An amusement park says "You must be 40 inches tall to ride" What percentage of this height is:
a. 34 inches?
b. 54 inches?

We can explain the process of multiplying the number of mittens lost by 3 kittens and then multiplying the result by the voting age in the U.S.

To calculate the answer, we first need to know the number of mittens lost. Let's assume it is represented by "M." Next, we multiply M by 3 kittens, which results in 3M. Finally, we need the voting age in the U.S., denoted by "V." By multiplying 3M by V, we obtain the answer, which is 3M * V.

Without specific values for M (number of mittens lost), the number of kittens, and V (voting age in the U.S.), we cannot provide a numerical answer. However, the multiplication process is outlined above. To find the actual answer, you would need to substitute the appropriate values into the equation 3M * V.

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Answer:

289 miles.

Step-by-step explanation:

4 and 15 mins is 4.25 hours.68 c 4.25 = 289.Hope this helps.

1.5·10⁸ kilometers

As a result, the Earth Sun distance is 150 million kilometers. To use scientific notation, pick a value between 1 and 10, then multiply it by 10ˣ.

So the number between 1 and 10 in 150,000,000 is 1.5, with 8 decimal points.

As a result, the solution is 1.5·10⁸

The benefits of Earth's prime placement in the solar system are numerous. We are just far enough away from the Sun for life to thrive.

Venus is excessively hot. Mars is quite chilly. Scientists refer to our region of space as the "Goldilocks Zone" because it looks to be ideal for life.

As previously stated, Earth's average distance from the Sun is around 93 million miles (150 million kilometers). That's one AU.

On this hypothetical scale, these so-called "linebackers" resemble minuscule specks rather than the massive linebackers of the NFL.

If all of the known asteroids in our solar system were combined, their total mass would be less than 10% that of Earth's moon.

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Answer:

Suppose A and B , both has initial volume, say x

120 ML is poured from B to A, then new volumes of A and B will be:

new volume of A (x-120)

new volume of B  (x+120)

Volume of B is now four times volume of A, then

(x+120)= 4(x-120)

(x+120)=4x-180

3x=600

x=200

So, the initial volume of A and B containers is 200

So, at the end, volume of container A = 200-120=80

Hence the answer is 80   :

Step-by-step explanation:

a) Approximate Doubling Time Dappx = 70/r, where r is the annual interest rate in percentage terms.Assuming that r = 5%, 10%, 20%, 40%, and 60%Doubling time for 5% = 70/5 = 14 yearsDoubling time for 10% = 70/10 = 7 yearsDoubling time for 20% = 70/20 = 3.5 yearsDoubling time for 40% = 70/40 = 1.75 yearsDoubling time for 60% = 70/60 = 1.1667 yearsb) Exact Doubling Time Dexact = ln2/r where r is the annual interest rate in decimal terms.

Assuming that r = 5%, 10%, 20%, 40%, and 60%For 5%: ln2/0.05 ≈ 13.86 yearsFor 10%: ln2/0.1 ≈ 6.93 yearsFor 20%: ln2/0.2 ≈ 3.47 yearsFor 40%: ln2/0.4 ≈ 1.73 yearsFor 60%: ln2/0.6 ≈ 1.16 yearsc)

The percentage error is given by:(Dexact − Dappx)/Dexact × 100%For 5%: (13.86 - 14)/13.86 x 100% ≈ 1.18%For 10%: (6.93 - 7)/6.93 x 100%

≈ 1.15%For 20%: (3.47 - 3.5)/3.47 x 100%

≈ -0.86%For 40%: (1.73 - 1.75)/1.73 x 100%

≈ -1.15%For 60%: (1.16 - 1.1667)/1.16 x 100%

≈ -0.60%Note that the percentage error is small for lower values of interest rates but increases as the interest rate increases.

Also, the percentage error is negative for 20%, 40%, and 60%, which means that the approximate doubling time is actually larger than the exact doubling time.

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To rewrite this expression using the function notation, we will have:

f (x) = -6x^3

To rewrite an expression using the function notation, we simply have to reorganize the expression in a way that f(x) can feature. For the provided mathematical expression above, this will mean replacing the figure y with the function notation. Thus, we will have:

f (x) = -6x^3

Let's say that we assign figure 2 to x, then the function will give us:

f (x) = -6(2)^3

f (x) = -6(8)

f (x) = -48

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Answer:

If each avocado costs 0.50, then 16 avocados would cost $8.00, 9 avocados would cost $4.50

Hope this helps! :)

Answer:

2.8125 gallons per hour

Step-by-step explanation:

gallon = 128 fl oz

hour = 60 minutes

(6/128) x 60 = 2.8125

Answer:

DC = 10 cm

Step-by-step explanation:

given a tangent and a secant drawn to the circle from an external point, then the square of the measure of the tangent is equal to the product of the secant's external part and the entire secant , that is

AC × AD = AB²

8(8 + x) = 12² = 144 ( divide both sides by 8 )

8 + x = 18 ( subtract 8 from both sides )

x = 10

that is DC is 10 cm

Answer:

180 degrees - 101 degrees - 65 degrees = 14 degrees

The average length of the queue and the Average number in the system.

the average time spent in the system can be calculated as:

W = Wq + (1 / μ)

The  M/G/1 system, we need to calculate the following parameters:

a. The probability that the system is idle.

b. The average length of the queue.

c. The average number in the system.

Let's solve each part step by step:

a. Probability that the system is idle (ρ):

The utilization factor (ρ) represents the ratio of the average arrival rate (λ) to the average service rate (μ). In an M/G/1 system, the probability that the system is idle can be calculated as:

P(Idle) = 1 - ρ

In this case, λ = 6 and μ = 9, so:

ρ = λ / μ = 6 / 9 = 2 / 3

Therefore,

P(Idle) = 1 - ρ = 1 - 2/3 = 1/3

b. Average length of the queue (Lq):

The average length of the queue can be calculated using Little's Law, which states that Lq = λ * Wq, where Wq represents the average time spent in the queue.

In an M/G/1 system, the average time spent in the queue (Wq) can be calculated using the Pollaczek-Khinchine formula:

Wq = ρ^2 / (2 * (1 - ρ)) * (σ^2 + (μ^2 / λ^2))

In this case, σ = 0.03, λ = 6, and μ = 9, so:

Wq = (2/3)^2 / (2 * (1 - 2/3)) * (0.03^2 + (9^2 / 6^2))

Simplifying the equation will give us the value of Wq.

c. Average number in the system (L):

The average number in the system (L) can be calculated as L = λ * W, where W represents the average time spent in the system. In an M/G/1 system,

Substituting the values of Wq and μ into the equation will give us the value of W. Then, we can calculate L by multiplying λ and W.

Lq and L, we can determine the average length of the queue and the average number in the system, respectively.

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Answer:

The area of the park is 1,11,739 square feet.

Step-by-step explanation:

Since, the area of a triangle is,

Where,  and  are the adjacent sides and  is the included angle of these sides,

Here, the two adjacent sides of the park are 533 feet and 525 feet, while, the angle included by these sides is 53°.

That is,   = 533 ft,  = 525 ft and  = 53°,

Hence, the area of the park is,

Step-by-step explanation:

Two adjacent sides of the park say x and y are,

x=533feet

y=525feet

A=53º

area=1/2*b*c*sin(A)

111739 feet^2

Answer:

(2x+3y)(x2+3x+2). it may helps you

Answer:

\(\tt 2x^3+3x^2y+6x^2+9xy+4x+6y\)

Step-by-step explanation:

\(\tt x^2(2x + 3y) + 3x (2x + 3y) +2 (2x + 3y)\)

Expand by distributing terms:-

\(\tt 2x^3+3x^2y+3x(2x+3y)+2(2x+3y)\)

Expand by distributing terms:-

\(\tt 2x^3+3x^2y+6x^2+9xy+4x+6y\)

~

Answer:

\(2x - 3 + \frac{1}{x-1}\)

Step-by-step explanation:

Attachment :)

We use long division

Answer:

1) For \(x^2 + y^2 - 4x + 12y - 20 = 0\), the standard form is \((x-2)^2 + (y+6)^2 = 60\\\)

2) For \(x^2 + y^2 + 6x - 8y - 10 = 0\), the standard form is \((x + 3)^2 + (y - 4)^2 = 35\\\)

3) For \(3x^2 + 3y^2 + 12x + 18y - 15 = 0\),  the standard form is \((x + 2)^2 + (y+ 3)^2 = 18\\\)

4) For \(5x^2 + 5y^2 - 10x + 20y - 30 = 0\),  the standard form is \((x - 1)^2 + (y+ 2)^2 = 11\\\)

5) For \(2x^2 + 2y^2 - 24x - 16y - 8 = 0\),  the standard form is \((x - 6)^2 + (y+ 4)^2 = 56\\\)

6) For\(x^2 + y^2 + 2x - 12y - 9 = 0\), the standard form is \((x+1)^2 + (y-6)^2 = 46\\\\\)

Step-by-step explanation:

This can be done using the completing the square method.

The standard equation of a circle is given by \((x - a)^2 + (y-b)^2 = r^2\)

1) For \(x^2 + y^2 - 4x + 12y - 20 = 0\)

\(x^2 - 4x + y^2 + 12y = 20\\x^2 - 4x + 2^2 + y^2 + 12y + 6^2 = 20 + 4 + 36\\(x-2)^2 + (y+6)^2 = 60\\\)

Therefore, for \(x^2 + y^2 - 4x + 12y - 20 = 0\), the standard form is \((x-2)^2 + (y+6)^2 = 60\\\)

2) For \(x^2 + y^2 + 6x - 8y - 10 = 0\)

\(x^2 + 6x + y^2 - 8y = 10\\x^2 + 6x + 3^2 + y^2 - 8y + 4^2 = 10 + 9 + 16\\(x + 3)^2 + (y- 4)^2 = 35\\\)

Therefore, for \(x^2 + y^2 + 6x - 8y - 10 = 0\), the standard form is \((x + 3)^2 + (y - 4)^2 = 35\\\)

3)  For \(3x^2 + 3y^2 + 12x + 18y - 15 = 0\)

Divide through by 3

\(x^2 + y^2 + 4x + 6y = 5\)

\(x^2 + y^2 + 4x + 6y = 5\\x^2 + 4x + 2^2 + y^2 + 6y + 3^2 = 5 + 4 + 9\\(x + 2)^2 + (y+ 3)^2 = 18\\\)

Therefore, for \(3x^2 + 3y^2 + 12x + 18y - 15 = 0\),  the standard form is \((x + 2)^2 + (y+ 3)^2 = 18\\\)

4)  For \(5x^2 + 5y^2 - 10x + 20y - 30 = 0\)

Divide through by 5

\(x^2 + y^2 - 2x + 4y = 6\)

\(x^2 + y^2 -2x + 4y = 6\\x^2 - 2x + 1^2 + y^2 + 4y + 2^2 = 6 + 1 + 4\\(x - 1)^2 + (y+ 2)^2 = 11\\\)

Therefore, for \(5x^2 + 5y^2 - 10x + 20y - 30 = 0\),  the standard form is \((x - 1)^2 + (y+ 2)^2 = 11\\\)

5) For \(2x^2 + 2y^2 - 24x - 16y - 8 = 0\)

Divide through by 2

\(x^2 + y^2 - 12x - 8y = 4\)

\(x^2 + y^2 - 12x - 8y = 4\\x^2 - 12x + 6^2 + y^2 - 8y + 4^2 = 4 + 36 + 16\\(x - 6)^2 + (y+ 4)^2 = 56\\\)

Therefore, for \(2x^2 + 2y^2 - 24x - 16y - 8 = 0\),  the standard form is \((x - 6)^2 + (y+ 4)^2 = 56\\\)

6) For \(x^2 + y^2 + 2x - 12y - 9 = 0\)

\(x^2 + 2x + y^2 - 12y = 9\\x^2 + 2x + 1^2 + y^2 - 12y + 6^2 = 9 + 1 + 36\\(x+1)^2 + (y-6)^2 = 46\\\)

Therefore, for\(x^2 + y^2 + 2x - 12y - 9 = 0\), the standard form is \((x+1)^2 + (y-6)^2 = 46\\\\\)

For Plato / Edmentum

Just to the test and got it right ✅

The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers. To calculate the t-value, the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

Given, M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers.

To calculate the t-value,

the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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Answer:

rational number

Step-by-step explanation:

a rational number can be written as a/b where a and b are integers

23/17 = a/b where a = 23 and b = 17

This is a rational number

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

Explanation:

The quickest way to get this answer is to add the angles given to get 87+46 = 133

This is through the use of the remote interior angle theorem.

Note how the angles 87 and 46 are interior, or inside the triangle. And also, they are not adjacent to the exterior angle we want to find. So that's where the "remote" portion comes in.

----------------

The slightly longer method involves letting x be the measure of the missing interior angle of the triangle.

The three interior angles add to 180

87+46+x = 180

133+x = 180

x = 180 - 133

x = 47

The missing interior angle of the triangle is 47 degrees.

Angle 1 is adjacent and supplementary to this 47 degree angle, so,

(angle1)+(47) = 180

angle1 = 180-47

angle1 = 133 degrees

This example helps confirm that the remote interior angle theorem is correct.

the answer is: (T R U E........)

There are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

The multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

To find the number of ways to choose 3 men from the 12 men, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).

where n is the total number of men and r is the number of men chosen

so, the number of ways to choose 3 men from the 12 men = ¹²C₃ = 1.

Similarly, we evaluate the number of ways to choose 2 women from the 8 women

as = ⁸C₂ = 14

Now, using the multiplication principle, we can find the total number of ways 3 men and 2 women be chosen if they are equally considered.

220 x 14 = 3080

Therefore, there are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

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Answer:

it’s already in it’s simplest form

To find the 90% confidence interval, using the following formula: Confidence interval = sample mean ± Z* (standard error)`where `standard error = (population standard deviation / √n)`n is the sample size Z is the Z-score at the 90% confidence level which is 1.645When we substitute the values in the formula, we get:
Confidence interval = 56 ± 1.645(13.3 / √36)
                       = 56 ± 4.54
                       = (51.46, 60.54)
Hence, the 90% confidence interval for the true population mean watermelon weight is (51.46, 60.54) ounces.

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Answer:

$7

Step-by-step explanation:

25x4=100

156-100=56

56/4=14

14 spent on earrings each earring was $7

If Four friends each brought matching necklaces and two pairs of earrings. The necklaces were priced at $25.00.If the total bill for all 4 friends was $156.00. Then 28 is the price of one pair of earrings

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

Based on the conditions formulate

Four friends each brought matching necklaces

Cost of each necklace is 25

25x4=100

So for four necklaces it is 100.

Now with remaining amount they purchased two pairs of ear rings

156-100=56

With 56 they purchased earrings

56/2=28

Cost of one pair of ear rings is 28.

Hence price of one pair of ear ring is 28

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Answer:

i think the answer is C. 1/2

Answer:

-8  7/9

Step-by-step explanation:

-9x+1=80

-9x+1-1=80-1

-9x=79

-9x=79

-9   -9

x= -8  7/9

Answer:

Mathematics NCERT Grade 7, Chapter 5: Lines and Angles is all about different lines, line segments, and angles.

A line segment has two end points.

A ray has only one end point (its vertex).

A line has no end points on either side.  

This chapter throws light on topics such as related angles, pair of lines. The chapter deals with different types of angles and lines. The types of angles discussed in this chapter are as follows:

Pairs of Angles          Condition

Two complementary angles Measures add up to 90°

Two supplementary angles Measures add up to 180°

Two adjacent angles Have a common vertex and a common arm but no common interior

Linear pair Adjacent and supplementary

A linear pair is a pair of adjacent angles whose non-common sides are opposite rays.

All the types are discussed in detail and are supplemented with examples and short questions.  

Under the topic pair of lines, various sub-sections are discussed namely:

Intersecting lines

Transversal  

Angles made by a transversal

When two lines intersect (looking like the letter X) we have two pairs of opposite angles. They are called vertically opposite angles. They are equal in measure.

A transversal is a line that intersects two or more lines at distinct points.

Six angles discussed in this section:

1. Interior angles

2. Exterior angles

3. Pairs of Corresponding angles

4. Pairs of Alternate interior angles

5. Pairs of Alternate exterior angles

6. Pairs of interior angles on the same side of the transversal

Transversal of parallel lines

The height on the wall that the ladder reaches is approximately 21.04feet.

Angle made by ladder against the wall = 68 degrees.

Distance between foot of the ladder and wall = 8.5 feet

Use trigonometry function  ,

Let us consider the height on the wall that the ladder reaches as 'h'.

Use the tangent function,

tan α = height on wall ladder reaches / distance between wall and foot of the ladder

⇒ tan(68°) = h / 8.5

Solving for h, we get,

⇒h = 8.5 × tan(68°)

⇒h = 8.5 × 2.475

⇒ h = 21.04 feet (Rounding to the nearest hundredth)

Therefore, ladder reaches a height of approximately 21.04 feet on the wall.

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Answer:

An equation in the form y = mx + b is in the 'slope y-intercept' form where m is the slope and b is the y-intercept. We can rewrite our equation, y = 4, in slope y-intercept form as follows: y = 0x + 4. Here, it is clear that the slope, or m, is zero. Therefore, the slope of the horizontal line y = 4 is zero