Simplify the following expression.

(7x3 + 8 – x2) + (5x3 – 7)

This question is incomplete

Complete Question

The weight of an organ in adult males has a bell shaped distribution with a mean of 320 grams and a standard deviation of 20 grams. Use the empirical rule to determine the following. A.) About 68% of organs will be between what weights? B.) what percentage of organs weighs between 280 grams and 360 grams? C.) what percentage of organs weighs less than 280 grams or more than 360 grams? D.) what percentage of organs weighs between 300 grams and 360 grams?

Answer:

A.) About 68% of organs will be between what weights?

Therefore, 68% of the organs will weigh between 300 and 340 grams.

B.) what percentage of organs weighs between 280 grams and 360 grams?

95%

C.) what percentage of organs weighs less than 280 grams or more than 360 grams?

5%

D.) what percentage of organs weighs between 300 grams and 360 grams?

81.5%

Step-by-step explanation:

Empirical formula states that:

68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

Where:

μ = Population mean

σ = Population standard deviation

From the above question, we have the following information

Mean weight = 320 grams

Standard deviation = 20 grams

a) About 68% of organs weight between:

To solve for this, we would use the empirical rule:

68% of the data values lie within 1 standard deviation of the mean

Hence, 68% of the data values lie in the range:

Mean - 1 standard deviation to Mean + 1 Standard Deviation.

Mean - 1 Standard Deviation

μ - σ

= 320grams - 20grams = 300 grams

Mean + 1 Standard Deviation

μ + σ

= 320grams + 20grams = 340 grams

Therefore, 68% of the organs will weigh between 300 and 340 grams.

B.) what percentage of organs weighs between 280 grams and 360 grams?

Mean weight = 320 grams

Standard deviation = 20 grams

Hence,

x - mean = 280 grams - 320 grams = -40 grams

x - mean = 360 grams - 320 grams = 40 grams

Note that both differences = 2 × standard deviation

Hence, from the empirical formula above,

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ applies

Therefore, 95% of the organs fall between 280 grams and 320 grams

C.) what percentage of organs weighs less than 280 grams or more than 360 grams?

Mean weight = 320 grams

Standard deviation = 20 grams

Hence,

x - mean = 280 grams - 320 grams = -40 grams

x - mean = 360 grams - 320 grams = 40 grams

So, from the empirical formula above,

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ applies

Therefore, 95% of the organs fall between 280 grams and 320 grams

It is important to note that finding the percentage of data that weighs less than or more than the given range of values, the formula is given as:

Percentage of Value outside( less than or more than) the range = 100% - Percentage of values within the range

100% - 95%

= 5%

Therefore, the percentage of organs weighs less than 280 grams or more than 360 grams is 5%

D.) what percentage of organs weighs between 300 grams and 360 grams?

Mean weight = 320 grams

Standard deviation = 20 grams

Hence,

x - mean = 300 grams - 320 grams = -20 grams

20 grams = 1 × standard deviation

For 300 grams, the empirical formula that states that:

68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ applies.

It is important to note that the percentage of values below the mean and above the mean must be the same.

But since this is a bell shaped distribution, the percentage of data between 300 and 320 grams = 68%/2

= 34%

x - mean = 360 grams - 320 grams = 40 grams

40 = 2 × standard deviation

For 360 grams , the empirical formula that states that,

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ applies

It is important to note that the percentage of values below the mean and above the mean must be the same.

Since this is a bell shaped distribution, the percentage between 320 and 360grams = 95%/2

= 47.5%

Therefore, the percentage of organs that weighs between 300 grams - 360 grams = 34% + 47.5%

= 81.5%

Answer:

h=10

Step-by-step explanation:

30 + 8h = 50 + 6h

8h-6h=50-30

2h=20

h=10

Answer:

Answer:

h=10

Step-by-step explanation:

Step-by-step explanation:

30 + 8h = 50 + 6h

8h-6h=50-30

2h=20

h=10

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

Explanation:

Use your calculator to find that 89/6 = 14.8333 approximately

The whole part 14 means each of the six people get 14 chips

That means 6*14 = 84 chips have been eaten so far, leaving 89-84 = 5 chips left over for her sister.

----------

In other words,

89/6 = 14 remainder 5

which can be found through long division as shown below

Answer:

option B is correct. Once have a look to this solution that I have answered

Your question is poorly formatted; However, the correct question is:

Point  A  ( 3 , 4 )  and point  M  (5.5,0) is the midpoint of point  A and point B. Determine the coordinates of B

Answer:

The coordinates of B is (8,-4)

Step-by-step explanation:

Given

Point  A  ( 3 , 4 )

Point  M  (5.5,0)

Required

Determine B

Since, M is the midpoint;

We'll solve this question using the following formula;

[tex]M(x,y) = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})[/tex]

Where [tex](x,y) = (5.5,0)[/tex] and [tex](x_1,y_1) = (3,4)[/tex]

Substitute values for x, y, x1 and y1 in the above formula;

This gives

[tex](5.5,0) = (\frac{3 + x_2}{2},\frac{4 + y_2}{2})[/tex]

By direct comparison, we have

[tex]5.5 = \frac{3 + x_2}{2}[/tex]  and [tex]0 = \frac{4 + y_2}{2}[/tex]

Solving [tex]5.5 = \frac{3 + x_2}{2}[/tex]

Multiply both sides by 2

[tex]11 = 3 +x_2[/tex]

Subtract 3 from both sides

[tex]11- 3 = x_2[/tex]

[tex]x_2 = 8[/tex]

Solving [tex]0 = \frac{4 + y_2}{2}[/tex]

Multiply both sides by 2

[tex]0 = 4 + y_2[/tex]

Subtract 4 from both sides

[tex]0 - 4 = y_2[/tex]

[tex]y_2 = -4[/tex]

Hence;

The coordinates of B is (8,-4)

Answer:

(8,-4)

I think it's right

This question is not complete

Complete Question

Kerrie is tiling the floor of a kitchen. The kitchen floor measures 11.3 feet by 9.25 feet. She orders enough tiles for 99 square feet. Which statement about the amount of tiles is correct?

a) Kerrie estimated correctly by rounding down. She has enough tile. The exact area is 104.5 square feet.

b) Kerrie estimated correctly by rounding up. She has enough tile. The exact area is 104.5 square feet.

c) Kerrie did not estimate correctly by rounding up. She does not have enough tile. The exact area is 104.5 square feet.

d) Kerrie did not estimate correctly by rounding down. She does not have enough tile. The exact area is 104.5 square feet.

Answer:

a) Kerrie estimated correctly by rounding down. She has enough tile. The exact area is 104.5 square feet.

Step-by-step explanation:

In mathematics we have what is defined as rounding up and rounding down.

Rounding up of numbers is when the number you want to round up is followed by number from 5 to 9(5, 6, 7, 8, 9)

E.g. 2.5 rounded up to the nearest whole number = 3

Rounding down of numbers is when the number you want to round up is followed by number from 1 to 4(1, 2, 3, 4)

E.g. 2.4 rounded down = 2

We are told in the question

Kerrie is tiling the floor of a kitchen. The kitchen floor measures 11.3 feet by 9.25 feet. She orders enough tiles for 99 square feet.

Kitchen floor is rectangular = Area = Length × Width

= 11.3 × 9.25 feet

= 104.525 square feet

We are told that Kerrie ordered for 99 square tiles.

But looking at the decimal, the number after the decimal are between 1 and 4.

Hence, she would be rounding down.

If Kerrie rounds down to the nearest whole number

11.3 feet = 11 feet

9.25 feet = 9 feet

Finding the area = 11 feet × 9 feet

= 99 square feet

Therefore, the correct statement = option a) Kerrie estimated correctly by rounding down. She has enough tile. The exact area is 104.5 square feet.

Answer:

104.05

Step-by-step explanation:

Answer:

Width is 5 cm

Step-by-step explanation:

Since we know that the width is 25 meters, and the scale we are using is 5 meters = 1 cm, we can divide 25 by 5 to find the scaled measurement.

25/5 = 5cm

I hope this helps!

-TheBusinessMan

Answer:

7x + 4

Step-by-step explanation:

You just need to read the question carefully

Answer:

$189 - $315 - $7x

Step-by-step explanation:

Given the following :

Amount in Mae's account = $189

Each month balance is below $750;

Amount charged = $7

She withdrew $315 from her account and makes no deposit or withdrawal for the next x months

Her balance :

Initial amount = $189

Withdrawal made = $315

Amount charged when balance falls below $750 = fee * number of months = 7 * x = 7x

Hence, her balance after x months will be :

$189 - $315 - $7x

The balance of Mae expressed algebraically will be 189 - 315 - 7x.

The following can be deduced from the question:

Therefore, the amount that is left in her account balance will be:

= 189 - 315 - (7 × x)

= 189 - 315 - 7x

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Answer:

y=3/5x + 1

Step-by-step explanation:

It says to translate UP 5 units, meaning the constant of -4 is the one being affected. The translation of 5 units is +5 on the graph, so -4+5=1. Everything else should be the same if i'm correct so y=3/5x + 1 is the answer

Inscribed angles are formed when two chords have 1 common endpoint. The measure of [tex]\angle ACB[/tex] and [tex]\overset{\huge\frown}{AC}[/tex]  are:

[tex]\angle ACB = 32^o[/tex]

[tex]\overset{\huge\frown}{AC} = 146^o[/tex]

Given that:

[tex]\overset{\huge\frown}{AB} = 64^o[/tex]

[tex]\angle ABC = 73^o[/tex]

See attachment

First, we calculate [tex]\angle ACB[/tex] using:

[tex]\angle ACB = \frac{1}{2} \times \overset{\huge\frown}{AB}[/tex] ----- An inscribed angle is half the arc it intercepts

So, we have:

[tex]\angle ACB = \frac{1}{2} \times 64^o[/tex]

[tex]\angle ACB = 32^o[/tex]

Using the same theorem, we calculate [tex]\overset{\huge\frown}{AC}[/tex] as follows:

[tex]\angle ABC = \frac{1}{2} \times \overset{\huge\frown}{AC}[/tex]

So, we have:

[tex]73^o = \frac{1}{2} \times \overset{\huge\frown}{AC}[/tex]

Multiply both sides by 2

[tex]2 \times 73^o = 2 \times \frac{1}{2} \times \overset{\huge\frown}{AC}[/tex]

[tex]2 \times 73^o =\overset{\huge\frown}{AC}[/tex]

[tex]146^o =\overset{\huge\frown}{AC}[/tex]

Hence:

[tex]\overset{\huge\frown}{AC} = 146^o[/tex]

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Answer:

your correct answers are 32 and 146

Step-by-step explanation:

to get 32, divide 64 by 1/2

To get 146, multiply 73 by 2

Hope I helped, got it right on test:)

Answers:

Figure a has been translated only (translated 9 units to the right)

Figure b has been reflected over the x axis

Figure c has been rotated and translated

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

Explanation:

Pick on a point like (-7,4) and note how it moves 9 units to the right to get to (2,4). All points on the upper left figure follow this same translation rule. This rules in figure a.

Figure b is a result of reflecting over the x axis. The rule used is [tex](x,y) \to (x,-y)[/tex]. The x coordinate stays the same while the y coordinate flips from positive to negative. So for example, (-7,4) flips to (-7,-4)

Figure c is a combination of rotating and translating the original figure. It looks like a 90 counterclockwise rotation has been applied followed by a translation. The actual translation and rotation rules used will depend on how you define the center of rotation.

The figure which is rotated and translated correctly about the x-axis is figure a.

The graph of a function f is that the set of ordered pairs, where\f(x)=y. within the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

We have been given four graphs of a function and first function has coordinates (-5,7) (-2,6) (-7,4) (-4,1) and that we must identify correct reflected graph.

The coordinates of a pure reflected graph are going to be (4,7) (2,4) (5,1) (7,6) which are the coordinates of figure a which is in first quadrant.

Hence the proper reflected graph of function having coordinates (-5,7) (-2,6) (-7,4) (-4,1) is that the graph of coordinates (4,7) (2,4) (5,1) (7,6).

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Answer:

a = 8/29 thus: Step 1 is wrong!

Step-by-step explanation:

Solve for a:

8 - a/2 = 3 (4 - 5 a)

Hint: | Put the fractions in 8 - a/2 over a common denominator.

Put each term in 8 - a/2 over the common denominator 2: 8 - a/2 = 16/2 - a/2:

16/2 - a/2 = 3 (4 - 5 a)

Hint: | Combine 16/2 - a/2 into a single fraction.

16/2 - a/2 = (16 - a)/2:

(16 - a)/2 = 3 (4 - 5 a)

Hint: | Make (16 - a)/2 = 3 (4 - 5 a) simpler by multiplying both sides by a constant.

Multiply both sides by 2:

(2 (16 - a))/2 = 2×3 (4 - 5 a)

Hint: | Cancel common terms in the numerator and denominator of (2 (16 - a))/2.

(2 (16 - a))/2 = 2/2×(16 - a) = 16 - a:

16 - a = 2×3 (4 - 5 a)

Hint: | Multiply 2 and 3 together.

2×3 = 6:

16 - a = 6 (4 - 5 a)

Hint: | Write the linear polynomial on the left hand side in standard form.

Expand out terms of the right hand side:

16 - a = 24 - 30 a

Hint: | Move terms with a to the left hand side.

Add 30 a to both sides:

30 a - a + 16 = (30 a - 30 a) + 24

Hint: | Look for the difference of two identical terms.

30 a - 30 a = 0:

30 a - a + 16 = 24

Hint: | Group like terms in 30 a - a + 16.

Grouping like terms, 30 a - a + 16 = (-a + 30 a) + 16:

(-a + 30 a) + 16 = 24

Hint: | Combine like terms in 30 a - a.

30 a - a = 29 a:

29 a + 16 = 24

Hint: | Isolate terms with a to the left hand side.

Subtract 16 from both sides:

29 a + (16 - 16) = 24 - 16

Hint: | Look for the difference of two identical terms.

16 - 16 = 0:

29 a = 24 - 16

Hint: | Evaluate 24 - 16.

24 - 16 = 8:

29 a = 8

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of 29 a = 8 by 29:

(29 a)/29 = 8/29

Hint: | Any nonzero number divided by itself is one.

29/29 = 1:

Answer: a = 8/29

Answer:

Coldest day on record =  -20°C

Step-by-step explanation:

Given:

Yesterday temperature = -4°C

Coldest day on record = 5 times than  yesterday

Find:

Coldest day on record

Computation:

Coldest day on record = 5 × Yesterday temperature

Coldest day on record = 5 × (-4)

Coldest day on record =  -20°C

Answer:

y = 5

Step-by-step explanation:

The answer is Adjacent angles.                            

Answer:

The answer is A: Adjacent angles.

Step-by-step explanation:

I know this cause I'm taking the test.

Step-by-step explanation:

z = 3-2a

a = 3/2 - 0.5z

...........................

Answer: I dont know which to slove for so im going to put both :)

Step-by-step explanation:

SOLVING FOR Z:

Subtract  4 a from both sides of the equation.

2 z = 6 − 4 a

Divide each term by  2

and simplify.  z = 3 − 2 a

SOLVING FOR A:

Subtract a from both sides of the equation

2z=6-4a

Divide each term by 2 then simplify

z=3-2a

Seeting up a porportion gives us,

[tex]\frac{15}{6}= \frac{x}{4}[/tex]

60=6x

10=x

HL=10

Answer:

The answer is 26.

Step-by-step explanation:

When you place the 2 next to the 8 you have to multiply it and then add the 10 to get the answer for the equation which is 26. Put it all in the calculator will be easier by putting it like this 8*2+10.

I hope this helps!

Answer:

Step-by-step explanation:

8w^2 +8w+9

8w

2

+8w+9

\color{dodgerblue}{w}=\color{dodgerblue}{2}

w=2

Given

8(\color{dodgerblue}{2})^2 +8(\color{dodgerblue}{2})+9

8(2)

2

+8(2)+9

Substitute \color{dodgerblue}{2}2 for \color{dodgerblue}{w}w

8(4) +8(\color{dodgerblue}{2})+9

8(4)+8(2)+9

Deal with exponent

32 +8(\color{dodgerblue}{2})+9

32+8(2)+9

Multiply

32 +16+9

32+16+9

Multiply

57

57

Add

Your Solution:

57

57

Answer:

Step-by-step explanation:

It shifted to the left 2 units

Answer:

Step-by-step explanation:

First, you need to get a common denominator.

You can do this by multiplying each fraction by 3 or 4.

See,

4/3 * 4/4=16/12

5/4 * 3/3=15/12

16+15=31

31/12

Answer:

2(7/12)

Step-by-step explanation:

First, try to match the denominators.

4/3+5/4

To match the denominators, multiply them with each other.If the denominator multiplys with each other, the numerator also have to multiply too.

=[tex]\frac{(4*4)}{(3*4)} +\frac{(5*3)}{(4*3)}[/tex]

= [tex]\frac{16}{12} +\frac{15}{12}[/tex]

= [tex]\frac{16+15}{12}[/tex]

= [tex]\frac{31}{12}[/tex] (If you want it as a improper fraction, you can stop here)But normally we continue till we get a mixed number if we get a improper fraction.

So 31/12 equals to 2(7/12) as a mixed number

Answer:

the answer is 59

Step-by-step explanation:

25×2=50

3×22=66

50+66=116

then you add 25 to 116=141

200-141=59

so he had left 59 dollars at the end

Answer:

£1600.

Step-by-step explanation:

The commission he earns in the week = 640 - 160 = £480.

This 480 is 30 percent or 0.30 of the value of his sales, so

the value of his sales = 480 / 0.30

= £1600.

Answer:

Step-by-step explanation:

The question is incomplete, the question does not state the claims of both Jenny and Chris.

though we can still move on to answer as the area of a triangle is expressed as

Area= half base time hight (pronounced)

and stated mathematically as

A= (1/2)b*h

the ideal of the area of a triangle is taken from the area of the rectangle divided into two from the diagonal to form two triangles

the area of a rectangle (shown in the attachment ) = b*h

now since the rectangle consists of two half triangle,

one triangle will have its area to be half the area of the rectangle

hence

area of the rectangle = (1/2)b*h

kindly find the attachment for your reference

Answer:

A

Step-by-step explanation:

Step-by-step explanation:

4x+3+8x-9+y=180

Answer:

easy

Step-by-step explanation:

1+2=92

Answer:

$112.80

Step-by-step explanation:

If he earns $0.235 per pack, and there are 480 packs, then our equation is:

0.235 x 480 = $112.80

The amount of money earned by Eddie for packing and sealing packs of 480 pens is $112.8

The method in which first we find the value of one unit and then the value of the required number of units is known as the Unitary Method.

According to the given question.

Amount of money charged by Eddie for packing and sealing a pack of pens = $0.235

Therefore,

The amount of money charged by Eddie for packing and sealing packs of 480 pens

= 480 × $0.235

= $112.8

Hence, the amount of money earned by Eddie for packing and sealing packs of 480 pens is $112.8

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