How do you solve the cube root function of x²/³ = 16?

The coordinates of the resulting triangle are L'(4, 1), M'(0, 1), and N'(4, 3)

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

Triangle LMN has vertices at L(−1, 4), M(−1, 0), and N(−3, 4

This means that

The rotation rule of 90° clockwise around the origin is

(x,y) becomes (y,-x)

So, we have

Image = (y, -x)

Substitute the known values in the above equation, so, we have the following representation

L'(4, 1), M'(0, 1), and N'(4, 3)

Hence, the coordinates of the resulting points, are L'(4, 1), M'(0, 1), and N'(4, 3)

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Answer:L′(4, 1), M′(0, 1), N′(4, 3)

Step-by-step explanation:

I am in the middle of taking the quiz and I believe this is the correct answer!

P(X ≤ 1) = P(X = 0) + P(X = 1) ≈ 0.901

So the probability that at most 1 customer in the sample orders for delivery is approximately 0.901, rounded to three decimal places.

To solve this problem, we can use the binomial distribution since we have a fixed number of trials (6) and each trial can result in one of two outcomes (ordering for delivery or not).

Let X be the number of customers in the sample who order for delivery. Then X follows a binomial distribution with parameters n = 6 and p = 0.11 (the probability of ordering for delivery).

We want to find the probability that at most 1 customer orders for delivery. This can be written as:

P(X ≤ 1) = P(X = 0) + P(X = 1)

To calculate these probabilities, we can use the binomial probability formula:

P(X = k) = (n choose k) *[tex]p^k[/tex]*[tex](1 - p)^(n - k)[/tex]

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n distinct items.

Using this formula, we can calculate:

P(X = 0) = (6 choose 0) * 0.11^0 * [tex]0.89^6[/tex] ≈ 0.530

P(X = 1) = (6 choose 1) * 0.11^1 * 0.89^5 ≈ 0.371

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If he visited all the cities in order A(O,4), B(4,1). C(3. 1) and D(-1. 2). then he traveled 12.3 units distance ( nearest tenth).

John visited four cities that form a rectangle on a coordinate grid at A(0, 4), B(4, 1), C(3, 1), and D(-1, 2). If he visited all the cities in order and ended up where he started, the distance he traveled can be found by calculating the perimeter of the rectangle.

Calculate the distance between consecutive points.
AB = √[(4-0)^2 + (1-4)^2] = √[16 + 9] = √25 = 5
BC = √[(3-4)^2 + (1-1)^2] = √[1 + 0] = √1 = 1
CD = √[(-1-3)^2 + (2-1)^2] = √[16 + 1] = √17 ≈ 4.1 (rounded to nearest tenth)
DA = √[(0-(-1))^2 + (4-2)^2] = √[1 + 4] = √5 ≈ 2.2 (rounded to nearest tenth)

Calculate the total distance traveled (perimeter of the rectangle).
Total Distance = AB + BC + CD + DA = 5 + 1 + 4.1 + 2.2 = 12.3

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"t" increases, and the number of digital subscriptions grows exponentially at a rate of 3.4% per month.

The function s(t) = 31,500(1.034)^t gives an approximation of the number of digital subscriptions s as a function of t months after the launch of the advertising campaign.

The parameters of the function s(t) are:

31,500: This is the initial number of digital subscriptions at t = 0, when the advertising campaign is launched.

1.034: This is the growth rate of the number of digital subscriptions per month. It represents the percentage increase in the number of subscriptions each month due to the advertising campaign. Specifically, each month the number of subscriptions is multiplied by 1.034, which is the same as increasing it by 3.4%.

t: This is the time in months after the launch of the advertising campaign. It is the independent variable of the function that determines the number of digital subscriptions at any given time t.

Statements interpreting the parameters of the function s(t) are:

The initial number of digital subscriptions at t = 0 is 31,500.

For every month after the launch of the advertising campaign, the number of digital subscriptions increases by 3.4%, or a factor of 1.034.

The parameter t represents the time in months after the launch of the advertising campaign. As t increases, the number of digital subscriptions grows exponentially at a rate of 3.4% per month.

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The probability that the smallest bell rings the first three days in a row is 1/27. when Each day three church bells are rung in a random order

In the given data there are 3 bells in the church in which there is a small bell and the three bells are rung in a random order. we need to find the probability that the smallest bell rings the first three days in a row.

The probability that the smallest bell rings on any given first day can be given as  = 1/3

Because there are three bells and each bell has an equal chance of being rung first. The probability that this happens three days in a row is given as

= (1/3) × (1/3) × (1/3)

= 1/27

Therefore, the probability that the smallest bell rings the first three days in a row is 1/27

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2a) The equation used to answer the question is (1/Time to fill the pool) = (1/Time taken by hose) - (1/Time taken by leak).

2b) It would take 40 minutes to fill the pool with water when there is a small hole causing a leak.

To solve this, we can use the concept of rates of work.

2a) The equation we would use to answer the question is:

(1/Time to fill the pool) = (1/Time taken by hose) - (1/Time taken by leak)

2b) Let's plug in the values given in the question:

(1/Time to fill the pool) = (1/30 minutes) - (1/120 minutes)

To find the time to fill the pool, we first need to find a common denominator for the fractions. The common denominator is 120, so we can rewrite the fractions as:

(1/Time to fill the pool) = (4/120) - (1/120)

Now, add the fractions on the right side:

(1/Time to fill the pool) = (3/120)

Next, take the reciprocal of both sides to solve for the time to fill the pool:

Time to fill the pool = 120/3

Time to fill the pool = 40 minutes

So, it would take 40 minutes to fill the pool.

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The ratio of adult to boys is 35:24

A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. For example, if the ratio of boys to girls in a class is 4:1. This means that the for every 4 boys therefore is a girl.

Represent the total number of adult, boys and girls in the club by x

This means number of boys = 4/7× x

number of adult = 5/6 × x

Therefore the ratio of adults to boys will be

5x/6 : 4x/7

= 5/6 : 4/7

multiply through by 42

= 35 : 24

therefore the ratio of adult to boys is 35: 24

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The probability of hitting the bulls eye (center circle) when we shoot an arrow with radius of the bulls eye is 2ft and the radius of the target is 6ft is 11.1%.

Assuming that we are shooting randomly at the target and the arrow can land anywhere within the target area, the probability of hitting the bull's eye (center circle) can be calculated as the ratio of the area of the bull's eye to the area of the entire target.

The area of the bull's eye can be calculated as follows:

Area of bull's eye = π x (radius of bull's eye)²
Area of bull's eye = 3.14 x 2²
Area of bull's eye = 12.56 square feet

The area of the entire target can be calculated as follows:

Area of target = π x (radius of target)²
Area of target = 3.14 x 6²
Area of target = 113.04 square feet

Therefore, the probability of hitting the bull's eye can be calculated as:

Probability of hitting bull's eye = Area of bull's eye / Area of target
Probability of hitting bulls eye = 12.56 / 113.04
Probability of hitting bulls eye = 0.111 or approximately 11.1%

So, the probability of hitting the bull's eye (center circle) when we shoot an arrow randomly at the target is approximately 11.1%.

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If velocity is negative,The body is moving backwards instead of forwards, so the displacement will be measured as a negative value.

An antiderivative of a velocity function can be used to find displacement of the body by integrating the velocity function over a given time interval. The result of this integration will give the total displacement of the body over that time interval.

If the velocity is negative, it means that the body is moving in the opposite direction to the positive direction of the coordinate system. This has an impact on the problem of finding displacement because the displacement will also be negative. In other words, the body is moving backwards instead of forwards, so the displacement will be measured as a negative value.

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If Mr. Vara's square pyramid post caps have a volume of 94.5 cubic centimeters, and he assumes that the height and side length are equal, then the side length of each cap should be approximately 6.04 centimeters.

Mr. Vara is designing post caps in the shape of a square pyramid for his fence. The caps are solid wood and have a volume of 94.5 cubic centimeters. To calculate the dimensions of the pyramid, we need to use the formula for the volume of a square pyramid, which is V = (1/3)bh, where b is the area of the base and h is the height of the pyramid.

Since the caps are square pyramids, the base is a square. Let's call the side length of the base s. Then the area of the base is s². We can rearrange the formula for volume to get h = (3V)/b. Plugging in the given volume of 94.5 cubic centimeters, we get:

h = (3 x 94.5) / s²
h = 283.5 / s²

We still need to find the side length s. We can use the fact that the volume of the pyramid is also equal to [tex](1/3)s^{2h[/tex]. Plugging in the volume and height from above, we get:

94.5 = (1/3)s²(283.5 / s²)
94.5 = 94.5

This equation simplifies to 1 = 1, which doesn't give us any information about s. However, we can make an assumption about the dimensions of the pyramid. Let's say that the height h is equal to the side length s. Then we can solve for s using the volume formula:

[tex]94.5 = (1/3)s^{2s[/tex]
94.5 = (1/3)s³
283.5 = s³
s = 6.04

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Hi! I'd be happy to help you create a stem and leaf plot using the provided set of data for US History class test scores.

Step 1: Arrange the data in ascending order.

54, 56, 62, 65, 66, 70, 72, 72, 74, 85, 85, 88, 88, 88, 90, 91, 92, 97, 99

Step 2: Determine the range of the data.

The data ranges from 50s to 90s, so we will need 5 stems: 5, 6, 7, 8, and 9.

Step 3: Create the stem and leaf plot using the stems and corresponding leaves (the units digits of the data).

5 | 4 6
6 | 2 5 6
7 | 0 2 2 4
8 | 5 5 8 8 8
9 | 0 1 2 7 9

Here is the completed stem and leaf plot for the US History class test scores. The stems represent the tens digits (50s, 60s, 70s, 80s, 90s), and the leaves represent the units digits of the scores in each range.

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Answer:

Step-by-step explanation:

Total of rides from Tyler's house to Cousin's house and Cousin's house to Tyler's house = 1.8km = 1800m

So, the distance from Tyler's house to his cousin's house is

= 1800m ÷ 2 = 900m

P(Dead l WH) = 0.23/0.48 = 0.4792

Here the western red cedar is relatively young.

(a) P(Dead l RC) = 0.02/0.20 = 0.10

P(Dead l DF) = 0.16/0.32 = 0.50

P(Dead l WH) = 0.23/0.48 = 0.4792

Here the western red cedar is relatively young.

(b) P(sapling l RC) = 0.08/0.20 = 0.4

P(sapling l DF) = 0.00/0.32 = 0

P(sapling l WH) = 0.04/0.48 = 0.08333

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The p-value for a t-score of -0.92 is approximately 0.18 and since it is greater than the significant level, the null hypothesis is rejected.

The first step in testing this hypothesis is to calculate the test statistic, which in this case is a t-score. The formula for the t-score is (y - mu) / (s / sqrt(n)), where y is the sample mean, mu is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

In this case, the sample mean is 25.9, the hypothesized population mean is 26, the sample standard deviation is 7.6, and the sample size is 50. Plugging these values into the formula, we get a t-score of -0.92.

Next, we need to find the p-value associated with this t-score. We can use a t-table or a calculator to do this. Using a t-table with 49 degrees of freedom (since we have a sample size of 50 and one parameter estimated from the sample), we find that the p-value for a t-score of -0.92 is approximately 0.18.

Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. In other words, we do not have substantial evidence to conclude that the population mean is less than 26. However, it is important to note that the sample mean is slightly below the hypothesized population mean, and the p-value is relatively close to the significance level. Therefore, it may be worthwhile to conduct additional studies with larger sample sizes or different populations to further investigate this question.

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By the rule of indices the  given expression is equivalent to x⁻² y⁻⁵.(option B)

What is index?

In mathematics, Index in plural indices  is the power or exponent which is raised to a number or a variable. For example, for the number 2⁵, 5 is the index of 2. Which gives the value 32.

Given expression is y⁻⁸ y³ x⁰ x⁻²

Here we use the law of indices.

By the law of indices it can be stated that the indices at the time of multiplication is being added up. That is zᵃ × zᵇ = zᵃ⁺ᵇ.

Using this concept of indices the given expression can be rewritten as

 y⁻⁸⁺³ x⁰⁻²

= y ⁻⁵ x⁻²

= x⁻² y⁻⁵

Hence, the given expression is equivalent to x⁻² y⁻⁵.

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The circumference of a circle is the distance around the edge or perimeter of the circle.

1) Radius = 5cm/2 = 2.5 cm

2) Radius = 28 mm/2 = 14 mm

3) Radius = 3 1/2 m * 1/2 = 3/4 m

4) diameter = 2 * 6cm = 12 cm

5) diameter = 2 * 2m = 4 m

6) diameter = 2 * 0.8 ft = 1.6 ft

Circumference can be calculated using the formula:

C = 2πr

7) circumference = 2πr = 2 * 3.14 * 10/2 = 31.4 in

8) circumference = 2 * 7 * 3.14 = 43.96 in

9) Circumference = 2 * 3.14 * 18/2 = 56.52 in

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You are an scalene triangle.

You are a scalene triangle.

A scalene triangle is a type of triangle where all three sides have different lengths, and no two angles are congruent. In this case, you mentioned that one of the angles has a measure of 100 degrees.

Here's a simple diagram of a scalene triangle to help illustrate:

    \

     \

      \

       \

        \

         \

In the diagram, the angles are not drawn to scale, but it represents a scalene triangle where one angle measures 100 degrees. The sides of the triangle would have different lengths, distinguishing it from an equilateral or isosceles triangle where at least two sides are congruent.

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Answer:

38,772.72

Step-by-step explanation:

The formula for a sphere is

V=4/3 pi r^3

=4/3 3.14 21^3

=4/3 3.14 9,261

=4/3 29,079.54

=38,772.72

[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=42 \end{cases}\implies V=\cfrac{4\pi (42)^3}{3}\implies \stackrel{ using~\pi =3.14 }{V\approx 310181.76}[/tex]

a)The amount in the account after 5 years, compounded annually, will be approximately $60,625.06.

b) The amount in the account after 5 years, compounded semiannually, will be approximately $61,588.88.

The amount in the account after 5 years can be calculated using the compound interest formula. For an initial investment of $47,000 at an annual interest rate of 5%, compounded annually or semiannually, the amount in the account will be different.

(a) For compounding annually:

The compound interest formula is given by:

A = P(1 + r/n)^(nt)

where:

A = the amount after time t

P = principal amount (initial investment) = $47,000

r = annual interest rate = 5% or 0.05 (as a decimal)

n = number of times interest is compounded per year = 1 (since it is compounded annually)

t = time period = 5 years

Plugging in the given values, we get:

A = 47000(1 + 0.05/1)^(1*5)

A = 47000(1.05)^5

A ≈ $60,625.06

So, the amount in the account after 5 years, compounded annually, will be approximately $60,625.06.

(b) For compounding semiannually:

The only difference from the above calculation is the value of 'n', which is the number of times interest is compounded per year. In this case, 'n' will be 2, as interest is compounded semiannually (twice a year).

Plugging in the given values, we get:

A = 47000(1 + 0.05/2)^(2*5)

A = 47000(1.025)^10

A ≈ $61,588.88

So, the amount in the account after 5 years, compounded semiannually, will be approximately $61,588.88.

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The number name of 346. 725 is three hundred forty-six point seven two five.

A number name refers to the name that is used to describe the number in words. This is helpful in communicating it orally.

To convert the given number to word form, we do as follows:

1. We check the digits of the number before decimals

In this case, the number of digits in the question is 3

2. The highest place value is then checked.

It comes out to be hundreds

3. We name it accordingly and add a suffix to the face value

This is 3 and the name comes out to be Three hundred

4. We continue it till we encounter the decimal

We get the number as Three hundred forty-six

5. Then we mention the word decimal or point

The result is Three hundred forty-six point

6. The number after the decimal is written as it is

Hence, the name comes out to be Three hundred forty-six point seven two five.

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Answer:

(8/√2)^2 = 64/2 = 32 square inches

Answer:

67. 50

Step-by-step explanation:

15x4.50= 67.5

The number of pupils who liked both biscuits and chocolates is 30.

The number of pupils who liked neither biscuits nor chocolates is 10.

Let's assume that the number of pupils who liked only biscuits is x, and the number of pupils who liked only chocolates is y.

According to the problem, twice as many pupils liked chocolates as those who liked biscuits. Mathematically, we can write this as:

y = 2x

Now, let's find the total number of pupils who liked at least one of the two:

Total = P(Biscuits) + P(Chocolates) - P(Biscuits and Chocolates)

Total = x + y + 30

Total = x + 2x + 30

Total = 3x + 30

We know that the total number of pupils is 130, and the number of pupils who liked neither is 10. Therefore,

Total = P(All pupils) - P(Neither)

130 = x + y + 30 + 10

130 = x + y + 40

130 - 40 = x + y

90 = x + y

We can now solve these two equations to get the values of x and y:

3x + 30 = 90

3x = 60

x = 20

y = 2x = 40

Therefore, 20 pupils liked only biscuits, 40 pupils liked only chocolates, and 30 pupils liked both biscuits and chocolates. And, 40 pupils liked exactly one of the two.

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Answer: C

Step-by-step explanation: after rotating, if you split it in half horizontally, you have two cones

The three-dimensional figure formed when the triangle is rotated around the dashed line through B and C is a cone.

A cone is a three-dimensional geometric form with a flat base and a smooth, tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that link the base's points to the apex, which is a common point on a plane that does not include the base.

When we rotate a two-dimensional shape around an axis, we create a three-dimensional solid. This process is known as "revolution" or "rotational symmetry".

In this particular case, we have a triangle that can be rotated around the line segment that connects points B and C. If we were to rotate the triangle around this axis, we would create a three-dimensional solid. To figure out what kind of solid this is, we can think about the cross-sections that would be created if we were to slice through the solid perpendicular to the axis of rotation.

If we were to slice through the solid perpendicular to the axis of rotation, we would get a circle. This means that the solid created by rotating the triangle is a cylinder.

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Answer:

34/73

Step-by-step explanation:

37 + 34 + 2 = number of customers = 73

73 is our denominator.

34 is the number of people who used a credit card.

34 is our numerator.

Put the two together, and you get 73! Enjoy!

If you select a marble without looking and then put it back if you do this 90 times, the probability of selecting an orange or a pink marble on any given trial is 1/2 or 0.5.

If you select a marble without looking and then put it back, the probability of selecting any particular marble on any given trial is the same for all marbles. Assuming there are only two possible outcomes - selecting an orange marble or a pink marble - the probability of selecting an orange or a pink marble on any given trial is 1/2 or 0.5.

Since the probability of selecting an orange or a pink marble on each trial is the same, the best prediction for the number of times you will select an orange or a pink marble out of 90 trials is an equal number of times for each color. Therefore, the best prediction for the number of times you will select an orange or a pink marble is 45 times each.

This is only a prediction based on probability, and the actual number of times you select an orange or a pink marble may differ from the prediction due to chance. However, over a large number of trials, the actual outcomes should approach the predicted probabilities.

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The height of the cylindrical ornament is approximately 5.7 centimetres (option b).

To find the height of the cylindrical ornament given that 450 cubic centimetres of wood is used and the radius of the base is 5 centimetres, you can use the formula for the volume of a cylinder: V = π × radius² × height.

Step 1: Write down the given values.
Volume (V) = 450 cubic centimetres
Radius (r) = 5 centimetres

Step 2: Plug the given values into the formula.
450 = π × (5)² × height

Step 3: Solve for the height.
450 = π × 25 × height
450 = 78.54 × height

Step 4: Divide both sides by 78.54 to find the height.
height = 450 / 78.54
height ≈ 5.7 centimetres

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If the line has a positive slope, it means that the amount is increasing, and if it has a negative slope, it means that the amount is decreasing.

Based on the given information, the function models the amount of money a new business has made over x months. Therefore, we can assume that the function is a linear function, and its graph is a straight line.

Given that negative values represent debt, we can assume that the slope of the line is positive over the interval where the function takes positive values. Therefore, the interval over which the amount is increasing is from zero to infinity, which means that the business is making money and not in debt.

It's essential to note that if the function has a negative slope over any interval, then the amount is decreasing, and the business is losing money. However, we cannot determine this information from the given function's information.

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