Mathematics College

## Answers

**Answer 1**

7 3/4 pounds contains 124 ounces

8 ounces = 0.5 pound

X ounces = 1 pound

X = 8 / 0.5 = 16 ounces

7 3/4 = 7.75

7.75 contains = 7.75 * 16

= 124 ounces

## Related Questions

5. What is the surface area of the figure below?

6

3

3

### Answers

Where is the figure??

The surface area of the given **figure **is 90 feet².

What is Surface Area?

The area of a three dimensional object on it's **outer surface** is called the surface area of the object.

The given figure is a **rectangular prism**.

A rectangular prism consists of 4 rectangular **lateral faces **and 2 rectangular **bases**.

Surface area of the rectangular prism is the area of each of the faces.

Combining all these area, area of a rectangular prism can be found by the **formula**,

Area = 2 (lw + wh + lh)

where l is the **length**, w is the width and h is the height.

Given, l = 3 feet, w = 3 feet and h = 6 feet

Area = 2 [ (3 × 3) + (3 × 6) + (3 × 6)]

= 2 (9 + 18 + 18)

= 90 feet²

Hence the surface area is 90 feet².

Learn more about **Surface Area** here :

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Moderne Furniture Company had sales of $2,000,000 during its first year of operation. If the sales increased by $200,000/year thereafter, find Moderne's sales in the fifth year and its total sales over the first 5 years of operation.

### Answers

2.8 million in the fifth year. 12 million total

please help me Find m

### Answers

**Answer:**

60 degrees

**Step-by-step explanation:**

any closed shape has a sum of 360 degrees, now if you subtract 150 from 360 it gives you 210 minus 90 degrees, it would equal to 120. Now 120 divided by 2 since we still need to find the other two corners we haven't found, that would equal to 60 degrees.

if the cos 30° = sqrt 3/2, then sin 60° =

a. 0

b. 1/2

c. sqrt of 3 /2

d. 1

### Answers

**Answer:**

C

**Step-by-step explanation:**

it's well known that the value of sin60 is sqrt 3/2

it's also the same as cos 30

100 points! Please help find the direction!

### Answers

The direction will be resultant

A=11iB=20i+9√3j

Now

R=√A²+B²+2ABcos60R=√(11i)²+(20i+9√3j)²+2(11i)(20+9√3j)(1/2)R=√1155.5R≈33.98°

Learn with an example

Felipe's lacrosse team will play in the Hickory Hills Tournament this weekend. They will

play 6 different teams, each with a 50% chance of winning. How likely is it that Felipe's

lacrosse team will win all 6 of their games?

Which simulation could be used to fairly represent the situation?

Flip a coin 6 times. Each time the coin lands on tails, it represents Felipe's

lacrosse team winning a game.

Create a deck of 6 cards, each labeled with a different number from 1 to 6.

Pick a card, then return it to the deck, 6 times. Each time a 6 appears, it

represents Felipe's lacrosse team winning a game.

Use a computer to randomly generate 6 numbers from 1 to 3. Each time 1 or

2 appears, it represents Felipe's lacrosse team

### Answers

**Answer:**

50% chance that they will win each game..and there's 6 games... so 3!

**Step-by-step explanation:**

A triangle has three sides 35cm 54 cm and 61 cm find its area Also find the smallest of its altitude

### Answers

**Answer:**

Area of given triangle is **9****3****9****.****1****5****c****m****²**** **and smallest altitude is **3****0****.****8****c****m**** **

Solution:

We are **given** **three sides** of a triangle, Let the sides be :

( a ) = 35 cm

( b ) = 54 cm

( c ) = 61 cm

We can find the area of the triangle with its three sides using **Heron's ****Formula **

**Heron's ****Formula**

Heron's formula was founded by **hero of** **Alexandria,** for finding the **area of triangle** in terms of the length of its sides. **Heron's formula** can be written as:

[tex] \sf{ \pmb { \longrightarrow \: \sqrt{s(s - a)(s - b)(s - c)} }}[/tex]

where ( s ) :

[tex] \sf \longrightarrow s = \dfrac{a + b + c}{2} [/tex]

Therefore, for the given triangle first we will **calculate ( s )**

[tex] \begin {aligned}\quad & \quad \longmapsto \sf s = \dfrac{a + b + c}{2} \\ & \quad \longmapsto \sf s = \dfrac{35 + 54 + 61}{2} \\ & \quad \longmapsto \sf s = \dfrac{150}{2} \\ & \quad \longmapsto \sf s = 75cm \end{aligned}[/tex]

Now, **Area ****of ****triangle**** **will be:

[tex] \begin{aligned}&:\implies \sf\quad \sf \: A = \sqrt{s(s - a)(s - b)(s - c)} \\ &:\implies \sf\quad \sf \: A = \sqrt{75(75 - 35)(75 - 54)(75 - 61)} \\&:\implies \sf\quad \sf \: A = \sqrt{75 \times 40 \times 21 \times 14} \\ &:\implies \sf\quad \sf \: A = \sqrt{5 \times 5 \times 3 \times 3 \times 2 \times 2 \times 7 \times 7 \times 2 \times 2 \times 5} \\ &:\implies \sf\quad \sf \: A =5 \times 3 \times 2 \times 7 \times 2 \sqrt{5} \\ &:\implies \sf\quad \sf \: A =420 \times 2.23 \\ &:\implies \sf\quad \sf \boxed{ \pmb{ \sf A =939.15 {cm}^{2} }} \end{aligned}[/tex]

Also, we have to find the **smallest altitude****,**** **and the **smallest altitude** will be on the **longest**** ****side.**** **So,

[tex] \begin{aligned}&:\implies \sf\quad \sf \: Area =939.15 \\ &:\implies \sf\quad \sf \: \dfrac{1}{2} \times b \times h =939.15 \\ &:\implies \sf\quad \sf \: \dfrac{1}{2} \times 61 \times h = 939.15 \\&:\implies \sf\quad \sf \: h =939.15 \times \dfrac{2}{61} \\&:\implies \sf\quad \sf \: h = \dfrac{1818.3}{61} \\ &:\implies \sf\quad \boxed{ \pmb{\sf \: h =30.79 \: (approx)}} \end{aligned}[/tex]

**Answer:**

Area = 939.15 cm² (2 d.p.)

Shortest Altitude = 30.79 cm (2 d.p.)

**Step-by-step explanation:**

**Heron's Formula** allows us to find the area of a triangle in terms its side lengths.

Heron's Formula

[tex]\sf Area = \sqrt{s(s-a)(s-b)(s-c)}[/tex]

where:

a, b and c are the side lengths of the triangles is half the perimeter

Given values:

a = 35 cmb = 54 cmc = 61 cm

Find the value of s:

[tex]\sf \implies s=\dfrac{a+b+c}{2}=\dfrac{35+54+61}{2}=75\:cm[/tex]

Substitute the values into the formula and solve for area:

[tex]\begin{aligned}\implies \sf Area & =\sf \sqrt{75(75-35)(75-54)(75-61)}\\& = \sf \sqrt{75(40)(21)(14)}\\& = \sf \sqrt{882000}\\& = \sf \sqrt{176400 \cdot 5}\\& = \sf \sqrt{176400}\sqrt{5}\\& = \sf 420\sqrt{5}\\& = \sf 939.15\:\:cm^2\:\:(2\:d.p.)\end{aligned}[/tex]

The **altitude **of a triangle is a perpendicular line segment drawn from a vertex of the triangle to the side opposite to it.

The **shortest altitude** of a triangle is drawn to the longest side.

Therefore, the shortest altitude will be the height of the triangle when the longest side is the base:

[tex]\begin{aligned}\textsf{Area of a Triangle} & = \sf \dfrac{1}{2} \times base \times height\\\implies \sf 420\sqrt{5} & = \sf \dfrac{1}{2} \times 61 \times altitude \\\implies \sf Altitude & = \sf \frac{2 \cdot 420\sqrt{5}}{61}\\& = \sf \dfrac{840\sqrt{5}}{61}\\ & = \sf 30.79\:\:cm\:\:(2\:d.p.)\end{aligned}[/tex]

Find the surface area of a square pyramid with side length 2 km and slant height 2 km

### Answers

*given**:*

*side length 2 km and slant height 2 km**.*

*to** **find**:*

*the** **surface** **area** **of** **the** **pyramid**.*

*solution**:*

*area** **of** **4** **triangle**=** **1**/**2** **×** **2** **×** **2** **×** **4*

*=** **8km*

*area** **of** **rectangle**=** **2**×**2*

*=** **4km*

*area**=** **4**+**8*

*=** **12km*

*so**,** **the** **surface** **area** **of** **the** **pyramid** **is** **12km**.*

IM CONFUSED CAN SOMEBODY HELP ME SOLVE THE EQUATION

### Answers

**Answer:**

y = - ½(x - 2)² + 3

**Step-by-step explanation:**

Which inequality is correct?

0.22<0.18

0.22>0.22

0.41<0.08

0.41>0.02

### Answers

**Answer:**

Correct answer is the first one I think. hope this helps

I. Elena wants to estimate what proportion of computers produced at a factory have a certain defect. A random sample of 200 computers shows that 12 computers have the defect. She is willing to assume independence between computers in the sample. Based on this sample, construct a 95% confidence interval for the proportion of computers that have the defect.

a

(0.4529, 0.5871)

b

(0.02709, 0.09291)

c

(0.02131, 0.09869)

d

(0.0309, 0.0691)

### Answers

The answer is (A) 0.4529, 0.5871

Slope Equations

What is the equation of the line that passes through the point (0,-4) and has a slope of 5?

y = 5x – 4

y= - 4x – 5

y= -5x +4

y=2x - 4

### Answers

**Linear Equations**

**Linear equations** are typically organized in slope-intercept form:

[tex]y=mx+b[/tex]

*m* = slope*b *= y-intercept (the value of y when x=0)

Solving the Question

We're given:

*m* = 5The line passes through the point (0,-4)

Because the slope of the line is 5, we know that the *m* value in y=mx+b has to be 5. This rules out all the options except for the first, which is the only equation in which the *m* vaue is 5.

On top of that, we know that the y-intercept occurs when x=0. Given that the line passes through the point (0,-4), we know that the y-intercept is -4.

The equation in the first option tells us this as well, as it has -4 as the *b* value in y=mx+b.

Answer

y = 5x - 4

When a certain number is divided by 20, the result is same when number is decreased by 361. What is the number?

### Answers

**Answer:**

The number is 380

**Step-by-step explanation:**

Let the number be 'x'

[tex]\sf \dfrac{x}{20}=x-361\\\\\text{multiply the entire equation by 20}\\\\20*\dfrac{x}{20}=20*(x-361)[/tex]

x = 20x - 20*361

x = 20x - 7220

**Now subtract '02x' from both sides**

x - 20x = -7220

-19x =-7220

**Divide both sides by (-19)**

x = (-7220) ÷ (-19)

** x = 380**

30x³ + 10x²

Help me please

### Answers

Question: Factorise the function ⇒ [tex]30x^3+10x^2[/tex]

*Definition of Factorize**: it is an algebraic expression that means writing the given expression as a product of its factor*

* *basically you write the function in its simplest term where you cannot *

* simplify it further*

* *So:

[tex]30x^3+10x^2 = 10(3x^3+x^2) = 10x^2(3x+1)[/tex]

**Answer:** [tex]30x^3+10x^2[/tex] when factorized ⇒ [tex]10x^2(3x+1)[/tex]

Hope that helps!

2 books are removed at random from a set of 2 mysteries, 1 biography, and 1 romance. What is the probability that the 2 books consist of 1 mystery and 1 biography? Draw a tree diagram to help you find the answer.

1/3

1/6

1/4

5/12

I did the problem and I know that 1/4 and 5/12 are wrong

### Answers

**Answer:**

1/6

**Step-by-step explanation:**

Check the attachment.

How many TRIANGLES can be constructed with sides measuring 8 cm, 9 cm, and 11

cm ?

### Answers

**Answer:**

1 -- Triangle

**Step-by-step explanation:**

*Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Also remember to rate answers to help other students, While leaving thanks to answers that help you. Have a great day!*

solve the right triangle (all sides and angles) please help!!!

### Answers

LUFFY to the right and LUFFY to the left

John's water bill this month was $19.67 . Looking at the water bill, it says he used exactly 10,000 gallons of water. How much does he pay per gallon of water used?

### Answers

**Answer:**

0.001967 per gallon

**Step-by-step explanation:**

19.67/10000 = 0.001967

How are the roots of a quadratic equation and the zeroes of a quadratic relation related?

### Answers

The **roots** of a *quadratic* **equation** and the **zeroes** of a *quadratic* **equation** are related in the following form: [tex]\sum\limits_{i= 0}^{2} c_{i}\cdot x^{i} = \prod \limits_{j= 1}^{2} (x-r_{j}) = 0[/tex].

What do represent the roots of a quadratic equation?

**Polynomials** are *algebraic* **entities** that satisfy the following condition:

[tex]p(x) = \sum\limits_{i= 0}^{n} c_{i}\cdot x^{i} = \prod \limits_{j= 1}^{n} (x-r_{j})[/tex] **(1)**

Where:

*x* - Independent variable*n* - Grade[tex]c_{i}[/tex] - i-th Coefficient[tex]r_{j}[/tex] - j-th Root

If we have that [tex]p(x) = 0[/tex], then there are *n* values of *x* such that the equation is satisfied and those values are called **zeroes**. For the case of a *quadratic* **equation**, there are two **zeroes**.

[tex]\sum\limits_{i= 0}^{2} c_{i}\cdot x^{i} = \prod \limits_{j= 1}^{2} (x-r_{j}) = 0[/tex] **(2)**

Please note that the right part of **(2)** contains the **roots** of the **polynomial** and (2) represents a relationship based on the **closure** **properties** for *algebraic* **fields**.

Therefore, the **roots** of a *quadratic* **equation** and the **zeroes** of a *quadratic* **equation** are related in the following form: [tex]\sum\limits_{i= 0}^{2} c_{i}\cdot x^{i} = \prod \limits_{j= 1}^{2} (x-r_{j}) = 0[/tex].

To learn more on **quadratic equations**, we kindly invite to check this **verified question**: https://brainly.com/question/5975436

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sestion 1

In one week, Neha spends hours cooking and y hours cleaning.

The time she spends cleaning is at least equal to the time she spends cooking.

This can be written as y > r.

She spends no more than 16 hours in total cooking and cleaning.

What are the two inequalities in x and /or y to show this information

### Answers

**Answer:**

Y ≥(greater than or equal to) R or Y ≤(less than or equal to) R

The phrase at least means about equal to, represented by that sign. In this case, equal to, because x + y = 16 total since she spent 16 hours cooking and cleaning. That would mean they both have to equal 8 to get 16. You can also do 10 + 6 to get 16. There are a few more solutions after this you can try, which I will not list at the moment.

__________________________________________________________

Questions?

Ask in the comments box.

From a club of 20 people, in how many ways can a group of three members be selected to attend a conference?

### Answers

**Answer: 1140**

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

Reason:

There are 20 ways to pick the first person, 19 for the next, and 18 for the last. We count down by one each time we fill up a slot since we cannot reselect any person more than once.

If order mattered, then we'd have 20*19*18 = 6840 permutations.

However, order does not matter because no member has a special seat or role. The individual members don't matter and instead it's all about the group.

Notice that for any group of 3 people, there are 3*2*1 = 6 ways to arrange such individuals. We have to divide by 6 to go from 6840 permutations to 6840/6 = **1140 combinations.**

-------------------------

Here's a more formulaic approach using the nCr combination formula.

Plug in n = 20 and r = 3

[tex]n C r = \frac{n!}{r!(n-r)!}\\\\20 C 3 = \frac{20!}{3!*(20-3)!}\\\\20 C 3 = \frac{20!}{3!*17!}\\\\20 C 3 = \frac{20*19*18*17!}{3!*17!}\\\\ 20 C 3 = \frac{20*19*18}{3!}\\\\ 20 C 3 = \frac{20*19*18}{3*2*1}\\\\ 20 C 3 = \frac{6840}{6}\\\\ 20 C 3 = 1140\\\\[/tex]

Simplify.

Rewrite the expression in the form a”.

(a”)? = 1

Please needhelp urgently

### Answers

**Answer:**

just randomly write a¹⁰

the ratio of the sides of a certain triangle is 2:7:8 if the longest side of the triangle is 40cm how long are the other two sides

### Answers

The **length **of the other **two sides** is** 10** and **35 **respectively.

What is a ratio?

A **ratio **is a quantitative relation showing the comparison between two or more numbers. It can also be written in the **fractional form **where the first part is the **numerator **and the second part is called the **denominator**.

From the given information:

The sides of the triangle = 2:7:8The total sides of the triangle = 2+7+8 = 17

We are being told that the **longest side** is the triangle is equal to **40**.

i.e.

[tex]\mathbf{\to\dfrac{8}{17}\times x = 40}[/tex]

[tex]\mathbf{x = 40 \div \dfrac{8}{17}}[/tex]

[tex]\mathbf{x = 40 \times \dfrac{17}{8}}[/tex]

x = 85

Now for the **other two sides 2 **and **7**, their length is as follows.

[tex]\mathbf{\dfrac{2}{17}\times 85 = 10}[/tex]

[tex]\mathbf{\dfrac{7}{17}\times 85 = 35}[/tex]

Therefore, we can conclude that the length of the other two sides is **10** and** 35** respectively.

Learn more about **ratios **here:

https://brainly.com/question/2328454

(-24uy^2+19u^3y^5)/(-3u^3y^5)

Simplify

### Answers

**Answer:**

8/(u^2y^3) -19/3

**Step-by-step explanation:**

The relevant **rules of exponents** are ...

(a^b)/(a^c) = 1/a^(c-b)

a^0 = 1

__

Your **expression can be simplified** like this:

[tex]\dfrac{-24uy^2+19u^3y^5}{-3u^3y^5}=\dfrac{24uy^2}{3u^3y^5}-\dfrac{19u^3y^5}{3u^3y^5}=\boxed{\dfrac{8}{u^2y^3}-\dfrac{19}{3}}[/tex]

What is 594 minus 236?

### Answers

**Answer:**

358

**Step-by-step explanation:**

the answer is 358 because

Write the equation of the line that is parallel to the line y=3x+7 and passes through the

point (-4,-14).

### Answers

**Answer:**

**Step-by-step explanation:**

hello :

note :

Use the point-slope formula.

y - y_1 = m(x - x_1) when : x_1= -4 y_1= -14

m= 3 (parallel means same slope)

an equation in the point-slope form is : y +14 =3(x+4)

Find the axis of symmetry and the vertex of the graph of y=3x^2+2x

### Answers

**Answer:**

Vertex is (-1/3, -1/3) and the axis of symmetry is x = -1/3

Hope this helps :)

HELP PLEASE!!

Discuss the steps that you used

to create your tangent line.

What was the most important

step?

Give an example of tangents in

the real world that have not

been presented in this lesson.

Explain how you know the

tangent and the radius are

perpendicular.

### Answers

Answer:

You need to have both the opposite and adjacent side of the right angled triangle. Tan = Opp/Adj

Step-by-step explanation:

Tangents are pretty much everywhere. A good example is maybe a slide at the playground. You’d need the tangent to figure out the angle of the slide and how it is.

The radius from the center of a circle to the point of tangency point shows that it would be perpendicular to the tangent line considering that anything with a radius is circular and the tangent line is… a line, making it impossible to be parallel.

PLEASE HELP!! TRYING TO PREPARE FOR A TEST!! TOTAL 50 POINTS WHEN GIVEN BRAINLIEST ANSWER!!

Change the Cartesian integral to an equivalent polar integral, and then evaluate.

∫₋₁₁¹¹ ∫₀√⁽¹²¹⁻ˣ²⁾ dy dx

\int\limits^{11}_{-11} \int\limits^{\sqrt{121-x^{2}} } _{0} dy dx

### Answers

It looks like the starting integral is

[tex]\displaystyle \int_{-11}^{11} \int_0^{\sqrt{121-x^2}} dy\,dx[/tex]

The key is recognizing the domain of integration as the semicircle centered at the origin with radius 11. In polar coordinates, this integral transforms to

[tex]\displaystyle \boxed{\int_0^\pi \int_0^{11} r \, dr \, d\theta}[/tex]

Help again please 33 points

### Answers

The answer is 56.

Firstly you have to multiply the 2 numbers together, which would be the places of b and h. This would give you 112.

Then, divide 112 by 2 to give you a final answer of 56.

**Answer:**

the answer is 56in2

**Step-by-step explanation:**

[tex]b = 14in \\ h = 8in \\ area \: of \: triangle = \frac{1}{2} b \times h \\ = \frac{1}{2} \times 14 \times 8 \\ = 56inches[/tex]