If you know answer please.
A water park has pools, slides, and rides that, in total, make use of 2.4 x 106 gallons
of water. They plan to add a ride that would make use of an additional 6,800 gallons
of water. Use scientific notation to express the total gallons of water made use of in
the park after the new ride is installed.

The requried equivalent fraction is 7/4. Option B is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Fraction is defined as the number of compositions that constitutes the Whole.

here,
7/6 divided by 2/3
= 7/6 ÷ 2/3
= 7/6 × 3/2
= 7/4

Thus, the requried equivalent fraction is 7/4. Option B is correct.

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Answer:

Step-by-step explanation:

You want the length of the hypotenuse of a right triangle with sides given as 3.6×10⁶ km and 1.6×10⁷ km.

The Pythagorean theorem tells you the relationship between the side lengths and the hypotenuse of a right triangle:

  c² = a² +b²

  RQ² = PQ² +PR²

  RQ = √((3.6×10⁶)² +(1.6×10⁷)²) = 1.64×10⁷ . . . . . use numbers, take the root

The distance between planets Q and R is 1.64×10⁷ km.

__

Additional comment

The "standard form" of a number is different by location. In the US, it is written with the decimal point to the right of the units digit. In other places, "standard form" has the decimal point to the right of the most-significant digit, and a power of ten as a multiplier.

You may recognize the ratio of the given numbers is 9:40, telling you these lengths are a multiple of the {9, 40, 41} Pythagorean triple. That is, the distance RQ is 41/40 times the distance RP.

Any spreadsheet or scientific or graphing calculator can do the necessary arithmetic using the numbers in "scientific notation" format. Spreadsheets, in particular, use E() to signify ×10^(). That is, 3.6×10⁶ is entered into a spreadsheet as 3.6E6. The attached calculator display shows it can use the same sort of format.

Just use Pythagoras theorem to find the shortest distance between the two planets, (as it is along its hypotenuse)

The distance QR is :

[tex] \qquad \sf \rightarrow d = \sqrt{(1.6 \times 10 {}^{7}) {}^{2} + (3.6 \times 10 {}^{6} ) {}^{2} } [/tex]

[tex] \qquad \sf \rightarrow d = \sqrt{2.56 \times 10 {}^{14} + 12.96 \times 10 {}^{12} {}^{} } [/tex]

[tex] \qquad \sf \rightarrow d = \sqrt{256\times 10 {}^{12} + 12.96 \times 10 {}^{12} {}^{} } [/tex]

[tex] \qquad \sf \rightarrow d = \sqrt{(256 + 12.96 )\times 10 {}^{12} {}^{} } [/tex]

[tex] \qquad \sf \rightarrow d = \sqrt{(268.96 )\times 10 {}^{12} {}^{} } [/tex]

[tex]\qquad \sf \rightarrow d = 16.4\times 10 {}^{6} {}^{} [/tex]

Answer:

Step-by-step explanation:

teaj

Answer:

Two blue = 6

Step-by-step explanation:

Let r = red

Let b = blue

2r + r + b = 21

r - b = 3    Can we rewritten  r = 3 + b  Substitute 3 + b  for r into the first equation

2r + r + b = 21

2(3 + b) + 3 + b + b =  21   Distribute the 2

6 + 2b + 3 + b + b = 21  Combine like terms

9 + 4b = 21  Subtract 9 from both sides

9 - 9 + 4b = 21 - 9

4b = 12  Divide both sides by 4

[tex]\frac{4b}{4}[/tex] = [tex]\frac{12}{4}[/tex]

b = 3

2 blues would equal 6.

Answer:

6

Step-by-step explanation:

Define the variables:

From the given blackboard, create a system of equations from the first three equations:

[tex]\begin{cases}3x + y = 21\\\;\:x - y = 3\\2x + y = 15\end{cases}[/tex]

Add the first equation to the second equation to eliminate y:

[tex]\begin{array}{lrcccr}& 3x & + & y & = & 21\\+ & (x & - & y & = & 3\\\cline{2-6} &4x &&&=&24\end{array}[/tex]

Solve the equation for x:

[tex]\implies \dfrac{4x}{4}=\dfrac{24}{4}[/tex]

[tex]\implies x=6[/tex]

Substitute the found value of x into the second equation and solve for y:

[tex]\implies 6-y=3[/tex]

[tex]\implies y=3[/tex]

Therefore, the value of the red pencil is 6 and the value of the blue pencil is 3.

Finally, substitute the found value of y into the last equation:

[tex]\implies 3 + 3 = \boxed{6}[/tex]

Answer:

$9,712.12 (nearest cent)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies A=9544\left(1+\frac{0.0525}{12}\right)^{12 \cdot \frac{1}{3}}[/tex]

[tex]\implies A=9544\left(1.004375\right)^{4}[/tex]

[tex]\implies A=9544\left(1.017615179\right)[/tex]

[tex]\implies A=9712.119269[/tex]

The balance of the account at the end of August will be $9,712.12 (nearest cent).

Answer: [tex]y \leq -\frac{x}{2}-\frac{7}{2}[/tex]

Step-by-step explanation:

[tex]-x-2y \geq 7\\\\x+2y \leq -7\\\\2y \leq -x-7\\\\y \leq -\frac{x}{2}-\frac{7}{2}[/tex]

Answer:

A.86

is the answer will show how it's solved if necessary on comment.

hope it helps!!!

Answer:

√192

Step-by-step explanation:

12 cos 30° + 2 tan 60°

Substitute the trig functions of the special angles.

12 (½√3) + 2 (√3)

Simplify.

6√3 + 2√3

8√3

Move under the radical.

√(8² · 3)

√192

Answer:

Step-by-step explanation:

The initial height of the rocket before it is launched can be found by evaluating the function h(t) at t=0. To do this, you can substitute 0 for t in the function:

h(0) = -5(0)² + 42(0) + 54

h(0) = 0 + 0 + 54

h(0) = 54

Therefore, the initial height of the rocket before it is launched is 54 meters.

Answer: 54 meters.

Step-by-step explanation: The initial height of the rocket before it is launched is represented by the constant term in the quadratic function, which is 54. This means that the rocket's height at time t = 0 (before it is launched) is 54 meters.

To confirm this, you can plug in t = 0 into the quadratic function to get:

h(0) = -5(0)² + 42(0) + 54 = 54 meters

This means that the initial height of the rocket before it is launched is 54 meters.

Answer: [tex]9x+4y=-20[/tex]

Step-by-step explanation:

Standard form is ax+by=c. What we can do is put the given point and slope into slope-intercept point, and then manipulate it to standard form.

[tex]y=-\frac{9}{4} x-5[/tex]                  [add both sides by [tex]\frac{9}{4} x[/tex]]

[tex]\frac{9}{4} x+y=-5[/tex]                   [multiply both sides by 4]

[tex]9x+4y=-20[/tex]

Therefore the standard form is [tex]9x+4y=-20[/tex].

The decimal point is to be placed three places to the left.

What are decimal numbers?

When we divide a whole number into smaller parts, we get decimals. Then, there are two parts to a decimal number: a whole number part and a fractional part. The whole component of a decimal number has the same decimal place value system as the complete number. After the decimal point, however, when we proceed to the right, we obtain the fractional portion of the decimal number.

Given that, in the question, the product of a decimal number between 350 and 400 and 0.48 results in the numbers 182136. As 0.48 is just 48/100, let's take a decimal number between 350 and 400.

If the number is 370.1, for example, we can write it as 3701/10 because it has one decimal point.

Our denominator will be 1000, because both the denominators are 100 and 10, which is equivalent three decimal places to the left of the result when we multiply 48/100 by 3701/10.

The result provided to us should therefore be written as 182.136, with the decimal point moved three spaces to the left.

The decimal point is to be placed three places to the left.

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Answer:

Step-by-step explanation:

• 12a - 2b - 4b - 15a + 2 (a = 0, b = 3)

→ apply the values

• 12x0 - 2x3 - 4x3 - 15x0 + 2

• 0 - 6 -12 - 0 + 2

→ use BODMAS formulae

• 0 - 6 - 12 - 2

= 0 - 6 - 10

→ zero wouldn't be counted so

- 6 - 10

(-) + (-) = (+) so:

= -16

Using geometry rules such as Vertically Opposite Angles and Triangle rules for sum of internal and external angles, The answer to the numbered angles in order is : [tex]92^{o} , 30^{o},91^{o},59^{o},57^{o},55^{o},135^{o}[/tex] .

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed. It implies that the internal angles of a triangle add up to 180 degrees.

The six types of triangles are:

<10 = 62+30 = [tex]92^{o}[/tex] (sum of opposite angle of triangle)

<11=[tex]30^{o}[/tex] (Vertically Opposite angles)

<13=[tex]59^{o}[/tex] (Vertically Opposite angles)

<12 = 180-59-30 = [tex]91^{o}[/tex] (Sum of angle of triangle is 180)

<16 = 59 +76 = [tex]135^{o}[/tex] (sum of opposite angle of triangle)

<14 = 180-59-64 = [tex]57 ^{o}[/tex] (Angle in a straight line is 180)

<15 = 112-57 = [tex]55^{o}[/tex] (sum of opposite angle of triangle)

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Using geometry rules such as Vertically Opposite Angles and Triangle rules for sum of internal and external angles, The answer to the numbered angles in order is :  

What is a triangle?

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed. It implies that the internal angles of a triangle add up to 180 degrees.

What are the 6 types of triangles?

The six types of triangles are:

<10 = 62+30 =  (sum of opposite angle of triangle)

<11= (Vertically Opposite angles)

<13= (Vertically Opposite angles)

<12 = 180-59-30 =  (Sum of angle of triangle is 180)

<16 = 59 +76 =  (sum of opposite angle of triangle)

<14 = 180-59-64 =  (Angle in a straight line is 180)

<15 = 112-57 =  (sum of opposite angle of triangle)

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Answer:

j = 4

Step-by-step explanation:

calculate the slope of the line passing through the goven points and equate to 2

calculate slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 7, - 10 ) and (x₂, y₂ ) = (0, j )

m = [tex]\frac{j-(-10)}{0-(-7)}[/tex] = [tex]\frac{j+10}{0+7}[/tex] = [tex]\frac{j+10}{7}[/tex] then equating gives

[tex]\frac{j+10}{7}[/tex] = 2 ( multiply both sides by 7 to clear the fraction )

j + 10 = 14 ( subtract 10 from both sides )

j = 4

Answer:

Questions and answers

Doubtnut

Question

How many ways can 2 identical red chairs and 4 identical blue chairs be arranged in one row ?

Answer · 21 votes

There is a formula that applies to this situation. The number of distinct permutations of n things, a of which are indistinguishable, b of which are indistinguishable, atc., is `(n!)/(a!b!...)` Here there are 6 chairs, 2 of which are indistinguishable and 4 of which are indistinguishable, so the number of permutations is `(6!)/(2!4!)=(6.5.4.3.2.1)/(2.1.4.3.2.1)=(6.5)/(2)=15`

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Question

18 blue chairs and 27 red chairs have to be arranged in rows in such a way that there are an equal no. of chairs of the same colour in each row, what is the maximum no. of chairs that can be arranged in each row and how many rows can the chairs be arranged in?

Answer · 27 votes

Answer: highest number of chairs in each row is 9Total rows is 5Step-by-step explanation:Find the Highest Common Factor of 18 and 27The HCF of 18, 27 is 9Thus the maximum no of chairs that can be arrranged in each row is 9Total rows is (18+27)/9 = 5Please brainlist my answer, if helpful!

More

There are 15 different ways to arrange the 2 identical red chairs and 4 identical blue chairs in one row.

To find the number of ways the 2 identical red chairs and 4 identical blue chairs can be arranged in one row, we need to calculate the total number of arrangements considering that the chairs of the same color are identical.

The total number of chairs is 2 red + 4 blue = 6 chairs.

Since the chairs of the same color are identical, the arrangements will be different only if the arrangement of colors is different. Therefore, we need to find the number of arrangements of 2 red and 4 blue chairs.

To calculate this, we can use the formula for permutations with repetition. The formula is given by:

P(n; n1, n2, ..., nk) = n! / (n1! * n2! * ... * nk!)

Where:

n is the total number of objects (chairs in this case).

n1, n2, ..., nk are the number of objects of each type (number of red and blue chairs in this case).

In our case, we have 6 chairs in total, and we want to arrange 2 red and 4 blue chairs. So, the number of arrangements is:

P(6; 2, 4) = 6! / (2! * 4!)

          = (6 * 5 * 4 * 3 * 2 * 1) / (2 * 1 * 4 * 3 * 2 * 1)

          = 15

Therefore, there are 15 different ways to arrange the 2 identical red chairs and 4 identical blue chairs in one row.

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The length of the other leg is (c) √43

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

Hypotenuse = 7

One leg = √6

The length of the other leg can be calculated using

The length of the other leg = √(Hypotenuse^2 - One leg^2)

So, we have

The length of the other leg = √(7^2 - √6^2)

Evaluate

The length of the other leg = √43

Hence, the length is (c) √43

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Complete question

A right triangle has a leg length of √6 and a hypotenuse length of 7. Determine the length of the other leg of the right triangle.

1) The two column proof for ΔLMN ≅ ΔLON is as developed below.

2) The  two column proof for ΔGHJ ≅ ΔKLM is as developed below

A two-column proof is defined as a geometric proof that consists of a list of statements, and then the reasons that we know those statements are deemed to be true.

1) The two column proof showing that ΔLMN ≅ ΔLON is;

Statement 1: LN bisects ∠MLO and LM ≅ LO

Reason 1: Given

Statement 2: MN ≅ ON

Reason 2: Line segment bisector

Statement 3: ∠MLN ≅ ∠OLN

Reason 3: def. of angle bisector

Statement 4: LN ≅ LN

Reason 4: Reflexive property of congruence

Statement 5: ΔLMN ≅ ΔLON

Reason 5: SSS Congruency postulate

2) The two column proof is as follows;

Statement 1: ∠G ≅ ∠K, ∠J ≅ ∠M

Reason 1: Given

Statement 2: ∠H ≅ ∠L

Reason 2: 3rd angle theorem

Statement 4: ΔGHJ ≅ ΔKLM

Reason 4: ASA Congruency Postulate

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Answer:

After one half-life,

50% of the atoms will change to a stable isotope and

50% will remain radioactive.

After three half-lives,

87.5% of the atoms will change to a stable isotope and

12.5% will remain radioactive.

Step-by-step explanation:

During the 1st half-life, 50% of the atoms change to a stable isotope, 50% radioactive left.

During the 2nd half-life, 50% of the left 50% radioactive change to a stable isotope, which is 25% of the total. 50% of 50% radioactive left, which is 25% of the total. Then 75% change to a stable isotope and

25% remain radioactive.

During the 3rd half-life, 50% of the left 25% radioactive change to a stable isotope, which is 12.5% of the total. 50% of 25% radioactive left, which is 12.5% of the total. Then 87.5% change to a stable isotope and

12.5% remain radioactive.

Answer:

below

Step-by-step explanation:

9x^2-3x-10 = 0     Use quadratic Formula with a = 9   b = -3  and c = -10

to find the zeroes are   x = 1/6 ± sqrt (41) / 6

Subtract 3

2y + 2xy – x + 4 from 9 - 7x + 3xy - 4

2y

In terms of the percentage of downloaded books, the sampling distribution's mean is 0.03 and its standard deviation is 0.0197.

Central Limit Theorem:

The sampling distribution of the sample percentage for a proportion p in a sample of size n will be roughly normal with a mean (μ = p) and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n} }[/tex].

In a given year, 3% of books checked out from the library are downloaded.

That means p = 0.03

and n = 75

By the Central Limit Theorem

Mean = μ = p = 0.03

Standard deviation =  [tex]s = \sqrt{\frac{p(1-p)}{n} }[/tex]

                                   [tex]s = \sqrt{\frac{(0.03)(0.97)}{75} }[/tex]

                                   [tex]s=0.0197[/tex]

Hence,

         In terms of the percentage of downloaded books, the sampling distribution's mean is 0.03 and its standard deviation is 0.0197.

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Answer: last option

Step-by-step explanation: every value can be divided by 21

Answer: D)

Step-by-step explanation: 21 x 6 = 126, 21 x 8 = 168, and 21 x 9 = 189

Answer:

(2½,1)

Step-by-step explanation:

(-1+6/2,5+-3/2)

(5/2,2/2)

(2½,1)

Answer:

C would be the answer

Step-by-step explanation:

constants are the numbers with no terms.

The measure of one of the congruent base angles is 65°.

It's important to note that any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane. In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane. A triangle has three sides, three angles and the sum of the angles equal 180°.

It should be noted that a triangle has 3 side, 3 angles and a sum of 180°.

In this situation, DEF is an isosceles triangle. If m∠D = (3x + 5)° , m∠E = (4x − 15)° and m∠F = (2x + 10)°.

The value will be illustrated thus:

3x + 5 + 4x - 15 + 2x + 10 = 180

Collect the like terms

9x = 180 - 5 + 15 - 10

9x = 180

x = 180 / 9

x = 20

The measure of one of the congruent base angles will be:

= 4x - 15

= 4(20) - 15

= 65°

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The value of y in the given diagram is 6cm.

What is triangle?

Three edges and three vertices make up a triangle, which is a polygon. It is among the fundamental shapes in geometry. Triangle ABC refers to a triangle with the vertices A, B, and C.

In Euclidean geometry, any three points that are not collinear determine a singular triangle and a singular plane at the same time.

Consider, the given triangle the two base angles are same.

So, the triangle is a isosceles triangle.

Since, when the base angles of an isosceles triangle are equal, the sides that face these angles are also equal.

Hence, the value of y in the given diagram is 6cm.

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Given that e1 and e2 have a high spearman correlation, what we can say about the Pearson correlation of e1 and e2 is; The Pearson correlation must be high

A correlation coefficient is defined as the measurement of the extent to which two variables tend to change together.

Now, the Pearson correlation is the type that evaluates the linear relationship that exists between two continuous variables. A relationship is said to be linear as a result of a change in one variable being associated with a proportional change in the other variable.

Meanwhile, the spearman correlation is one that evaluates the monotonic relationship between two continuous or ordinal variables.

If the relationship described above tells us that one variable increases when the other increases, but then the amount is not consistent, then it means that the Pearson correlation coefficient is positive but less than +1. However, the Spearman coefficient still equals +1 in this case.

Thus, we conclude that as the spearman correlation is high, then the Pearson correlation is also high.

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The coordinates of Point E are (-4,2) and Point E is a reflection of point D across the X-axis.

Point E has the same y-coordinate as point D, which is 2. However, the x-coordinate of point E is the opposite of the x-coordinate of point D. The x-coordinate of point D is 4, so the x-coordinate of point E must be -4. Therefore, the coordinates of Point E are (-4,2).

As for the reflection, you can imagine a mirror placed on the x-axis (horizontally) and Point D and E being on the same side of that mirror.

Therefore, As Point D is reflected on the mirror, it will be flipped and the x-coordinate changes its sign and becomes -4. Therefore Point E is a reflection of point D across the X-axis.

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See full question below

Point E has the same y-coordinate as point D, but the x-coordinate of point E is the opposite of the x- coordinate of point D. Drag tiles to complete the statements. (4,2) (4,-2) (-4,2) (-4,-2) X-axis y-axis The coordinates of Point E are --- &Point E  is a reflection of point D across the ---

The value of x for the expression is equal to -5 and -2.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the logarithmic expression is log₂ (x+4) + log₂ (x + 3) = 1. The value of x will be calculated as,

log₂ (x+4) + log₂ (x + 3) = 1

log₂ { (x+4)(x + 3) } = 1

x² + 7x + 12 = 2

x²+ 7x + 10 = 0

Solve the above quadratic equation,

x²+ 7x + 10 = 0

x² + 5x + 2x + 10 =0

x ( x + 5 ) + 2 ( x + 5 ) = 0

(x + 5 ) ( x + 2 ) = 0

x  = -5 and -2

The values of x are -5 and -2.

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0-4 can be the domain of positive real numbers but can not be the domain of whole numbers.

Numbers an arithmetical value used in counting and calculating that is expressed as a word, symbol, or figure that represents a specific quantity.

Let's understand what is positive real numbers.

That is all the real numbers that are greater than or equal to zero.

real numbers are numbers which include both rational and irrational numbers.

whole numbers are positive integers that mean only positive integers.

that means 0-4 can be the domain of positive real numbers but can not be the domain of whole numbers because 0.5 and 0.6 these numbers are not whole numbers.

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