10=3$.[/tex]

Given: [tex]$\log _b \frac{x}{y}$[/tex]

We have to prove,

(a) [tex]$\log _b \frac{x}{y}=\log _b x+\log _b y^{-1}$[/tex]

(b) [tex]$\log _b \frac{x}{y}=\log _b x-\log _b y$[/tex]

(a) Consider, [tex]$\log _b \frac{x}{y}=\log _a x+\log _b y^{-1}$[/tex]

L. H. S [tex]$=\log _b \frac{x}{y}$[/tex]

Using the Identity:  [tex]$\frac{1}{\nu}=y^{-1}$[/tex]

L.H.S [tex]$=\log _b x y^{-1}$[/tex]

Using Identity: [tex]$\log _b m n=\log _b m+\log _b n$[/tex]

[tex]$$\Rightarrow \text { L.H.S }=\log _b x+\log _b y^{-1}$$[/tex]

Hence, L.H.S = R.H.S

(b) Consider [tex]$\log _b \frac{x}{y}=\log _b x-\log _b y$[/tex]

L.H.S [tex]$=\log _b \frac{x}{y}$[/tex]

Using the Identity

[tex]$$\begin{aligned}& \log _b \frac{m}{n}=\log _b m-\log _b n \\& \Rightarrow \text { L.H.S }=\log _b x-\log _b y \\& \text { L.H.S = R.H.S }\end{aligned}$$[/tex]

Hence, proved.

Hence, by using the logarithmic properties we can probe that,

(a) [tex]$\log _b \frac{x}{y}=\log _h x+\log _b y^{-1}$[/tex]

(b) [tex]$\log _b \frac{x}{y}=\log _b x-\log _b y$[/tex]

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Answer:

=C

=A

=D

=B

Step-by-step explanation:

Correct on Edge

Answer:

1 mile is about 1.6 km

1 feet is 30cm.

Safe to say a mile is bigger.

Answer:

Miles are bigger than feet.

Step-by-step explanation:

In 1 mile, there are 5,280 feet. So miles would be 5,280 times bigger than feet.

The volume of the cylinder is 301.44 cm³. We use the radius that is half of diameter length in the formula for the volume of a cylinder.

The formula for the volume of a cylinder is

V = πr²h

Where

A cylinder has

Using π = 3.14, find the volume of the cylinder!

We find the radius of the cylinder.

r = ½d

r = ½(8) cm

r = 4 cm

The volume of the cylinder would be

V = πr²h

V = (3.14)(4)²(6)

V = 18.84 (16)

V = 301.44 cm³

Hence, the volume of a cylinder with the diameter of 8 cm and height of 6 cm is 301.44 cm³.

The correct option is (c).

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Answer:

301.44

Step-by-step explanation:

v=3.14 times radius squared times height

Diameter is the radius times 2

8 the diameter divided by 2 is 4

replace those

v=(3.14)4^2(6)

final answer is 301.44