When dividing 456.3 by 100, how should the decimal point be moved?



1. Move the decimal point three places to the right.



2. Move the decimal point two places to the right.



3. Move the decimal point three places to the left.



4. Move the decimal point two places to the left.

Answer:

The median is 69.5

Step-by-step explanation:

The median is also known as the middle value. To find the median, you first arrange your data in numerical order.

Numerical order:

50, 50, 53, 55, 55, 57, 62, 63, 64, 64, 65, 68, 68, 69, 69, 70, 71, 71, 71, 72, 72, 73, 75, 75, 75, 77, 77, 78, 79, 80

There are 30 numbers, which means that the median is between the 15th and 16th value (69 and 70).

69 + 70 = 139

139/2 = 69.5

Therefore, the median of this data set is 69.5

Hope this helps!

The equation involves both sin²(φ) and cos²(φ), as well as sin²(θ), which indicates that the surface has a more complex shape, possibly involving rotational symmetry.

To identify the surface whose equation is given as ρ²(sin²(φ) sin²(θ) + cos²(φ)) = 81, we can follow these steps:

Rewrite the equation
We have the equation: ρ²(sin²(φ) sin²(θ) + cos²(φ)) = 81

Isolate ρ²
We can rewrite the equation as: ρ² = 81 / (sin²(φ) sin²(θ) + cos²(φ))

Find ρ
Take the square root of both sides to find ρ: ρ = √(81 / (sin²(φ) sin²(θ) + cos²(φ)))

The given equation represents a surface in spherical coordinates (ρ, φ, θ). Since ρ (the radial distance) is expressed in terms of φ and θ, the surface is not a simple sphere or ellipsoid. The equation involves both sin²(φ) and cos²(φ), as well as sin²(θ), which indicates that the surface has a more complex shape, possibly involving rotational symmetry.

However, without further information, it's difficult to provide a specific name for this type of surface.

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Answer:

12 boys

Step-by-step explanation:

30 in total - 18 girls = x boys

30 - 18 = 12 boys

Answer:

No

Step-by-step explanation:

They are not the same size.

Answer:

No, they are not congruent.

Step-by-step explanation:

Congruency is defined as moving, rotating, etc. without changing its shape or size.

Answer:

6

Step-by-step explanation:

123

132

213

231

312

321

which totals to 6 overall combinations

The difference of length of Tom's pencil from Ellen's pencil is given by the equation A = 3x + 1/5 cm

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

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

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the difference of length be represented as A

Now , the equation will be

The length of Ellen's pencil is p = 2x + 1/5 cm

The length of Tom's pencil is q = 5x + 2/5 cm

Now , the difference of length A = q - p

Substituting the values in the equation , we get

The difference of length A = 5x + 2/5 cm - 2x + 1/5 cm

On simplifying the equation , we get

The difference of length A = ( 5x - 2x ) + ( 2/5 - 1/5 ) cm

The difference of length A = 3x + 1/5 cm

Therefore , Tom's pencil is longer than Ellen's pencil by 3x + 1/5 cm

Hence , the equation is A = 3x + 1/5 cm

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Answer:

?

Step-by-step explanation:

Answer:

Step-by-step explanation:

I cant read 1 and 2 but i can answer the rest

3: 30 apples

4: Ronald jumped higher by 9 inches

5: 0.9 seconds faster

:)

Answer:

A

You plug in the same x value for each and see the answer. So 2(5)*10^4= 100000. And for the other we do 4(5)*10^2 which is 200. Since is says that 2x10^4 is 50 times as great as 4x10^2, we know that a is right because 200 * 50 = 100000.

According to the question 42% of investment managers were bullish on the stock market, and the average expected return for equities was 11.8%.

1. The average expected return over the next 12 months for equities was 11.8%.

The average expected return for equities, based on the responses of the investment managers surveyed, was found to be 11.8%. This indicates the average anticipated profitability of investments in equities over the next year.

2. 42% of managers classified themselves as bullish or very bullish on the stock market.

Out of the investment managers surveyed, 42% expressed a bullish or very bullish outlook on the stock market. This suggests that a significant portion of the surveyed managers held an optimistic view of the stock market's performance.

In conclusion, the descriptive statistics gathered from the survey of investment managers indicate that the average expected return for equities is 11.8%, and 42% of managers classified themselves as bullish or very bullish on the stock market.

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Answer: A = \(-\frac{13}{18} - \frac{9}{-14}\)

                  =>(x7) \(-\frac{13}{18} + \frac{9}{14}\)  (x9)

                  => \(\frac{-91+81}{126}\)

                  => \(\frac{-10}{126}\) (÷2)

                  => \(-\frac{5}{63}\)

B = \(-\frac{17}{28} + \frac{15}{36}\) (÷3)

   =>(x3) \(-\frac{17}{28} + \frac{5}{12}\) (x7)

   => \(-\frac{51}{84} + \frac{35}{84}\)

   => \(\frac{-51+35}{84}\)

   => \(\frac{-16}{84}\) (÷4)

   => \(-\frac{4}{21}\)

Answer:

185 dimes and 73 quarters

Step-by-step explanation:

q + d = 258

25(q) + 10(d) = 3675

The type of sampling used in each scenario is as follows:

Stratified sampling, Convenience sampling, Cluster sampling, Random sampling, Convenience sampling, Cluster sampling, Systematic sampling

The psychologist selects a specific number of boys and girls from each math class, which indicates stratified sampling. The population (students) is divided into strata (math classes) and samples are taken from each stratum.

The conclusion is based on responses from questionnaires that were distributed conveniently to students, indicating convenience sampling. The sample is not randomly selected but consists of those who chose to respond.

The biologist surveys all students from randomly selected classes, indicating cluster sampling. The population (students) is divided into clusters (classes), and all members of the selected clusters are included in the sample.

The game show organizer shuffles and randomly selects contestant names, indicating random sampling. Each name has an equal chance of being selected.

Family planning polls a specific number of men and women, suggesting convenience sampling. The individuals surveyed are conveniently selected and may not represent the entire population.

The hospital researcher interviews all diabetic patients in randomly selected hospitals, indicating cluster sampling. The population (diabetic patients) is divided into clusters (hospitals), and all members of the selected clusters are included in the sample.

Smart selects every 100th cell phone from the assembly line, indicating systematic sampling. A sampling interval is used to select samples at regular intervals, ensuring a systematic and consistent approach.

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Answer:

One-fourth equals three-twelfths

Step-by-step explanation:

From the above question:

The fractions

One-fourth

: A fraction bar divided into 4 parts. 1 is shaded.

One-half

A fraction bar divided into 2 parts. 1 is shaded

Three-twelfths:

A fraction bar divided into 12 parts. 3 are shaded.

Which is a correct comparison of these fractions?

Comparing the options

a) One-fourth equals three-twelfths

= 1/4 = 3/12

Divide numerator and denominator by 3

= 3 ÷ 3 /12 ÷ 3

= 1/4

Option a is correct

b) One-half is less than three-twelfths

1/2 < 3/12

This statement above is wrong.

One half is greater than three twelfths

1/2 is > 3/12

1/2 > 1/4

c) One-fourth is greater than one-half

1/4> 1/2

This statement above is wrong.

1/2 is greater than 1/4

d) Three-twelfths is greater than one-fourth

This is statement is wrong. Three -twelfths is equal to one - fourths

The correct comparison of these fractions is One-fourth equals three-twelfths.

Answer:

1 : 2

Step-by-step explanation:

The original ratio would be 3 : 6, so now you need to simplify it.

To simplify ratios, you divide the number on each side by their greatest common factor. The GCF(greatest common factor) for 3 and 6 would be 3, so divide 3 by 3 =1 and divide 6 by 3 =2, so then your simplified ratio of circles to triangles would be 1 : 2

Hope this helps! :)

Answer: yield = ($70 / $875) x 100% = 8% (rounded to the nearest hundredth)

Step-by-step explanation:

To calculate the yield on a corporate bond, we need to use the following formula:

yield = (annual coupon payment / bond price) x 100%

In this case, the bond has a face value of $1000 and pays a fixed interest rate of 7%. The bond was purchased at a discount price of $875. The annual coupon payment can be calculated as:

annual coupon payment = face value x coupon rate = $1000 x 7% = $70

Using the formula above, we can calculate the yield as:

yield = ($70 / $875) x 100% = 8%

Therefore, the yield on this corporate bond is 8% rounded to the nearest hundredth.

Answer:

B

Step-by-step explanation:

it grows b

The rate of constant for the above-given first-order reaction is b.) 8.77 × 10–3 h–1.

The half-life of a first-order reaction can be calculated using the equation t1/2 = ln(2)/k, where t1/2 is the half-life and k is the rate constant.

In this case, we know that the reaction goes to half completion in 79 hours. Therefore, the half-life is also 79 hours.

Plugging this into the equation, we get:

79 = ln(2)/k

Solving for k, we get:

k = ln(2)/79

Using a calculator, we can evaluate this expression to get:

k = 8.77 × 10–3 h–1

Therefore, the correct answer is b) 8.77 × 10–3 h–1.

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The correct option is E. The population mean is less than 125. As, 125 is does not comes in the interval of 135 to 160, the interval tends to refute the claim that the population mean is less than 125.

The 90% confidence interval for the mean of the population is computed to be 135 to 160. This means that we are 90% confident that the true population mean falls within this range.

Since 125 is not within the interval of 135 to 160, the interval tends to refute the claim that the population mean is less than 125.

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The question asks for the description of the Galois group of the polynomial x^4 - 5x^2 + 6 in Q[x] over Q, where Q represents the field of rational numbers.

The Galois group of a polynomial refers to the group of automorphisms of the field extension generated by the roots of the polynomial. In this case, the polynomial x^4 - 5x^2 + 6 has coefficients in the field of rational numbers, denoted by Q. To determine the Galois group, we need to find the roots of the polynomial and analyze their relationships.

By factoring the polynomial, we can rewrite it as (x^2 - 2)(x^2 - 3). The roots of the polynomial are ±√2 and ±√3. Since all these roots are real, the Galois group is the trivial group, denoted by {e}, where e represents the identity element. In other words, there are no non-trivial field automorphisms that permute the roots of the polynomial, indicating that the polynomial is not a Galois extension over the field of rational numbers.

In summary, the Galois group of the polynomial x^4 - 5x^2 + 6 in Q[x] over Q is the trivial group, {e}. The roots of the polynomial are all real, and there are no non-trivial automorphisms that permute the roots.

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Answer:

You can use the quadratic formula

Step-by-step explanation:

X= -b +/- √b^2-4(a)(c)÷ 2(a)

Substitute and simplify to find x

Therefore, the total distance Gabe will paddle is 2x + 400 meters. The exact value of x depends on the width of the river, which is not provided in the given information.

To find the total distance Gabe will paddle, we need to consider the distance he will travel from Q to P, then from P to R, and finally from R back to Q.

First, let's consider the distance from Q to P. Since Gabe will paddle in a diagonal line across the river, this distance can be calculated using the Pythagorean theorem.

The length of the bridge (PR) is given as 400 meters, which is the hypotenuse of a right triangle. The width of the river can be considered as the perpendicular side, and the distance Gabe will paddle from Q to P is the other side. Let's call this distance x.

Using the Pythagorean theorem, we have:

x^2 + (width of the river)^2 = PR^2

Since the width of the river is not given, we'll represent it as w. Therefore:

x^2 + w^2 = 400^2

Next, let's consider the distance from P to R. Gabe will paddle along a route beside the bridge, which means he will travel the length of the bridge (PR) again. So, the distance from P to R is also 400 meters.

Finally, Gabe will paddle back from R to Q along the shore. Since he will follow the shoreline, the distance he will paddle is equal to the distance from Q to P, which is x.

To find the total distance, we add up the distances:

Total distance = QP + PR + RQ

= x + 400 + x

= 2x + 400

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The number of unique combinations that can be formed by picking one object from each set is =960. That is option C.

Number combination is a mathematical technique that shows the number of possible arrangements in a collection of items.

The first set of objects = 4. There are a total of 4 possibilities.

The second set of objects = 5. There are a total of 5 possibilities

Therefore from first and second set, the total number of possibilities = 4×5 = 20

For the whole set, the total possibilities;

= 4×5×6×8

= 960

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Answer:

b = 24

Step-by-step explanation:

\(10^{2} +b^{2} =26^{2} \\100+b^{2}=676\\b^{2}=576\\\sqrt{b^2} =\sqrt{576} \\b= 24\)

Answer:

The answer is 0.68 seconds.

Step-by-step explanation:

Distance  -100 meter

Average time - 1 0.4 seconds

Standard deviation -  0.1 seconds.

If Randall's times are normally distributed, we have a 99.7% expectation that his finishing time for his next race will be greater than 0.68 seconds.

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Answer:

Linear

Step-by-step explanation:

The y is increasing constantly by 5 each time. The equation that would represent this is y=5x-7 because when x is 0 y is -7, so that is your y intercept, and the m, or slope, of your graph is 5, because of the constantly increasing y.

The given  table is representing linear function. So Option B is correct.

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Given that,

A table

x   0    1    2    3    4    5  

y   -3   5   13  21   29  37

Lets us first check that data for linear relationship,

Consider a function,

y = mx + c

lets put value (0, -3)

-3  = m0 + c

c = -3

y = mx -3

Now putting second point

5 = mx1 -3

m = 8

y = 8x - 3

If third point satisfies the given condition

then it will be linear function

x = 2 & y = 13

y = 8x -3

13 = 8x2 - 3

13 = 13

hence proved

Thus, the given table represents the linear function.

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Data can be divided on the basis of qualitative nature into two types as follows:

Thus, it is clear that nominal data can not be ranked or ordered but ordinal data are the type of qualitative data that are categorised and then ranked or ordered.

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Answer:

f(x)=20+4x = -5

Step-by-step ;

answer is -5 .

Zero: \(z = 1.5\) (from the numerator), Poles: \(z = 0.5k\) (from the \(z - 0.5k\) factor) and \(z = \frac{-1 + j}{2}\), \(z = \frac{-1 - j}{2}\) (from the quadratic factor \(z^{2} + z + 0.5\)).

To find the poles and zeros of the given z-transfer function \(D(z)\), we need to examine the factors in the numerator and denominator of \(D(z)\) and determine their roots.

The numerator of \(D(z)\) is \(z - 1.5\). This expression represents a linear factor. To find its root, we set \(z - 1.5 = 0\) and solve for \(z\):

\(z - 1.5 = 0\)

\(z = 1.5\)

Therefore, the numerator has one zero at \(z = 1.5\).

Now let's focus on the denominator of \(D(z)\). It can be factored as follows:

\(z^{2} + z + 0.5 = (z - r_1)(z - r_2)\)

To find the roots of this quadratic equation, we can use the quadratic formula:

\(r_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

In this case, \(a = 1\), \(b = 1\), and \(c = 0.5\). Plugging these values into the quadratic formula:

\(r_{1,2} = \frac{-1 \pm \sqrt{1 - 4(1)(0.5)}}{2(1)}\)

\(r_{1,2} = \frac{-1 \pm \sqrt{1 - 2}}{2}\)

\(r_{1,2} = \frac{-1 \pm \sqrt{-1}}{2}\)

\(r_{1,2} = \frac{-1 \pm j}{2}\)

Therefore, the roots of the quadratic factor are complex conjugates, given by \(r_1 = \frac{-1 + j}{2}\) and \(r_2 = \frac{-1 - j}{2}\).

The denominator also includes another factor \(z - 0.5k\). This factor will introduce another pole at \(z = 0.5k\) as \(k\) is a real number.

These poles and zeros play a crucial role in understanding the stability and behavior of the digital control system described by the z-transfer function \(D(z)\).

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Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

What is matrix ?

A matrix is a rectangular array of numbers or other mathematical objects, typically arranged in rows and columns. Matrices are often denoted using capital letters, such as A, B, and C. Each element of a matrix is identified by its row and column indices,

1) False, If two row interchanges are made in succession, the determinant of the new matrix is the negative of the determinant of the original matrix.

2) False, If the determinant of a matrix is zero, it does not necessarily mean that two rows or two columns are the same or a row or column is zero, it only means that the matrix is singular, i.e. non-invertible and it also can mean that the matrix is linearly dependent.

3) False, The determinant of a matrix is not always equal to the product of the diagonal entries, it is a scalar value calculated through a specific method called matrix expansion which is based on the entries of the matrix and it depends on the size of the matrix.

4) False, The determinant of a matrix is a scalar value, it cannot be equal to another matrix.

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

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