Mathematics College

Simplify this expression.
(2 - 5/6) 3/2
O 6V2 - 1576
62 - 15/12
O 672-876
O 672-30/3

Answers

Answer 1

Answer:

The second one is correct

Answer 2

Answer:

Step-by-step explanation:

Related Questions

I'm have some issues with the problem shown in the screenshot and would love some help.

Answers

The dimensions and volume of the largest box formed by the 18 in. by 35 in. cardboard are;

Width ≈ 8.89 in., length ≈ 24.89 in., height ≈ 4.55 in.

Maximum volume of the box is approximately 1048.6 in.³

How can the dimensions and volume of the box be calculated?

The given dimensions of the cardboard are;

Width = 18 inches

Length = 35 inches

Let x represent the side lengths of the cut squares, we have;

Width of the box formed = 18 - 2•x

Length of the box = 35 - 2•x

Height of the box = x

Volume, V, of the box is therefore;

V = (18 - 2•x) × (35 - 2•x) × x = 4•x³ - 106•x² + 630•x

By differentiation, at the extreme locations, we have;

[tex] \frac{d V }{dx} = \frac{d( 4 \cdot \: {x}^{3} - 106 \cdot \: {x}^{2} + 630\cdot \: {x} ) }{dx} = 0[/tex]

Which gives;

[tex] \frac{d V }{dx} =12\cdot \: {x}^{2} - 212\cdot \: {x} + 630 = 0[/tex]

6•x² - 106•x + 315 = 0

[tex]x = \frac{ - 6 \pm \sqrt{106 ^2 - 4 \times 6 \times 315} }{2 \times 6} [/tex]

Therefore;

x ≈ 4.55, or x ≈ -5.55

When x ≈ 4.55, we have;

V = 4•x³ - 106•x² + 630•x

Which gives;

V ≈ 1048.6

When x ≈ -5.55, we have;

V ≈ -7450.8

The dimensions of the box that gives the maximum volume are therefore;

Width ≈ 18 - 2×4.55 in. = 8.89 in.

Length of the box ≈ 35 - 2×4.55 in. = 24.89 in.

Height = x ≈ 4.55 in.

The maximum volume of the box, V ≈ 1048.6 in.³

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Complete the frequency table:

Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 18 165
Age 15 and above 65 195
Column totals 152 110 98 360

What percentage of students age 15 and above travel to school by bus? Round to the nearest whole percent.

Answers

The percentage of students age 15 and above travel to school by bus is 47%

How to complete the table?

The table of values is given as:

Method of Travel to School

Walk/Bike Bus Car Row totals

Under age 15 18 165

Age 15 and above 65 195

Column totals 152 110 98 360

Using the column total of column 1, we have:

Under age 15 + 65 = 152

This gives

Under age 15 = 87

Using the column total of column 2, we have:

Age 15 and above + 18 = 110

This gives

Age 15 and above = 92

Using the row total of row 1, we have:

Car + 87 + 18 = 165

This gives

Car = 60

Using the row total of row 2, we have:

Car + 65 + 92 = 195

This gives

Car = 38

So, the complete frequency table is

Method of Travel to School

Walk/Bike Bus Car Row totals

Under age 15 87 18 60 165

Age 15 and above 65 92 38 195

Column totals 152 110 98 360

The percentage of students age 15 and above travel to school by bus is:

Percentage = 92/195 * 100%

This gives

Percentage = 47%

Answers

The price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit is 62.13

Quadratic equation

y = -14x² + 1035x - 10266

solve the quadratic equation

-14x² + 1035x - 10266 = 0

x = -b ± √b² - 4ac / 2a

= -1035 ± √1035² -4(-14)(-10266) / 2(-14)

= -1035 ± √1071225 - 574896 / -28

= -1035 ± √496329 / -28

x = 1035 / 28 ± √496329 / 28

x = 11.80 or 62.13

The maximum value of x is 62.13

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The Royal Fruit Company produces two types of fruit drinks. The first type is 55% pure fruit juice, and the second type is 80% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 140 pints of a mixture that is 70% pure fruit juice?

Answers

We need 56 pints of the 55 % pure fruit juice and 84 pints of the 80 % pure fruit juice to prepare 140 pints of 70 % pure fruit juice.

How to use weighted averages to find the correct juice concentration

In this problem we have to use two kinds of juice with different concentrations. To get a certain concentration, we must adjust quantities of each kind and weighted averages offers a method that is easy to apply:

70 · 140 = 55 · x + 80 · (140 - x)

70 · 140 = 80 · 140 - 25 · x

25 · x = 10 · 140

x = 56

We need 56 pints of the 55 % pure fruit juice and 84 pints of the 80 % pure fruit juice to prepare 140 pints of 70 % pure fruit juice.

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The profit function for a certain commodity is given by () = 110 − 2 − 1000. Find the level of production that yields maximum profit and hence find the maximum profit.

Answers

Based on the profit function given, the level of production that yields the maximum profit is 55 units. The maximum profit is $2,025.

What is the maximum profits unit?

With a profit function:

=-x² + 110x - 1,000

Using a parabola function, we know:

= -b / 2a

The maximum units is:

= -110 / (-2 x 1)

= 55 units

The maximum profit is:

= -(55)² + (110 x 55) - 1,000

= $2,025

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Question 1 (3 points)
Solve the following linear system:
y = -2x - 5
y = 2/3x + 3
as an ordered pair (x,y)

Answers

Answer:

Step-by-step explanation:

hello : y = -2x - 5

y = 2/3x + 3

means : -2x-5 = 2/3 x+3

-6x-15 = 2x +9

-8x=24 so : x = -3

put the value for : x in the first equation :y = -2(-3)-5 =1

the ordered pair (-3;1) is solution

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used
Match each statement with its contrapositive.

Answers

Option 4,option 6, and option 2 is the respective contrapositive to the statements given. This can be obtained by understanding what contrapositive is and converting the statements.

What is contrapositive? Contrapositive: A statement which is obtained by interchanging both the hypothesis and conclusion of a given statement after contradicting them. For "if p then q" the contrapositive is "if not-q,then not-p "For example,

Statement = If a figure is a square, then it is a quadrilateral.

Contrapositive = If a figure is not a quadrilateral, then it is not a square.

Here,

Statement 1: If two figures are congruent, then their corresponding sides are equal.

Contrapositive: If the corresponding sides of two figures aren't equal, then the two figures aren't congruent. (Option 4)

Statement 2: If two numbers are even, then their product is even.

Contrapositive: If the product of two numbers isn't even, then the two numbers aren't even. (Option 6)

Statement 3: If a figure is a pentagon, then the sum of its interior angles is 540°.

Contrapositive: If the sum of the interior angles of a figure isn't 540°, then the figure isn't a pentagon. (Option 2)

Hence Option 4,option 6, and option 2 is the respective contrapositive to the statements given.

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find x and y pls help

Answers

30 + 110 + 30 + 110 = 280

360-280 = 80

2y = 80

y = 40 degrees

If y is 40. Then the angle next to 30 is also y due to vertically opposite angles.

30 + 40 = 70

The line with 2 arrows is parallel to the line with x degrees. So, I use co-interior angles adds to 180.

In that c shaped, we got the bottom angle to be 70 & the top to be 110 because co-interior angles =180

Forget the c shape exists, and move onto the triangle that's visible. The top angle is 110 as found.

Angles in triangle add to 180.

180 - 110 - 30 = 40.

Thus, x = 40 degrees

There's a short cut I realise now because we can have alternate angles are equal; creating a z shape to find what x is equal to & that turns out to be the same value as y. ( due to vertically opposite angles)

Hope this helps!

The following are the ages (years) of 5 people in a room:

14
,

16
,

16
,

13
,

A person enters the room.
The mean age of the 6 people is now 21.
What is the age of the person who entered the room?

Answers

Answer:

67 years old. (you only gave 4 people and missed out one person)

Step-by-step explanation:

take all the ages first and put the unknown (age of the person who entered the room) as x.

14, 16, 16, 13, x

all of these numbers added to together would be:

59 + x

Because the question is talking about the mean age, to find mean:

add all the values in the data (ages) and divide by the total number of values on the list. (in your case would be 6 people (following your question) but you gave only 5 people including the x).

then (59 + x) / 6 = 21

21 x 6 = 126

126 = 59 + x

x = 67

Sets A,B , and C are subsets of the universal set U.

These sets are defined as follows.

U= {f,g,h,p.q.r.x.y.z}

A={f,h,p.q.r}

B={q,r,y,z}

C={g,h,p,q,y}

Find (B' U A) ∩ C.

Write your answer in roster form or as Ø.

Answers

[tex]B'=\{f,g,h,p,x\}\\B'\cup A=\{f,g,h,p,q,r,x\}\\(B'\cup A)\cap C=\{g,h,p,q\}[/tex]

Calculate the geometric center of the grapg under the function

Answers

The geometric center of the graph under the function is 5/3

How to determine the geometric center of the graph under the function?

The equation of the function is given as:

f(x) = 3 - |x - 2|

The interval is given as:

x ∈ [0, 3]

The geometric center (gc) of the graph under the function is calculated using

gc = ∫x f(x) dx/∫f(x) dx

Substitute the known values in the above equation

gc = ∫x * (3 - |x - 2|) dx/∫3 - |x - 2| dx

Integrate the numerator and the denominator of the above equation

gc = [-1/6(x - 2)((2|x -2| - 9)x + 2|x - 2| - 18)]/[3x - 1/2[|x - 2|(x - 2)]]

Recall that the interval is given as x ∈ [0, 3]

Substitute the interval values in the above equation.

The equation is then simplified using a graphing calculator.

So, we have

gc = (65/6)/(13/2)

Express the quotient expression as a product

gc = (65/6) * (2/13)

Divide 65 by 13

gc = 5/6 * 2

Divide 2 by 6

gc = 5/3

Hence, the geometric center of the graph under the function is 5/3

Answers

We can simplify the inequality to:

y > (-1/5)*x - 2

From that, we conclude that the correct option is the last one.

Which is the graph of the given inequality?

Here we have the inequality:

5y + x > -10

If we isolate y, we get:

y > (-10 - x)/5

y > (-1/5)*x - 2

Then the inequality will be a dashed/dotted line with a negative slope, that passes through the point (0, -2), such that the region above and to the right of the line is shaded.

From that we conclude that the correct option is the last one:

"Number graph ranging from negative ten to ten on the x and y axes. A dotted line passes through (zero, negative two) and (five, negative three). The area above the line is shaded gray."

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Answers

The percentage of students age 15 and above travel to school by bus is 47%

How to complete the table?

The table of values is given as:

Method of Travel to School

Walk/Bike Bus Car Row totals

Under age 15 18 165

Age 15 and above 65 195

Column totals 152 110 98 360

Using the column total of column 1, we have:

Under age 15 + 65 = 152

This gives

Under age 15 = 87

Using the column total of column 2, we have:

Age 15 and above + 18 = 110

This gives

Age 15 and above = 92

Using the row total of row 1, we have:

Car + 87 + 18 = 165

This gives

Car = 60

Using the row total of row 2, we have:

Car + 65 + 92 = 195

This gives

Car = 38

So, the complete frequency table is

Method of Travel to School

Walk/Bike Bus Car Row totals

Under age 15 87 18 60 165

Age 15 and above 65 92 38 195

Column totals 152 110 98 360

The percentage of students age 15 and above travel to school by bus is:

Percentage = 92/195 * 100%

This gives

Percentage = 47%

Answers

Answer:

Step-by-step explanation:

$30.00 ÷ 5 = $6.00

$6.00 × 3 = $18.00

Answer 18 (a)
First we need to find out the cost of one CD
We can do that by 30/5 =6
One CD cost 6 $
But the questions ask the cost of 3 CD
So the price for 3 CD is 18

solve for x by completing the square: x2 − 8x + 13 = 0. show all work

Answers

There are two real roots for the quadratic equation x² - 8 · x + 13 = 0, contained in the number x = 4 ± √2.

How to find the roots of a polynomial by completing the square

In this question we must apply algebraic handling to simplify a quadratic equation and find the roots that satisfy the expression. Completing the square consists in transforming part of the equation into a perfect square trinomial, and then we clear for x:

x² - 8 · x + 13 = 0

x² - 8 · x + 16 = 3

(x - 4)² = 3

x - 4 = ± √2

x = 4 ± √2

There are two real roots for the quadratic equation x² - 8 · x + 13 = 0, contained in the number x = 4 ± √2.

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The plot below shows the volume of paint left in 444 cans.
All measurements are rounded to the nearest \dfrac12
2
1

start fraction, 1, divided by, 2, end fraction pint.
A line plot labeled Volume in pints shows, moving left to right, labeled tick marks at two, two and one-half, three, three and one-half, four, four and one-half, five, five and one half, and six. Dots are plotted as follows: 1 dot above two and one-half; 2 dots above four; and 1 dot above five and one-half.

A line plot labeled Volume in pints shows, moving left to right, labeled tick marks at two, two and one-half, three, three and one-half, four, four and one-half, five, five and one half, and six. Dots are plotted as follows: 1 dot above two and one-half; 2 dots above four; and 1 dot above five and one-half.
If we split the total amount of paint so that each can had the same amount, how much paint would be in each can?

Answers

The amount of paint that would be contained in each of the can would be 8.

How to solve for the amount of paint.

Using the information in the question we have the following

We have to solve the equation as

(2 1/2) + 2(4) + 1(5 1/2) =

2.5 + 8 + 5.5

= 16

Each of these would have to hold 16/2 = 8 pints.

Answers

Hello there, I am unable to use the “less than” symbol. Sorry :( .

1/5x "less than" 8
x “Less than” 40

Prime number is 37,41.
Therefore x is 37.

Question 2: Xiulin and Meifang had an equal number of postcards. Meifang gave some of her postcards to Xiulin. After that, Meifang had 76 fewer postcards than Xiulin. Given that Meifang had 72 postcards left, find the number of postcards Xiulin had at first.

Answers

110 postcards Xiulin had at first.

What is algebric equation?

Algebric equation is a mathematical statement in which two equation set equal to each other.

Let the number of postcards belonging to Xiulin and Meifang be x.

Let the number of postcard Meifang gave to Xuilin be 'a'

Number of postcard left with meifang

=> x-a = 72

=> x = 72+a

Meifang had 76 fewer postcards than Xiulin.

so, (x+a)-72=76

72+a+a-72=76

2a = 76

a = 38

meifang give 38 cards to xuilin

x = 72+38

= 110

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Theodore invests $20,000 at 6% simple interest for 1 year. How much is in the account at the end of the 1
year period?
Answer:

Answers

Answer:

$21200

Step-by-step explanation:

6% × 20000 = 1200.

20000 + 1200 = 21200

basically yout find 6% of 20000 then add it the original 20000

solve the following portion for x/11=8/3. round to nearest tenth

Answers

Answer is 29.3
Step by step
X/11 = 8/3
Cross multiply
3x = 88
Solve for x, divide both sides by 3
X = 29.333
Round to nearest tenth
X = 29.3

Please Help! Brainliest Avaliable! Literally Multiple Choice!

Answers

It's very simple. Subract 554.26 from 866.32

then, we got the difference is

312.06

thank you

Brainlist please.

Complete the table. Each column should contain equivalent values. One column has been completed for you. Make sure the fractions are stated in simplest form.
Fraction Decimal Percent
0.39 39%
0.82
22%
0.8

Answers

The complete table will be:

Fraction Decimal Percent

39/100 0.39 39%

82/100 0.82 82%

22/100 0.22 22%

3/4 0.75 75%

80/100 0.8 80%

Percentage

The percentage is the given definition for a fraction whose denominator is equal to 100. It is represented by %. See the following example:

[tex]\frac{25}{100} =0.25*100=25%[/tex]

The percentage is considered a math tool with several applications and areas, for example: medicine, engineering, investments, supermarkets, drugstores,banks etc.

Line 1

Fraction Decimal Percent

39/100 0.39 0.39*100=39%

Line 2

Fraction Decimal Percent

82/100 0.82 0.82*100=82%

Line 3

Fraction Decimal Percent

22/100 0.22 22%

Line 4

Fraction Decimal Percent

3/4 0.75 0.75*100=75%

Line 5

Fraction Decimal Percent

80/100 0.8 0.80*100=80%

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for this graph, mark the statements that are true.

Answers

Answer:

C,D

Step-by-step explanation:

C: Range refers to the y axis and all values shown on this graph (and even beyond the graph) are greater than 0

D: The domain refers to the x-axis. The line goes on forever both to the right and the left therefore meaning all x values are used.

I NEED ANSWER ASAP please and thank you

Answers

Answer:

hexagon and pentagon structure. also known as a truncated icosahedron

Step-by-step explanation:

hope that gives you a good enough description.

Please help me put them in correct place

Answers

The inequalities that match the given expressions are

x ≤ 95

x > 100

5x ≤ 100

20 ≤ x ≤100

respectively

Writing linear inequalities

From the question, we are to match the statements with the corresponding inequalities

Nora's height(x) is at least 5 cm less than Stacy who is 100 cm tall

x ≤ 100 -5

x ≤ 95

Temperature(x) is greater than the boiling point of water (100 °C)

x > 100

John buys x chocolates worth $5 each but he has only $100 in his pocket

5x ≤ 100

Ronny decided not to exceed 100L of water usage and ends up using at least 1/5th of this limit every day

x ≤ 100

and

x ≥ 1/5 × 100

x ≥ 20 ≡ 20 ≤ x

∴ 20 ≤ x ≤100

Hence, the inequalities that match the given expressions are

x ≤ 95

x > 100

5x ≤ 100

20 ≤ x ≤100

respectively

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answer this please only the ones that are blank

Answers

Answer:

#3 5(2a+4)

#4 5(a+2+4)

#5 5a+5(2+4)

Step-by-step explanation:

I think so, I am probably wrong

help me pls: what is
four and two eighths minus two and five eighths equals

Answers

Answer:

13/8

Step-by-step explanation:

4 2/8 - 2 5/8

34/8 - 21/8 = 13/8

1 5/8 as a mixed fraction

Officially, variable names in Python can be any length and can consist of uppercase and lowercase letters ( A-Z, a-z ), digits ( 0-9 ), and the underscore character ( _ ). An additional restriction is that, although a variable name can contain digits, the first character of a variable name cannot be a digit. Python’s most-followed style guide, PEP8 also suggests we limit each line to 79 characters, so, to be extra careful, we will assume variables can be of at most 7 characters in length.How many variable names can there be in Python if we abide by these two rules?

Answers

Abiding by the two rules, the number of variable names we can have in Python are; 63

How to name variables in Python Programming?

The rules for python are given as;

1) Variable names in Python can be any length and can consist of uppercase and lowercase letters ( A-Z, a-z ), digits ( 0-9 ), and the underscore character ( _ ).

1b) An additional restriction is that, although a variable name can contain digits, the first character of a variable name cannot be a digit.

2) We limit each line to 79 characters, so, to be extra careful, we will assume variables can be of at most 7 characters in length.

Now, abiding by the two rules above, the number of variable names we can have in Python are;

26( A-Z) + 26(a-z) + 10(0-9) + 1 ( _ ) = 63 variable names

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– 42 – 54 + 96 =

what is the answer

Answers

Answer:

Answer:the answer is zero

Answer:the answer is zero Step-by-step explanation:

Answer:the answer is zero Step-by-step explanation:when we add -42 and -54 the answer we get is -96. -96and +96 cut each other and then the answer is zero

[tex] - 42 - 54 + 96 = 0[/tex]

How many full cases and additional items are needed to fulfill the order? 50 8

Answers

The computation illustrate that there'll be 13 cases and 2 additional units.

How to illustrate the information?

From the information given, it was stated that 80 units are needed, 6. units per case.

Therefore, the number of cases will be:

= 80/6

= 13 remainder 2.

Therefore, there'll be 13 cases and 2 additional units

Complete information

80 units are needed, 6. units per case. What is the number of cases and the number of additional units?

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Simplify this expression. (2 - 5/6) 3/2 O 6V2 - 1576 62 - 15/12 O 672-876 O 672-30/3

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Simplify this expression.
(2 - 5/6) 3/2
O 6V2 - 1576
62 - 15/12
O 672-876
O 672-30/3