6 1/2 lb= _ oz

104
108
112
136

The product of a fraction between 0 and 1 and a whole or mixed number is always less than the whole number or mixed number.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

The product of the whole number by 1 will be the same number.

For example 4 × 1 = 4

If we multiply the whole number by greater than 1 then the result will be increased.

For example 4 × 1.2 = 4.8

But if we multiply the whole number by less than 1 then the value is going to be decreased.

For example

4 × 0.8 = 3.2

Hence "The product of a fraction between 0 and 1 and a whole or mixed number is always less than the whole number or mixed number".

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In set-builder notation, the same set can be expressed as {x|x (N and 4<x<10)}, which reads as "the set of all x such that x is a natural number and 4 < x < 10."

How to solve the question?

a. The set of natural odd numbers greater than 2, but less than 11 can be expressed using the roster method as {3, 5, 7, 9}. The set includes all the odd natural numbers between 2 and 11, excluding the endpoints, since 2 is not odd, and 11 is not less than 11.

b. The set {x|x (N and 4<x<10)} can be expressed using the roster method as {5, 6, 7, 8, 9}. The set includes all the natural numbers greater than 4 and less than 10, since x is a natural number (N) and satisfies the condition 4 < x < 10.

In set-builder notation, the same set can be expressed as {x|x (N and 4<x<10)}, which reads as "the set of all x such that x is a natural number and 4 < x < 10." The vertical bar separates the description of the elements of the set (the condition) from the set itself.

The roster method and set-builder notation are both ways of describing sets, but the roster method lists all the elements of a set, while the set-builder notation describes the properties or conditions that define the set. Both methods are useful in different situations and depend on the specific context and the purpose of the set description.

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Your complete question is :-

express each set using the roster method.

a. the set of the natural odd numbers greater than 2, but less than 11

b.{x|x (N and 4

Answer:

7300000 in scientific notation can be written as 7.3 x 10^6

Answer:

A) 2 : 3

Reason: Since their scale factor is 2 / 3, meaning that the object 2 / 3 of the other same object, so the volume also 2 / 3 of the other object

Answer:

35

Step-by-step explanation:

The answer might be 7 i don't know

Answer:

w = 7 feet

Step-by-step explanation:

The area of the rectangle, 70 ft², is equal to the length, 10 ft, times the width, w.

So, to find w, we can divide the area by the length.

w = 70 / 10

w = 7

The width is equal to 7 feet.

We can check this by multiplying the given length by the width that we've calculated to see if the area is equal to 70 feet².

10 · 7 = A

70 = A

Because the area we found is equal to the given area, our calculations are correct.

I hope this helps ^^

Good luck n.n

$26.40

ten percent is 88 divided by 10= 8.8

8.8 multiplied by 3 is 26.40

The number of codes that can be made using the 5 letters given is 120 as calculated using permutation and combination.

Now when no letters are repeated:

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 4 options , third digit has 3 options , fourth digit has 2 options and the final digit will have only 1 option left.

So total number of codes = 5 × 4 × 3 × 2 × 1 = 120 codes

if letters can be repeated

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 5 options , third digit has 5options , fourth digit has 5 options and the final digit will have only 5 options also.

So total number of codes = 5 × 5 × 5× 5× 5= 3125 codes

if adjacent letters cannot be repeated

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 4 options , third digit has 4 options , fourth digit has 4 options and the final digit will have only 4 options also.

So total number of codes = 5 × 4 × 4× 4× 4 = 1280 codes

Hence the total number of codes as calculated by permutation and combination is 1280.

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Answer:

50.24

Step-by-step explanation:

8÷2 is the radius. 3.14×4^2=50.24 m^2

^= where the exponent is supposed to go

Find the area and the circumference of a circle with diameter 8 m .

1)

\( \pink{\boxed{ \sf{Area \: of \: circle = \pi r {}^{2} }}}\)

2)

\( \pink{\boxed{\sf{Circumference of circle = 2\pi r}}}\)

We know that radius of circle is always halves of its diameter . So radius of circle :

1) Finding area :

Therefore, area of circle is 50.24 m² .

2) Finding circumference :

Therefore, circumference of circle is 25.02 m

The point charges placed 0.500 m apart are 10.4 nC and 43.9 nC. Then, the electric field halfway between these charges will be -4824 N/C.

The physical field that surrounds particles with an electrical charge is called an electric field. All other charged particles in the field are affected by it, either being attracted to it or being repelled by it.

The electric field because of a point charge q is written as \(E=\frac{kq}{r^2}\)

Positive point charges cause the electric field to point away from the point, whereas negative point charges cause the electric field to point in the direction of the point. Then, the electric field of the midpoint p in the diagram is written as,

\(\begin{aligned}E_p&=\mathrm{\frac{k(10.4\;nC)}{(0.25\;m)^2}-\frac{k(43.9\;nC)}{(0.25\;m)^2}}\\&=\mathrm{\frac{k(10.4-43.9)\times10^{-9}\;C}{(0.25\;m)^2}}\\&=-\mathrm{\frac{9\times 10^9\;Nm^2/C^2\times 33.5\times10^{-9}\;C}{(0.25\;m)^2}}\\&=-\mathrm{4824\;N/C}\end{aligned}\)

The required answer is -4824 N/C.

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Answer:

x

=

7

2

−

y

2

Step-by-step explanation:

The value of m that satisfies the equation -3 + m = 9 is m = 12.

To solve the equation -3 + m = 9, we can isolate the variable m by moving the constant term -3 to the other side of the equation.

-3 + m = 9

To move -3 to the other side, we can add 3 to both sides of the equation:

-3 + 3 + m = 9 + 3

Simplifying, we have:

m = 12

Therefore, the value of m that satisfies the equation -3 + m = 9 is m = 12.

None of the provided answer options (A, B, C, D) match the correct solution.

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Step-by-step explanation:

so beacuse these triangles are similiar

we have

SD/SB=CD/AB

6/72=5.2/AB

AB=72×5.2/6=62.4

Given that ΔSCD and ΔSAB are similar triangles, the distance across the lake is: AB = 62.4 m.

Similar triangles possess corresponding side lengths that are proportional to each other, which means the ratio of their corresponding sides are equal.

Thus, since ΔSCD is similar to ΔSAB, therefore:

SD/SB = CD/AB

6/(6 + 66) = 5.2/AB

6/72 = 5.2/AB

AB = (72×5.2)/6

AB = 62.4 m

Therefore, given that ΔSCD and ΔSAB are similar triangles, the distance across the lake is: AB = 62.4 m.

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"Parameter" is the descriptive measure of the population. The description, that if the data refuses the assumption of a parameter is the main goal of the tests of hypothesis.

There are many population parameters. Some examples of the population parameters include:

In general, it is not possible to measure the parameters of a population, as it requires to collect information from each and every member of the population. That is why, 'sample statistics' is conducted.

What is a sample statistics?

In sample statistics, samples are collected from each and every aspect of the population and then the samples are tested in order to derive a conclusion. For example: the mean diastolic blood pressure of more than one sample, the mean body weight of more than one population, etc.

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1. Length of side DE = 9

Length of side DF = 15

2. Length of side DE = 5.625

Length of side EF = 4.96

3. Length of side DF = 10

Length of side EF = 6.61

Given,

Two triangles

Triangle ABC and Triangle DEF ; These are similar triangles

That is,

AB = DE, BC = EF, AC = DF

Here,

AB = 3

BC = 4

1. EF = 12

AB/BC = DE/EF

3/4 = x/12

x = (12 x 3) / 4

x = 3 x 3 = 9

Length of side DE = 9

DF = \(\sqrt{9^{2} +12^{2} }\) = \(\sqrt{81 + 144}\) = √225 = 15

Now,

2. DF = 7.5

AB/BC = DE/DF

3/4 = x/7.5

x = (7.5 x 3) / 4

x = 5.625

Length of side DE = 5.625

EF =  \(\sqrt{7.5^{2}-5.625^{2} }\) = \(\sqrt{56.25-31.64}\) = √24.61 = 4.96

Next,

3. DE = 7.5

AB/BC = DE/DF

3/4 = 7.5/x

x = (7.5 × 4) / 3 = 30/3

x = 10

Length of side DF = 10

EF =  \(\sqrt{10^{2}-7.5^{2} }\) = \(\sqrt{100-56.25}\) = √43.75 = 6.61

That is,

1. Length of side DE = 9

Length of side DF = 15

2. Length of side DE = 5.625

Length of side EF = 4.96

3. Length of side DF = 10

Length of side EF = 6.61

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Answer: -2x + 12

Step-by-step explanation:

2A + B = 2(-2x + 8) + (2x - 4) = -4x + 16 + 2x - 4 = -2x + 12

f(x)=x^2−2x+1

Yw and pls mark me brainiest

Answer:

-infty<xinfty

Step-by-step explanation:

Answer:

13 out of 16 (13/16)

Step-by-step explanation:

Add all of the items together.

5 stress balls + 3 notepads + 2 gift cards + 6 sticky notes = 16 items

So, now you have to find the probability out of 16.

Since there are 5 stress balls and 2 gift cards, there is a 5 out of 16 chance of passing out stress balls(5/16) and a 2 out 16 chance of handing out gift cards(2/16)

So, she has a 3 out 16 chance of handing out stress balls more than gift cards.

hope this helps and makes sense:)

Probability of red = \(\frac{4}{10}\) , blue = \(\frac{5}{10}\) , green = \(\frac{1}{10}\).

Meaning of probability :

Probability is calculation of how likely some event will happen. Whenever we are not sure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are going to happen.

The analysis of events governed by probability is called statistics.

According to the given information :

Red section = \(\frac{2}{5}\)

multiply numerator and denominator by \(2\) we get

Red section = \(\frac{4}{10}\)

 Blue section = \(\frac{1}{2}\)

 multiply numerator and denominator by \(5\) we get

 Blue section = \(\frac{5}{10}\)

 Green section = \(1\)- Red section - Blue section

 Green section =\(1-\frac{4}{10} -\frac{5}{10}\)

  Green section = \(\frac{1}{10}\)

Therefore Probability of red = \(\frac{4}{10}\) , blue = \(\frac{5}{10}\) , green = \(\frac{1}{10}\).

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The calculated time of is that the baseball game was 1 7/12 hour longer than the movie

The given parametes in the question are

Movie = 1 3/4 hours

Baseball = 3 1/3 hours

To calculate how much longer was the baseball game than the movie, we subtract

So, we have

Longer = 3 1/3 - 1 3/4

Evaluate

Longer = 19/12

This gives

Longer = 1 7/12

Hence, the baseball game was 1 7/12 hour longer than the movie

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The coordinates of the vertex of the parabola are (3, -7). The focus of the parabola is located at (3, -3). The equation of the directrix is y = -11.

The given equation of the parabola is in the form (x - h)^2 = 4p(y - k), where (h, k) represents the vertex and p represents the distance between the vertex and the focus/directrix.

Comparing the given equation with the standard form, we can see that the vertex is at (3, -7).

The coefficient 4p in this case is 16, so p = 4. Since the parabola opens upward, the focus will be p units above the vertex. Therefore, the focus is located at (3, -7 + 4) = (3, -3).

To find the directrix, we need to consider the distance p below the vertex. Since the parabola opens upward, the directrix will be p units below the vertex. Hence, the equation of the directrix is y = -7 - 4 = -11.

In summary, the coordinates of the vertex are (3, -7), the focus is located at (3, -3), and the equation of the directrix is y = -11.

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Answer:

The family of all prime numbers such that \(a^{2} + b^{2} + c^{2} -1\) is a perfect square is represented by the following solution:

\(a\) is an arbitrary prime number. (1)

\(b = \sqrt{1 + 2\cdot a \cdot c}\) (2)

\(c\) is another arbitrary prime number. (3)

Step-by-step explanation:

From Algebra we know that a second order polynomial is a perfect square if and only if \((x+y)^{2} = x^{2} + 2\cdot x\cdot y + y^{2}\). From statement, we must fulfill the following identity:

\(a^{2} + b^{2} + c^{2} - 1 = x^{2} + 2\cdot x\cdot y + y^{2}\)

By Associative and Commutative properties, we can reorganize the expression as follows:

\(a^{2} + (b^{2}-1) + c^{2} = x^{2} + 2\cdot x \cdot y + y^{2}\) (1)

Then, we have the following system of equations:

\(x = a\) (2)

\((b^{2}-1) = 2\cdot x\cdot y\) (3)

\(y = c\) (4)

By (2) and (4) in (3), we have the following expression:

\((b^{2} - 1) = 2\cdot a \cdot c\)

\(b^{2} = 1 + 2\cdot a \cdot c\)

\(b = \sqrt{1 + 2\cdot a\cdot c}\)

From Number Theory, we remember that a number is prime if and only if is divisible both by 1 and by itself. Then, \(a, b, c > 1\). If \(a\), \(b\) and \(c\) are prime numbers, then  \(2\cdot a\cdot c\) must be an even composite number, which means that \(a\) and \(c\) can be either both odd numbers or a even number and a odd number. In the family of prime numbers, the only even number is 2.

In addition, \(b\) must be a natural number, which means that:

\(1 + 2\cdot a\cdot c \ge 4\)

\(2\cdot a \cdot c \ge 3\)

\(a\cdot c \ge \frac{3}{2}\)

But the lowest possible product made by two prime numbers is \(2^{2} = 4\). Hence, \(a\cdot c \ge 4\).

The family of all prime numbers such that \(a^{2} + b^{2} + c^{2} -1\) is a perfect square is represented by the following solution:

\(a\) is an arbitrary prime number. (1)

\(b = \sqrt{1 + 2\cdot a \cdot c}\) (2)

\(c\) is another arbitrary prime number. (3)

Example: \(a = 2\), \(c = 2\)

\(b = \sqrt{1 + 2\cdot (2)\cdot (2)}\)

\(b = 3\)

Answer:

3(12 + 7)

Step-by-step explanation:

To find the GCF of 36 and 21, list out their factors.

36: 1, 2, 3, 4, 6, 9, 12, 18, 36

21: 1, 3, 7, 21

The greatest factor which both numbers share is 3.

Therefore, you can factor 36 + 21 as 3(12 + 7)

Given:

Required:

To find the range of the function (uv)(x).

Explanation:

We know that

The horizontal asymptote of this function is at y=3.

So, the range of this function is from

Final Answer:

The range of (uv)(x) is

Given

Slant height 0.75 foot

Perimeter 1.2 feet equilateral base

Area 0.07 sq foot

Procedure

This is an example, now let apply to the problems

Area of base = 0.07 sq ft

Area of face = 1/2*0.4*0.75 = 0.15 sq ft

Total

3*0.15 + 0.07

0.52

The total area would be 0.52 sqft

Answer:

a

The  null hypothesis is   \(H_o  :  \mu =  32.48\)          

The alternative  hypothesis is   \(H_a  :  \mu  <  32.48\)

b

  \(t  =  -1.504\)

c

There is no sufficient evidence to conclude that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48

Step-by-step explanation:

From the question we are told that

   The mean price of   is  \(\mu = \$ 32.48\)

   The  sample size is n  =  56  

    The sample mean is  \(\=  x  =  \$30.15\)

     The standard deviation is  \(\sigma =  \$12\)

The  null hypothesis is   \(H_o  :  \mu =  32.48\)          

The alternative  hypothesis is   \(H_a  :  \mu  <  32.48\)

Generally the test statistic is mathematically represented as

       \(t =  \frac{\= x  - \mu }{\frac{\sigma }{\sqrt{n} } }\)

=>    \(t =  \frac{30.15  - 32.48 }{\frac{12 }{\sqrt{60} } }\)

=>    \(t  =  -1.504\)

Generally the p-value  is mathematically represented as

      \(p-value  =  P (t < -1.504 )\)

From the z-table  

    \(P(t <  -1.504) =   0.066291\)

So  

    \(p-value  = 0.066291 \)

From the value we obtain we see that  

    \(p -value  >  \alpha\)

Then we fail to reject the null hypothesis  

   Hence there is no sufficient evidence to conclude that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48

Answer:

x = 3/2 or x = -1

Step-by-step explanation:

2x² - x - 3 = 0

2*(-3) = -6

Factors of -6:

(-1, 6), (1, -6), (-2, 3), (2, -3)

We need to find a pair that adds up to the co-eff of x which is (-1)

Factors :(2,-3)

2 - 3 = -1

so, 2x² - x - 3 = 0 can be written as:

2x² + 2x - 3x - 3 = 0

⇒ 2x(x + 1) -3(x + 1) = 0

⇒ (2x - 3)(x + 1) = 0

⇒ 2x - 3 = 0 or

x + 1 = 0

⇒ 2x = 3 or x = -1

⇒ x = 3/2 or x = -1

The probability that the next person will purchase one or more costumes can be found by dividing the number of visitors who purchased one or more costumes by the total number of visitors.

The total number of visitors is 105 + 41 + 8 = 154.

The number of visitors who purchased one or more costumes is 41 + 8 = 49.

So the probability that the next person will purchase one or more costumes is 49/154, which is approximately 0.32 to the nearest hundredth.

The given coordinate's line of reflection is the x-axis, Option D.

After intersecting the co-ordinates A(-3,5), B(2,8) and C(-4,-5) of line 1 and co-ordinates A'(-3,-5), B'(2,-8) and C'(-4,5) of line 2. It is deduced that both lines are similar.

The point of intersection of lines 1 and 2 is on the X-axis as the reflection of the coordinate,

A(-3,5) on the negative x-axis and positive y-axis is A'(-3,-5) on the negative y-axis and the negative x-axis.

B(2,8) on the positive x-axis and positive y-axis is B'(2,-8) on the negative y-axis and the positive x-axis.

C(-4,-5) on the negative x-axis and negative y-axis is C'(-4,5) on the positive y-axis and the negative x-axis.

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The distance between points R and S is  \(\sqrt{ (185)\). The correct answer is D. She made no errors.

Heather's work to find the distance between two points, R(-3,-4) and S(5,7), is shown:

RS = √(-4) (-3))² + (7 − 5)²

= √(-1)² + (2)²= √1 + 4

= √5

The error is with the order of subtraction in the formula for the distance between two points.

Heather did not make any errors in calculating the distance between two points. Therefore, the correct answer to the question above is (OD) She made no errors.

The formula for the distance between two points, A (x1, y1) and B (x2, y2), in the coordinate plane is given as;

dAB = \(\sqrt{  ((x^2 - x1)^2 + (y2 - y1)^2)\)

Comparing the given question with the formula above, we have;

A = R (-3, -4) and B = S (5, 7)The distance, AB = RS.

Therefore, we have;

RS = \(\sqrt{ ((5 - (-3))^2 + (7 - (-4))^2)\)

On solving the above equation;RS = \(\sqrt{ ((5 + 3)^2 + (7 + 4)^2)\)RS

= \(\sqrt{ (8^2 + 11^2)RS\)

= \(\sqrt{ (64 + 121)RS\)

= \(\sqrt{ (185)\)

Therefore, the distance between points R and S is  \(\sqrt{ (185)\).

From the calculation, it is clear that Heather did not make any errors while calculating the distance between two points. The answer obtained by Heather is correct.

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