NEED HELP ASAP PLEASE.....

Since m and k(k+1)/2 are both integers, we can conclude that (k+1)(k+2)(k+3) is an integer multiple of 6. Thus, by the principle of mathematical induction, the formula n(n+1)(n+2) is an integer multiple of 6 for all non-negative integers n

Mathematical induction is a proof technique used to establish a statement for all positive integers by proving it for the base case and showing that if the statement holds for an arbitrary integer, it must also hold for the next integer. It is a powerful method to prove mathematical statements that follow a pattern or recursive structure.

To prove by mathematical induction that n(n+1)(n+2) is an integer multiple of 6 for all non-negative integers n, we will first show that the formula holds true for the base case n=0.

Base case:

When n = 0, we have:

0(0+1)(0+2) = 0 * 1 * 2 = 0, which is an integer multiple of 6 since 0 = 6 * 0.

Induction hypothesis:

Assume that for some k >= 0, k(k+1)(k+2) is an integer multiple of 6.

Induction step:

We need to show that the formula holds true for k+1, assuming that it holds true for k. That is, we need to show that (k+1)(k+2)(k+3) is also an integer multiple of 6.

Expanding the formula, we get:

(k+1)(k+2)(k+3) = (k² + 3k + 2)(k+3) = k³ + 6k² + 11k + 6

Now, we can use the induction hypothesis that k(k+1)(k+2) is an integer multiple of 6 to write k(k+1)(k+2) = 6m, where m is some integer. Substituting this into the above equation, we get:

k³ + 6k² + 11k + 6 = 6m + k³ + 3k² + 2k

Factoring out 3k² + 3k, we get:

k³ + 6k² + 11k + 6 = 6m + 3k(k+1) + 2k

Factoring out 2k from the last two terms, we get:

k³ + 6k² + 11k + 6 = 6m + 3k(k+1) + 2k = 6(m + k(k+1)/2)

Since m and k(k+1)/2 are both integers, we can conclude that (k+1)(k+2)(k+3) is an integer multiple of 6. Thus, by the principle of mathematical induction, the formula n(n+1)(n+2) is an integer multiple of 6 for all non-negative integers n

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Hence, the volume of the pyramid is 48 cubic inches.

A pyramid is a geometric shape that consists of a polygonal base (usually a square or a triangle) and triangular faces that meet at a single point at the top, called the apex. Pyramids have been built by many ancient civilizations as monumental structures, including the ancient Egyptians, Aztecs, and Mayans. The most famous of these is the Great Pyramid of Giza in Egypt, which was built over 4,500 years ago and is one of the Seven Wonders of the Ancient World. Pyramids have also been used as symbols in many cultures and can represent strength, stability, and spirituality.

The volume of a square pyramid can be calculated using the formula V = (1/3) * B * h, where B is the area of the base and h is the height.

In this case, the base of the pyramid is a square with a side length of 3 in, so the area of the base is:

[tex]B = s^2 = 3^2 = 9 sq. in.[/tex]

The height of the pyramid is given as 16 in.

Therefore, the volume of the pyramid is:

[tex]V = (1/3) * B * h = (1/3) * 9 * 16 = 48 cubic inches.[/tex]

Hence, the volume of the pyramid is 48 cubic inches.

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If the debt is normally distributed with a population standard deviation of $1100 and 15% of college seniors owe less than the amount of money is equals to the $2121.96.

The area under the standard normal curve represents to probability. The total area under the curve is equals to one. A Standard Normal Cumulative Probability, is a table which provides the cumulative probability of the left tail, as in the values less than the z-score in question. Here,

population mean, μ = $3262

standard deviation, σ = 1100

P- value = 15%

Using the normal distribution table, Z-score value is equals to - 1.0364. Now, we can use Z-scores formula is written [tex]Z = \frac{X - \mu}{\sigma }[/tex]

Substitutes the known values in above formula, - 1.0364 = (X - 3262 )/1100

=> X - 3262 = 1100× ( - 1.0364)

=> X = 3262 - 1140.04

=> X = 2121.96

Hence, required value is $ 2121.96.

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To solve the problem, we can use trigonometry and create a right triangle with one leg being the height of building B, the other leg being the distance between building A and B, and the hypotenuse being the line of sight from the top of building A to the top of building B.

Let's call the height of building B "h". Using trigonometry, we can determine the length of the other leg:

tan(30°) = h / x => x = h / tan(30°)

tan(60°) = h / (10√3 - x) => x = 10√3 - h / tan(60°)

Setting these two expressions equal to each other and solving for h, we get:

h / tan(30°) = 10√3 - h / tan(60°)

h (1/tan(30°) + 1/tan(60°)) = 10√3

h = 10√3 / (1/tan(30°) + 1/tan(60°)))

Plugging in the values, we get:

h = 10√3 / (1/(1/√3) + 1/√3)

h = 20√3

Answer:

Step-by-step explanation:

Let's call the height of building A "hA" and the height of building B "hB". We can use trigonometry to solve for hB.

First, let's draw a diagram:

   B

  /|

hB/ |

/  |

/ 60°\

-----

|   /

|  /

| /

|/

A

We know that the distance between building A and B is 10√3. Let's call this distance "d".

Using the angle of depression of 30°, we can form a right triangle with a leg of hA and a hypotenuse of d. The opposite angle is 60°, so the adjacent side is hA/tan(60°) = hA/√3.

Using the angle of depression of 60°, we can form another right triangle with a leg of hB and a hypotenuse of d. The opposite angle is 30°, so the adjacent side is hB/tan(30°) = hB√3.

We know that the sum of the heights of building A and B is equal to the distance between them, so hA + hB = d.

Putting all of this together, we can set up an equation:

hA/√3 + hB√3 = 10√3

Multiplying both sides by √3:

hA + 3hB = 30

But we also know that hA + hB = d = 10√3, so we can substitute:

hB = 10√3 - hA

Substituting into the previous equation:

hA + 3(10√3 - hA) = 30

Simplifying:

-2hA + 30√3 = 30

-2hA = 30 - 30√3

hA = (15√3 - 15)/(-1) = 15 - 15√3

Finally, we can use hA + hB = 10√3 to solve for hB:

hB = 10√3 - hA = 10√3 - (15 - 15√3) = 25√3 - 15

Therefore, the height of building B is 25√3 - 15.

The value of XZ is approximately equal to 96.86.

What is inequality ?

An inequality is a mathematical statement that compares two values, expressions, or quantities using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

We can start by using the transitive property of equality to find that XY = YZ = 95 means that XY + YZ = XZ = 190.

Next, we can use the given information about WX and WZ to write an equation for XZ in terms of u. Since WZ = WX + XZ, we can substitute the given expressions to get:

7u = (u + 66) + XZ

Simplifying and solving for XZ, we have:

7u - u - 66 = XZ

6u - 66 = XZ

Now, we can substitute this expression for XZ into our earlier equation to get:

XZ = 190 = 95 + 95 = XY + YZ = (WX - 66) + (6u - 66)

Simplifying and solving for u, we get:

6u - 66 = 190 - WX

6u = 256 - WX

u = (256 - WX)/6

Substituting this value of u back into the expression for XZ, we get:

XZ = 6u - 66 = 6[(256 - WX)/6] - 66 = 190 - WX

Therefore, XZ = 190 - WX, where WX = u + 66 = (256 - WX)/6 + 66. We can solve for WX by multiplying both sides by 6:

6WX = 256 - WX + 396

7WX = 652

WX = 93.14 (rounded to two decimal places)

Substituting this value into our expression for XZ, we have:

XZ = 190 - WX = 190 - 93.14 = 96.86 (rounded to two decimal places)

Therefore, XZ is approximately equal to 96.86.

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The mean of the sampling distribution of the sample means is 55 and the standard deviation is approximately 1.79 (rounded to one decimal place).

Standard deviation is a measure of the amount of variation or dispersion of a set of data values from its mean or expected value. It is a statistic that represents how spread out the data is from the mean.

The standard deviation is calculated by taking the square root of the variance, which is the average of the squared differences of each data point from the mean. The standard deviation is expressed in the same units as the data and is usually denoted by the symbol "σ" (sigma) for a population or "s" for a sample.

In the given question,

We can start by using the properties of the mean and standard deviation of a sampling distribution:

The mean of the sampling distribution of the sample means (Mx) is equal to the population mean (μ), which is given as 55.

The standard deviation of the sampling distribution of the sample means (Ox) is equal to the population standard deviation (σ) divided by the square root of the sample size (n), i.e.,

Ox = σ / sqrt(n)

where n = 5 (the sample size) and σ = 4 (the population standard deviation).

Substituting these values into the formula, we get:

Ox = 4 / sqrt(5) ≈ 1.79

Therefore, the mean of the sampling distribution of the sample means is 55 and the standard deviation is approximately 1.79 (rounded to one decimal place).

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The group who has the largest percentage of people who prefer to travel by automobile is given as follows:

Adult.

A bar graph, also known as a bar chart, is a type of graph used to represent and compare data. It consists of rectangular bars of equal width and varying heights, where the height of each bar represents the value of the data being graphed.

Automobiles are represented by the green bars, hence we must observe the input for which the green bar has the largest value, which is for adults, hence adults compose the largest percentage of people who prefer to travel by automobile.

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The length of EC is 8 and the length of CD is 16

How to solve the question?

Pythagoras theorem is a fundamental theorem in mathematics named after the ancient Greek mathematician Pythagoras. It states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).

The theorem can be expressed mathematically as:

c^2 = a^2 + b^2

where c is the length of the hypotenuse and a and b are the lengths of the other two sides. This means that if we know the lengths of any two sides of a right-angled triangle, we can use Pythagoras theorem to find the length of the third side.

The theorem has many practical applications, including in construction, engineering, and physics. It is also a key concept in trigonometry and is used extensively in various fields of science and mathematics.

We can use the Pythagorean theorem to solve this problem. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. In this case, we know that the length of the hypotenuse (c) is 10 and the length of one leg (a) (the base) is 6. We can use this information to find the length of the other leg (b) (the perpendicular) as follows:

c² = a²+ b²

10²= 6² + b²

100 = 36 + b²

b²= 64

b = 8

Therefore, the length of the perpendicular (EC) is 8 units.

for CD it is given in question that EC=ED  there fore

ED=8

CD=EC+ED

CD=8+8

CD=16

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[tex](2^{2})^{4} *5^{4}[/tex][tex](2^{2})^{4} *5^{4}[/tex]The expression is [tex]4^{4} *5^{4}[/tex] is therefore a single power of [tex]2[/tex] and [tex]5[/tex]

[tex]4^{4} *5^{4} =2^{8} *5^{4}[/tex]

A grouping of numbers, symbols, and mathematical operations (such as addition, subtraction, multiplication, and division) is called an expression, and it is used to represent an amount or relationship. Expressions as basic as "[tex]2+3x[/tex]" or as complex as "[tex]3x^{2} +5x-2[/tex]" are both permissible.

Additionally, they might include variables, which are representations of unknown values represented by symbols, such as "[tex]y+2x[/tex]." In algebra, calculus, and other areas of mathematics, expressions are commonly used to discuss problems and describe mathematical properties.

Since [tex]4[/tex] and[tex]5[/tex] may be stated as [tex]2^{2}[/tex] and [tex]5^{1}[/tex] so the [tex](2^{2})^{4} *5^{4}[/tex]

[tex]4^{4} *5^{4} =2^{8} *5^{4}[/tex] [tex]=(2^{2})^{4} *5^{4}[/tex]

So the expression for [tex]4^{4} *5^{4} =2^{8} *5^{4}[/tex] as there are single power of [tex]2[/tex] and [tex]5[/tex]

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The value of the technological equipment when it was new according to an exponential decay model is approximately $37,633.52.

It is given to us that the value of a new technological equipment depreciates (decreases) after it is purchased, the value of the technological equipment depreciates according to an exponential decay model.

We know that the value of the equipment is $20000 at the end of 6 years, and its value has been decreasing at the rate of 10% per year.

Let the purchase price of machine be $P

Rate of depreciation = 10% p.a.

Period years.

∴ Present value = $20,000

Depreciated value can be calculated by t(6) ---> [∵ Depriciated value = A]

⇒ $20,000 = P(1−10/100)⁶

⇒ $20,000 = P(9/10)⁶

⇒ P = $20,000 (9/10)⁶ A = P(1-100)t

⇒ P = $20,000 × 10/9 × 10/9 × 10/9 × 10/9 × 10/9 × 10/9

⇒ P = $37,633.528463178 ≈ 37,633.52

The value of the technological equipment when it was new was approximately $37,633.52.

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Step-by-step explanation:

A   xy = 40   is the same as x = 40/y    an inverse relationship

D   this is the samething as A

Don't know about F...it is truncated

Answer:

9x + 6 = 8

Step-by-step explanation:

"Sum" indicates addition problem. 9 times a number can be represented as 9x (with 9 and 'a number' being x). Then you add 6 because it states 'and 6'. Then, you add equals 8 (=8)

So your equation looks like:

9x + 6 = 8

Answer:

The answer to your problem is, D. [tex]-2, \frac{4}{5}[/tex]

Step-by-step explanation:

Using the a-c method to factor the quadratic

The factors of the product 5 x -8 = -40

Which sum to +6 are + 10 and -4

Split the middle term using these factors:

[tex]5x^{2} + 10x - 4x - 8[/tex]

[tex]= 5x(x + 2 ) -4 ( x + 2 )[/tex]

We will then take out the common factor: ( x + 2 )

= ( x + 2 )( 5x - 4 )

[tex]5x^{2} + 6x - 8 = ( x + 2 )( 5x - 4 )[/tex]

Thus the answer to your problem is, [tex]-2, \frac{4}{5}[/tex]

Answer:

Move terms to the left side

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

Evaluate the exponent

Multiply the numbers

Add the numbers

Evaluate the square root

Multiply the numbers

Answer:

x= 4/5

x= -2

so the answer is A

Answer:

Step-by-step explanation:

To find the equation of a circle that passes through three given points, we can use the fact that the perpendicular bisectors of the chords joining the points intersect at the center of the circle.

Let's first find the midpoint and slope of the chords joining the three points:

The midpoint and slope of the chord joining (-1, 2) and (4, 2):

Midpoint: $((4 - 1)/2, (2 + 2)/2) = (3/2, 2)$

Slope: $(2 - 2)/(4 - (-1)) = 0$

The midpoint and slope of the chord joining (-1, 2) and (-3, 4):

Midpoint: $((-3 - 1)/2, (4 + 2)/2) = (-2, 3)$

Slope: $(4 - 2)/(-3 - (-1)) = 1/2$

The midpoint and slope of the chord joining (4, 2) and (-3, 4):

Midpoint: $((-3 + 4)/2, (4 + 2)/2) = (1/2, 3)$

Slope: $(4 - 2)/(-3 - 4) = -1/2$

Now we can find the equations of the perpendicular bisectors of these chords:

The equation of the perpendicular bisector of the chord joining (-1, 2) and (4, 2) is the horizontal line $y=2$.

The equation of the perpendicular bisector of the chord joining (-1, 2) and (-3, 4) is the line passing through the midpoint $(-2, 3)$ with slope $-2$:

$$y - 3 = -2(x + 2)$$

Simplifying, we get $y = -2x - 1$.

The equation of the perpendicular bisector of the chord joining (4, 2) and (-3, 4) is the line passing through the midpoint $(1/2, 3)$ with slope $2$:

$$y - 3 = 2(x - 1/2)$$

Simplifying, we get $y = 2x + 2$.

The center of the circle is the point where these perpendicular bisectors intersect. Solving the system of equations formed by setting any two of the perpendicular bisectors equal to each other, we get the center of the circle as $(1, 2)$.

Finally, the radius of the circle is the distance from the center to any of the three given points. We can use the distance formula to find that the radius is $\sqrt{10}$.

Putting it all together, the equation of the circle is:

$$(x - 1)^2 + (y - 2)^2 = 10$$

or expanding and simplifying:

$$x^2 + y^2 - 2x - 4y + 5 = 0$$

Therefore, the general equation for the circle that passes through the points (-1, 2), (4, 2), and (-3, 4) is $x^2 + y^2 - 2x - 4y + 5 = 0$.

The p-value for the given mentioned test, with the test static of -2.01  is calculated out to be  0.0456.

To calculate the p-value for this test, we first need to determine the appropriate null and alternative hypotheses.

Null hypothesis: The proportion of customers who wait longer than 5 minutes at the drive-through for this franchise is equal to the national value of 12%.

Alternative hypothesis: The proportion of customers who wait longer than 5 minutes at the drive-through for this franchise differs from the national value of 12%.

We can use a two-tailed Z-test to test this hypothesis, with a significance level of alpha = 0.05.

The test statistic is given as -2.01. Since this is a two-tailed test, we need to find the area in both tails of the standard normal distribution that is at least as extreme as the test statistic.

Using a standard normal distribution table or a calculator, we find that the area to the left of -2.01 is 0.0228. The area to the right of 2.01 is also 0.0228. Therefore, the total p-value is the sum of these two probabilities:

p-value = 0.0228 + 0.0228 = 0.0456

Therefore, the p-value for this test is 0.0456. This means that there is a 4.56% chance of obtaining a test statistic as extreme as -2.01, assuming that the null hypothesis is true. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that the proportion of customers who wait longer than 5 minutes at the drive-through for this franchise differs from the national value of 12%.

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The sum of the arithmetic series 12 + 22 + ... + 142 is 1078.

The sum of an arithmetic series can be found by multiplying the average of the first and last terms by the number of terms.

The following formula can be used to get the sum of an arithmetic series:

S = (n/2)(a + l)

where S is the sum of the series, n is the number of terms, a is the first term, and l is the last term.

In this case, we can see that a = 12, d = 10 (the common difference), and l = 142. We can find n by using the formula for the nth term of an arithmetic sequence:

an = a + (n-1)d

Setting this equal to l and solving for n, we get:

142 = 12 + (n-1)10

130 = 10(n-1)

n-1 = 13

n = 14

Now that we know n, we can use the formula for the sum of an arithmetic series to find S:

S = (n/2)(a + l)

S = (14/2)(12 + 142)

S = 7(154)

S = 1078

Therefore, the sum of the arithmetic series 12 + 22 + ... + 142 is 1078.

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Answer:)

O segment XW

Explanation:)

hope it helps :)

Brainliest pls:)

The sοlutiοn οf the given equatiοn is x=7 and cοrrect.

The equal sign ('=') cοnnects twο expressiοns tο fοrm a mathematical statement. There needs tο be at least οne unknοwable variable fοr the result tο be determined. An example οf an equatiοn is 3x - 8 = 16. When this equatiοn is sοlved, the result is x = 8.

Part A:

Given equatiοn is

3x+2(4+6x)= 113----------(1)

Multiplying the bracket term by 2 we get

3x+8+12x=113

Arranging the similar terms in the left hand side we get,

3x+12x+8=113

Subtracting 8 frοm bοth sides we get,

3x+12x+8-8=113-8

⇒(3x+12x)= 105

Adding the similar terms in the left hand side we get,

15x = 105

Dividing bοth sides by x= 105/15=7

Sο sοlving the equatiοn we get x=7.

Part B:

Checking fοr the sοlutiοn:

If the sοlutiοn is right then putting the value οf x in the left hand side οf the  given equatiοn will prοduce the right hand side.

putting x=7 in the left hand side οf equatiοn (1),

3x+2(4+6x)

= 3×7+2(4+6×7)

= 21+2(4+42)

= 21+ 2×46

= 21+ 92

= 113

Which is the right hand side οf equatiοn (1).

Sο, the sοlutiοn is cοrrect and checked.

Hence, the sοlutiοn οf the given equatiοn is x=7 and cοrrect.

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19) Length of AB is a fourth of the circumference of the circle.

C=2πr

Length of AB = [tex]\frac{1}{4} 2\pi r=\frac{1}{2} \pi r[/tex]

=0.5π(12)

Length of AB =1 8.8495559215 in

Area = 1/4*π*r²

Area = 1/4*π*12²

Area = 113.097335529 in²

20) Arc length = θr

[tex]\frac{3 }{4} \pi *10[/tex]

Length = 23.5619449019 in

Area = [tex]\frac{angle}{2\pi } *\pi r^{2}[/tex]

= [tex]\frac{3\pi }{8} *10^2[/tex]

Area = 117.80972451 in²

-68/1 is  in the form of rational number.

What is an example of an integer?

A whole number that can be positive, negative, or zero is called an integer. It is not a fraction. Examples of numbers include: -5, 1, 5, 8, 97, and 3,043. The following numbers are examples of non-integers: -1.43, 1 3/4, 3.14,.09, and 5,643. 1. A positive integer and a negative integer cannot be multiplied.

                            Two positive integers can be multiplied to make a positive number. As an integer is only a collection of numbers, there is no specific formula for it. When doing mathematical operations on numbers, such as addition, subtraction, etc., there are nonetheless specific guidelines that must be followed.

-68 as a quotient of integers

In form of rational number

 - 68 = -68/1

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We can solve this problem using trigonometry and the properties of triangles.

Let C be the location of the radio transmitter. Then, ACB is a triangle with sides AC = x (the distance from A to the transmitter), BC = y (the distance from B to the transmitter), and AB = 2.00 mi.

We can use the fact that the sum of the interior angles of a triangle is 180 degrees to find the angle at C:

angle ACB = 180 degrees - angle BCA - angle CAB

From the information given in the problem, we know that:

angle CAB = N 36° 20' E

angle BCA = N 43° 40' W

To add or subtract angles, we need to convert them to a common direction. We can do this by adding or subtracting 180 degrees, or by using the fact that 1 degree = 60 minutes (') and 1 minute = 60 seconds ("). Therefore:

angle CAB = 36 degrees + 20/60 degrees = 36.3333... degrees

angle BCA = 180 degrees - (43 degrees + 40/60 degrees) = 136.6666... degrees

Substituting these values into the equation for angle ACB, we get:

angle ACB = 180 degrees - 136.6666... degrees - 36.3333... degrees = 7.0000... degrees

Now, using the law of sines, we can write:

x / sin(angle CAB) = 2.00 mi / sin(angle ACB)

y / sin(angle BCA) = 2.00 mi / sin(angle ACB)

Solving for x and y, we get:

x = 2.00 mi * sin(angle CAB) / sin(angle ACB) = 2.00 mi * sin(36.3333... degrees) / sin(7.0000... degrees) = 9.0734... mi

y = 2.00 mi * sin(angle BCA) / sin(angle ACB) = 2.00 mi * sin(136.6666... degrees) / sin(7.0000... degrees) = 1.1878... mi

Therefore, the distance of the transmitter from B is y = 1.1878... mi (rounded to 4 decimal places).

The statue is about 9.8 - 1.5 = 8.3 meters taller than Kimberly.

What is height?

Height typically refers to the measurement of how tall or high something or someone is, usually measured from the ground or a given baseline. It is often used as a physical descriptor of an object or person, and can be measured in various units such as feet, meters, or inches. Height can also be used to describe the vertical extent or distance of an object or structure, such as the height of a building or the height of a mountain.

We can use the Pythagorean theorem to solve the problem.

Let h be the height of the statue. Then, we have:

h² = 4² + 9²

h² = 16 + 81

h² = 97

h ≈ 9.8

Therefore, the statue is about 9.8 - 1.5 = 8.3 meters taller than Kimberly.

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Answer:

Hery is 3. Jai is 4

Step-by-step explanation:

3×4=12

Therefore, the sales tax rate on the washer and dryer set was 5.25%.

Sales tax rates vary depending on the country, state, and even city or municipality where the sale is taking place. Therefore, it's difficult to provide a single answer without more information about the specific location you're asking about.

For example, in the United States, the sales tax rate can range from 0% in some states to as high as 10.25% in certain cities or counties. In Canada, the federal sales tax is 5%, but provinces and territories may also have their own sales tax rates.

To find the sales tax rate, we need to divide the sales tax by the total cost of the washer and dryer set:

Sales tax rate = sales tax / total cost

Total cost = $2900 (cost of washer and dryer set)

Sales tax = $152.25\2900

Sales tax rate = 152.25 / 2900

Sales tax rate = 0.0525 or 5.25%

Therefore, the sales tax rate on the washer and dryer set was 5.25%.

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The total difference between 4 5/6 and 9 1/6 on a number line using shorter jumps to the nearest integers is 4 1/3.

To find the difference between 4 5/6 and 9 1/6 on a number line using shorter jumps to the nearest integers, we can follow these steps:

Step 1: Convert the mixed numbers to improper fractions.

4 5/6 = (6 x 4 + 5) / 6 = 29/6

9 1/6 = (6 x 9 + 1) / 6 = 55/6

Step 2: Find the distance between the two fractions on the number line by taking the absolute value of their difference.

|29/6 - 55/6| = |-26/6| = 26/6

Step 3: Simplify the fraction and convert it back to a mixed number, if necessary.

26/6 can be simplified to 13/3, which is an improper fraction.

To convert 13/3 back to a mixed number, we divide the numerator (13) by the denominator (3) and write the remainder as a fraction:

13 ÷ 3 = 4 with a remainder of 1

So, 13/3 = 4 1/3

Therefore, on a number line with shorter jumps to the nearest integers, the total distance between 4 5/6 and 9 1/6 is 4 1/3.

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All the items are in the correct order as follows:

Order from least to greatest:

4, 2, 3, 1

The reason for the order from least to greatest is based on the number of possible combinations in each situation.

Neither the letters nor the numbers can be repeated: In this situation, there are 26 choices for the first letter, 25 choices for the second letter (since the first letter has already been chosen and cannot be repeated), 8 choices for the first digit (since it can be any number from 1 to 9), 7 choices for the second digit (since the first digit has already been chosen and cannot be repeated), and 6 choices for the third digit. Therefore, the total number of possible combinations is 26 x 25 x 8 x 7 x 6 = 1,872,000.

The letters can repeat, but the number cannot repeat: In this situation, there are 26 choices for each letter and 9 choices for each digit. Therefore, the total number of possible combinations is 26 x 26 x 9 x 8 x 7 = 328,968.

The number can repeat, but the letters cannot repeat: In this situation, there are 26 choices for the first letter, 25 choices for the second letter, and 9 choices for each digit. Therefore, the total number of possible combinations is 26 x 25 x 9 x 9 x 9 = 5,565,750.

The letter "O" cannot be used but there are no restrictions on repeating the other letters or numbers: In this situation, there are 25 choices for each letter (since "O" cannot be used) and 9 choices for each digit. Therefore, the total number of possible combinations is 25 x 25 x 9 x 9 x 9 = 15,506,250.

Based on the above calculations, the order from least to greatest is 4, 2, 3, 1.

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The text format of the question in the picture:

Use the arrows to move each item into the correct order. Click the up arrow to move the item up, or click the down mow to move the them down. Once all the items are in the correct order, submit your response.

A bike license consists of 2 letters, using any of the 26 letters in the alphabet, followed by 3 digits from 1 to 9. Calculate the number of possible license plates in each situation, then, order them from least to greatest.

The letters can repeat, but the number cannot repeat

The number can repeat, but the letters cannot repeat

Neither the letters nor the numbers can be repeated

The letter "O" cannot be used but there are no restrictions on repeating the other letters or numbers.

Probability that a shipment will be returned if the true sample proportion of defective cartridges in the shipment is 0.06 is equals to the 99.4457%.

We have A manufacturer of computer printers purchases plastic ink cartridges from a vendor.

Sample size for cartridge sample, n

= 238

Sample proportion of defective cartridges is more than 0.02.

true proportion of defective cartridges in the shipment = 0.06

Population Mean, μ = Σ(x) = 0.06 × 238

= 14.28

standard deviations, σ = sqrt(V(x))

= sqrt(238×0.06×0.94) = 3.74

If there are more than 0.02× 238 = 4.76 defective, the sample will be returned. This probability is 1 subtracted by the pvalue of Z when x = 4.8

Using Z- score in normal distribution formula, z = (x - μ) / σ

=> z = (4.8 - 14.3) / 3.74 = -2.54

=> P(Z < -2. 54) = 0.00554

This means that there is a 1 - 0.00554

= 0.994457376556917.

Hence, required probability is 99.4457%.

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Complete question:

A manufacturer of computer printers purchases plastic ink cartridges from a vendor. When a large shipment is received, a random sample of 230 cartridges is selected, and each cartridge is inspected. If the sample proportion of defective cartridges is more than 0.02, the entire shipment is returned to the vendor. (a) What is the approximate probability that a shipment will be returned if the true proportion of defective cartridges in the shipment is 0.06?

The size of the x in the regular pentagon is 36 degrees.

In a regular pentagon, all the sides are congruent and all the angles are congruent. To find the internal angle of a regular pentagon, we can use the formula:

Interior angle = (n-2) x 180 / n

where n is the number of sides of the polygon.

For a regular pentagon, n = 5, so we can substitute this value into the formula:

Interior angle = (5-2) x 180 / 5

Interior angle = 3 x 180 / 5

Interior angle = 540 / 5

Interior angle = 108 degrees

For the value of x, we have

x = 108 degrees/3

Evaluate

x = 36 degrees

Therefore, the value of x in the regular pentagon is 36 degrees.

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These notes provide a comprehensive guide to solving linear equations using the substitution method, and would be a helpful resource for students studying this topic.

When note-taking with vocabulary and core concepts, follow these steps:
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Create headings or sections for each core concept: Organize your notes into sections with headings for each core concept.

This will help you structure your notes and make it easier to find information later on.
Define and highlight key vocabulary: As you take notes, pay attention to important terms or jargon related to the core concepts.

Define these terms in your notes and highlight or underline them for easy reference.
Use bullet points and abbreviations: Keep your notes concise by using bullet points and abbreviations to summarize information.

This will help you understand and remember the material better.
Incorporate examples or explanations: Include examples or explanations that help illustrate the core concepts and vocabulary.

This will help you better understand the material and provide context for the vocabulary.
Review and revise your notes: After taking notes, review and revise them to ensure they accurately reflect the material and incorporate the key vocabulary and core concepts.

This will help reinforce your understanding and improve retention of the information.

By following these steps, you'll create organized and effective notes that incorporate vocabulary and core concepts, making it easier to study and understand the material.

The notes provide several examples with detailed explanations on how to apply the substitution method to solve linear equations.

The examples include equations with coefficients, constants, and variables, and demonstrate how to rearrange the equations to solve for the variables.

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