Mathematics College

## Answers

**Answer 1**

The simplest **fraction** form of the given expression 4/5^3 is** 4/125.**

What is a fraction?

A** fraction** is part of a whole. In arithmetic, numbers are represented as the quotient of the numerator divided by the denominator. In simple fractions, both are integers. A complex fraction has a fraction in the numerator or denominator. A true fraction has the numerator less than the denominator

What is a fraction's simplest form?

Simplifying a fraction means finding the equivalent **fraction**, truncated as much as possible.

According to the information from the question given:

Simplified form of fraction= 4/5^3

=4/(5x5x5)

=**4/125**

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## Related Questions

What is the remainder when 287 is divided by 5?

### Answers

**Answer:**

2

**Step-by-step explanation:**

Any multiple of 5 ends in 0 or 5.

To find the remainder when a number is divided by 5, we can find the highest number **less than or equal to** the given number that ends in 0 or 5, then subtract that number from the given number.

In this case, the highest number that ends in a 0 or 5 that is less than or equal to the given number is 285.

When we subtract that from the given number, 287, we get:

287 - 285 = **2**

Find the distance d. Round your answer to the nearest tenth

A. 5.4

B. 29

C. 4.6

D. 6

### Answers

I believe c is the right answer

Without graphing determine whether the function represents exponential growth or exponential decay. Y=4(5/6)^xY=12(17/10)^xY=129(1.63)^x

### Answers

The function y = 4(5/6)^x is exponential **decay**. The function y = 12(17/10)^x is exponential **growth**. The function y = 129(1.63)^x is exponential **growth**.

To determine if a function represents exponential growth or exponential decay, we need to look at the base of the **exponential function**.

For the function y = 4(5/6)^x, the base (5/6) is between 0 and 1. Therefore, this function represents exponential **decay**.

For the function y = 12(17/10)^x, the base (17/10) is greater than 1. Therefore, this function represents exponential **growth.**

For the function y = 129(1.63)^x, the base (1.63) is also greater than 1. Therefore, this function also represents exponential **growth.**

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Nancy earns a gross weekly salary of $564.20. What is her weekly net pay if she pays $69.73 in federal income tax, $34.98 in Social Security tax, $8.18 in Medicare tax, and $8.47 in state tax?

### Answers

Nancy's weekly **net pay** is $442.84.

What is Equation?

Two or more expressions with an **Equal sign **is called as Equation.

Given that Nancy **earns** a gross weekly salary of $564.20

We need to find the net pay if she pays $69.73 in federal income tax, $34.98 in** Social Security tax**, $8.18 in Medicare tax, and $8.47 in state tax

**Net pay** = Gross salary - (Federal tax + Social Security tax + Medicare tax + State tax)

Net pay = $564.20 - ($69.73 + $34.98 + $8.18 + $8.47)

= $564.20 - $121.36

= $442.84

Hence, Nancy's weekly **net pay **is $442.84.

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Triangle abc was dilated using the rule. If ca = 8, what is c'a'? 10 units 12 units 16 units 20 units.

### Answers

**Triangle** ABC was dilated using the rule Dy 5/4. If ca = 8, the c'a' is 10 units.Here the concept is the** scale factor**.

Scale factor which is a number used to compare two different measurements of the same thing. It is used to describe how much larger or smaller one measurement is than the other.

We are given that the triangle ABC was dilated using the dy ,5/4, if CA is 8 units so, the** length **for c'a' can be calculated as:

scale factor = **dimension **for triangle/ dimension for the original triangle

=> c'a' / ca

=> ( 5 / 4 ) x ca = c'a'

=> c'a'= ( 5 / 4 ) x 8 = 10 units.

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Triangle ABC was dilated using the rule Dy, 5/4If CA = 8, what is C'A'?

10 units

12 units

16 units

20 units

89. Set A has 3 elements & set B has 4 elements. The number of injections that can be defined from A into B is

### Answers

The number of **injections** that can be defined from **set** A into B is 24.

What is permutation?

An arrangement of items in a specific order is referred to as a **permutation**. Here, the components of sets are arranged in a linear or sequential order. For instance, the set A=1,6 has a permutation of 2, which is 1,6,1. There is no other way to organize the components of set A, as you can see.

While the order of the items doesn't important in **combination**, it should be followed while performing permutations.

Given that,

Set A = 3 elements

Set B = 4 elements

The total number of injective functions from Set A and Set B is given as:

4P3 = 4! / (4 - 3)! = (4)(3)(2)(1) = 24

Hence, the number of injections that can be defined from A into B is 24.

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the transverse tire company produces all types of tires at its factory due to fixed costs associated with running the factory, the company starts with a loss of $200,000, or profit of -$200,000, at the beginning of each month. the first major hurdle the company faces each month is to break even or reach the point at which the profit is 0. the tires are sold in batches of 1000. the company earns $40,000 for each batch of tires they manufacture and sell.

### Answers

The **company **needs to sell 5000 **batches** of tires in order to break even each month.

The company starts with a** loss** of $200,000, or profit of -$200,000, at the beginning of each month.

Stating it in mathematical terms, total cost is equal to total revenue at that point.

Total cost = **Total revenue****Fixed cost** + **variable cost** = Total revenue

To determine how many batches of tires the Transverse Tire Company needs to sell in order to break even each month, we need to find when the **profit** is equal to 0.

The profit is calculated as the revenue minus the costs. Since the company starts with a loss of $200,000 each month, we need to calculate how much revenue is needed to reach 0 profit.

⇒Revenue = number of batches * $40,000 per batch

⇒Profit = Revenue - $200,000

Setting profit equal to 0:

⇒0 = Revenue - $200,000

⇒Revenue = $200,000

Dividing both sides by $40,000 per batch:

⇒0 = 5000 batches

Therefore, the company needs to sell 5000 batches of tires in order to break even each month.

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Calculate all of the angles and arc measures needed to complete the table below.

### Answers

By applying **Inscribed angle theorem** the angles and arc measures can be calculated as follows:

∠C = 26°∠B = 26°∠BSD = 97°∠CSE = 97°∠E = 57°Arc BC = 114°

**Inscribed angle theorem** states that the measure of the **central angle** is equal to twice the **inscribed angle** if both angles face the same arc.

central angle = 2 x inscribed angle, where:

Central angle = the angle formed by the center point and any two points that lie on the circle.Inscribed angle = the angle formed by three points that lie on the circle.

The total angles in a triangle are 180°.

Now we look at the picture and apply this theorem:

∠C = 1/2 * ∠DSE

= 1/2 * 52 = 26°

∠B = 1/2 * ∠DSE

= 1/2 * 52 = 26°

∠B + ∠D + ∠BSD = 180°

26° + 57° + ∠BSD = 180°

∠BSD = 97°

∠CSE = ∠BSD = 97°

∠C + ∠E + ∠CSE = 180°

26° + ∠E + 97° = 180°

∠E = 57°

mBC = 2 * ∠E = 2 * ∠D

= 2 * 57°

= 114°

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Are these pairs of ratios proportional or not

proportional? Show you work

2/4 and 6/14

### Answers

Answer:

no

Step-by-step explanation:

2/4=1/2

1/2x7/7=7/14

7/14 doesn’t equal 6/14 therefore it is not proportional.

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A eyeglasses store is checking their inventory. The table shows the relationship between the number of days since the opening of the eyeglasses store and the total amount of sunglasses in their inventory.

Sunglasses Inventory

Number of Days Total Amount of Sunglasses

2 52

5 46

7 42

10 36

Which graph shows the relationship given in the table?

### Answers

A **graph** that shows the **relationship** between the **number **of **days **and the total **amount of sunglasses **is shown in the image attached below.

**What is a scatter plot?**

This is the **term** that is used to refer to the **graphical** **description** that is used to show the **relationship** that would exists between two various **variables**. These **variables** would be on the y and the x **coordinates** of the **scatter plot.**

From the scatter plot (see attachment) which models the relationship between the number of days and the total amount of sunglasses, a linear equation for the line of best fit is given:

y = -2x + 62

Hence, we can** reasonably** infer and **logically deduce **that the **scatter plot **indicates an **inverse relationship** between the **number of days** and the total** amount of sunglasses**.

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Rework problem 17 from section 2.1 of your text, involving an experiment with three possible outcomes. For this problem, assume that outcome O1 has frequency 4/a, outcome O2 has frequency 12/a, and outcome O3 has frequency 3/a.

What is the value of a?

### Answers

If outcome O₁ has a **frequency** 4/a, outcome O₂ has a frequency 12/a, and outcome O₃ has frequency 3/a, then the value of **a** is 19

Frequency of **outcome** O₁ = 4/a

Frequency of outcome O₂ = 12/a

Frequency of outcome O₃ = 3/a

Let's say 1/a = x

Now, the Frequency of outcome O₁ = 4x

Frequency of outcome O₂ = 12x

Frequency of outcome O₃ = 3x

The **sum** of the respective frequencies must **equal 1**.

So, 4x + 12x + 3x = 1

19x = 1

x = 1/19

That means that the “a” in the problem is 19.

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5m (2n−7)

Use the Distributive Property to rewrite the expression in its equivalent form.

### Answers

**Answer:**

5m * (2n - 7) can be rewritten using the distributive property as:

10mn - 35m

If y varies inversely as the square of x,

and y = 4 when x = 2, then what is the

value of y when x = 3?

### Answers

**Answer:**

**y = 9**

Because 3 squared is 9.

**Step-by-step explanation:**

Hope it helps! =D

How many solutions does the system of equations have? Explain.

y = 2x + 1

-4x + 2y = 2

### Answers

The **number of solutions **of the system of equations is given as follows:

Infinity.

How to solve the system of equations?

The system of equations in the context of this problem is **defined **as follows:

y = 2x + 1.-4x + 2y = 2.

The system is solved by **substitution**, replacing the first equation into the second, hence:

-4x + 2(2x + 1) = 2

-4x + 4x + 2 = 2

0x = 0.

0 = 0.

As we have zeros on both sides of the equality, the system has an **infinite **number of solutions.

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the difference of b and 4 is atleast 16

### Answers

answer:

b is 20 ♀️♀️

**Answer: b-4 ≥ 16 || Solved: b≥ 20**

**Step-by-step explanation:**

The keywords in this math problem: The **DIFFERENCE** between b and 4, and this shows subtraction. So, b - 4. **AT LEAST** means greater than or equal to.

Now we have the equation b-4 ≥ 16.

To solve this, we add 4 to both sides of the equation- 4+4 cancels out, and 16+4 = 20.

That leaves the variable alone and the final answer is **b ≥ 20.**

Hope this helps!

The Book Club purchased a bundle of 6 books for $71.94. Calculate the unit rate per book.

hurrry

### Answers

$11.99Answer:

Step-by-step explanation: 71.94÷6=11.99

Eric is baking cupcakes. His recipe calls for 25% sugar, 25% egg, and 50% flour. he has plenty of sugar, 200 grams of egg, and 380 grams of flour. Which is the limiting ingredient? If one cupcake is 20 grams, how many cupcakes can Eric make?

### Answers

38 **cupcakes** can Eric make.

What is Percentage?

percentage, a relative value indicating **hundredth** parts of any quantity.

According to the recipe, one cupcake requires 25% **sugar**, 25% egg, and 50% flour.

To convert the **percentages** to actual quantities, we can multiply the amount of each ingredient by 20 (the weight of one cupcake) and **divide** by 100.

Sugar: 25% × 20g = 5g

**Egg**: 25% × 20g = 5g

Flour: 50% × 20g = 10g

Eric has 200 grams of egg,

200g / 5g = 40 **cupcakes**.

Eric has 380 grams of flour

380g / 10g = 38 cupcakes.

Hence, 38 **cupcakes** can Eric make.

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What will be the volume of water vapor produced when 8 grams of h2 reacts at stp?.

### Answers

The **volume **of the **Erlenmeyer flask **when filled with water is 249 cm³.

What is volume?

**Volume **is a measure of the amount of three-dimensional space an object occupies. It is measured in cubic units, such as cubic centimeters (cm³) or cubic meters (m³). **Volume **is an important concept in many areas of science, including **physics**, **chemistry **and **geology**. It can also be used to describe the capacity of a container, such as a bottle, or the amount of liquid it can hold. Knowing the volume of a substance or object is important in many everyday situations, from measuring food portions to calculating the amount of paint needed to cover a wall.

This is calculated by subtracting the weight of the empty flask (246.3 g) from the **weight **of the **flask filled **with water (495.0 g) and then dividing by the density of water (1.00 g/cm³).

When filled with chloroform, the flask and its contents weigh 581.1 g. To calculate this, we multiply the density of chloroform (1.48 g/cm³) by the **volume **of the flask (249 cm³), which gives us 371.52 g. We then add the weight of the flask (246.3 g) to the weight of the chloroform (371.52 g), which gives us a total of 617.82 g. The **weight **of the **flask **when filled with chloroform is 581.1 g.

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The sum of two numbers is twenty-three. One number is forty-seven less than six times the other. Find the numbers.

### Answers

**Answer:**

10, 13

**Step-by-step explanation:**

Lets call the other x

*x* + 6x - 47 = 23

7*x* - 47 = 23

7*x* = 70

*x* = 10

6 x 10 - 47= 60 - 47 = 13

**Hope this helps!**

Select the correct answer. A circle with center O (0,0) has point B (4,5) on its circumference, which is joined by a line to O. What is the general form of the equation for the given circle centered at O(0, 0)? A. x2 + y2 + 41 = 0 B. x2 + y2 − 41 = 0 C. x2 + y2 + x + y − 41 = 0 D. x2 + y2 + x − y − 41 = 0

### Answers

The **equation **of a graph is a mathematical statement true only for points of that graph. The **equation **of specified **circle **is: x² + y² −41 = 0

What is the equation of a circle with radius r units, centered at (x, y)?

If a circle O has **radius **of r units length and that it has got its center positioned at (h, k) point of the coordinate plane, then, its **equation **is given as: (x-h)²+(y-k)² = r²

For given case, we have h = 0, and k = 0,

We know that,

The **shortest distance** (straight line segment's length connecting both given points) between points (p, q) and (x, y) is:

D = √(x-p)² + (y-q)² units.

Also,

Radius = **distance **between O and B as length of **radius**, which is

r = √[(4-0)² + (5-0)²] = √[16+25] = √41 units.

Thus, we have the **equation **as:

(x-h)² + (y-k)² = r²

x²+ y² = (√41)²

x² + y² = 41

x² + y² - 41 = 0

Hence, The **equation **of specified circle is: Option b) x² + y² - 41 = 0

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The data show the number of pieces of mail delivered to a single home address each day for three weeks.4, 0, 2, 6, 1, 0, 3, 4, 0, 2, 4, 1, 5, 2, 3, 1, 1, 2Which statement is true about a graph representing the data? Check all that apply.The number line of a dot plot would start at 1.A dot plot would show 7 points for numbers greater than 2.The intervals on a histogram should be 0 to 2, 3 to 4, and 5 to 6.A histogram would have a maximum of 7 bars.A histogram should not show a bar that includes 0 pieces of mail.

### Answers

A **dot plot **would show 7 points for numbers greater than 2 and a histogram would have a **maximum **of 7 bars. Hence, Both **statements b **and **d **are true about a **graph **representing the data.

**Statement b:** A dot **plot **would show 7 points for numbers greater than 2. This is true because there are 7 **data **points (2, 3, 4, 4, 4, 5, 6) in the data set that is **greater **than 2.

**Statement d**: A **histogram **would have a maximum of 7 bars. This is because there are 7 **unique **values in the **data set **(0, 1, 2, 3, 4, 5, 6), and each unique value would correspond to a bar in the histogram.

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find the vector form of the equation of the line in that passes through and is perpendicular to the plane with general equation .

### Answers

The **vector **form is x - y +z = 0

**Standard equation**

The standard form of a** linear equation** is Ax + By=C. To change an equation written in slope-intercept form (y = mx + b) to standard form, you must get the x and y on the same side of the **equal sign** and the** constant **on the other side.

The **vector form** of the **equation** of the line in that passes through** origin **and is** perpendicular** to the **plane** with general point [1,1,1].

The **standard equation** is of the form, Ax + By + Cz = 0

The** equation** of the **plane** that passes through the origin(0, 0, 0) and is perpendicular to [1,1,1] is

A = 1, B = 1, C = 1

x = y = z = 0 (at origin)

A(x-0) + B(y-0) + C(z-0) = 0

(x - 0) -1(y-0) + 1(z-0) = 0

x - y +z = 0.

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The acceleration function (in m/s^2) and the initial velocity are given for a particle moving along a line. Find the the distance traveled during the given time interval? a(t) = t + 4, v(0) = 5, 0 less than or equal to t less than or equal to 10

### Answers

The **distance** traveled during the time **interval** 0 ≤ t ≤ 10 is 500 m.

To find the distance traveled by a particle with a given **acceleration **function and initial velocity, we need to first find the velocity function and then **integrate** it to get the position **function**.

The velocity function, v(t), is obtained by integrating the acceleration function:

v(t) = ∫a(t) dt = ∫(t + 4) dt = [tex](\frac{1}{2}) t^2 + 4t + C[/tex]

where C is the constant of integration. To determine the value of C, we use the **initial velocity**, v(0) = 5:

[tex]v(0) = \frac{1}{2} * 0^2 + 4 * 0 + C = 5[/tex]

Solving for C, we find that C = 5. Therefore, the velocity function is:

[tex]v(t) = (\frac{1}{2} )t^2 + 4t + 5[/tex]

Next, we integrate the velocity function to find the position function, x(t):

x(t) = ∫v(t) dt = ∫[tex][(\frac{1}{2} )t^2 + 4t + 5] dt = (\frac{1}{6} )t^3 + 2t^2 + 5t + D[/tex]

where D is another constant of integration. To determine the value of D, we need an initial position, x(0). If the initial position is not given, we assume that x(0) = 0:

[tex]x(0) = (\frac{1}{6} ) * 0^3 + 2 * 0^2 + 5 * 0 + D = 0[/tex]

Solving for D, we find that D = 0. Therefore, the position function is:

[tex]x(t) = (\frac{1}{6} )t^3 + 2t^2 + 5t[/tex]

Finally, to find the distance traveled during the time interval 0 ≤ t ≤ 10, we evaluate the position function at t = 10 and subtract the position at t = 0:

[tex]x(10) - x(0) = (\frac{1}{6} ) * 10^3 + 2 * 10^2 + 5 * 10 - 0 = 500 m[/tex]

So, the distance traveled during the time interval 0 ≤ t ≤ 10 is 500 m.

Therefore, the distance traveled during the time interval is 500 m.

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help! You are debating about whether to buy a new computer for $800.00 or a refurbished computer with the same equipment for $640.00. If a savings account earns 4.5% APR interest, how much do you really save with a refurbished computer if you put the difference into the savings account for a year? Be sure to include the following in your response: The answer to the original question The mathematical steps for solving the problem demonstrating mathematical reasoning

### Answers

The difference in price is** $160.00**

The interest earned is **$7.20**

The total amount after a year is **$167.20**

The real saving is **$632.80.**

What is the difference price between the new and refurbished computers?

The **difference** in price between the new and refurbished computers is **$800.00 - $640.00** = $160.00.

If you invest this **$160.00 **into a savings account that earns 4.5% APR interest for a year, the interest earned would be $160.00 * 0.045 = **$7.20.**

So, the total amount after a year would be $160.00 + $7.20 = **$167.20.**

Therefore, you would really save $800.00 - $167.20 = $632.80 if you buy the r**efurbished computer** and invest the difference in price into the savings account for a year.

**Mathematical steps for solving the problem:**

Calculate the difference in price: $800.00 - $640.00 = **$160.00**

Calculate the interest earned: $160.00 * 0.045 = **$7.20**

Calculate the total amount after a year: $160.00 + $7.20 = **$167.20**

Calculate the real savings: $800.00 - $167.20 = **$632.80.**

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Jason borrowed money from his father,interest free, to purchase computer equipment for a startup business. The question below shows the amount of the loan ,y, he has left to pay after X months of repayment

### Answers

The remaining loan balance, y, after X months of repayment can be calculated by subtracting the amount of money that has been paid back so far from the total loan amount. The result of dividing the loan amount (numerator) by the **interest** amount (numerator) yields the interest rate (denominator).

What are interest?

The amount that the lender charges the borrower over and beyond the **principal** amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.

The result is then expressed as a percentage by multiplying this quotient by 100.

Due to inherent risks and the time worth of money, the interest rate represents the cost of borrowing.

Equipment cost is £2,400.

**Mortgage** term equals two years (24 months)

£116.00 in monthly payments

£2,784 total payments (£116 divided by 24)

Interest paid totals £384 (£2,784 minus £2,400).

Total interest expressed as a % of the total amount borrowed is 16%. (£384/£2,400 x 100)

Jon can afford a maximum interest rate of £150.

(£150/£2,400 multiplied by 100) Equals 6.25% interest rate

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Complete the table to show the missing numbers of particles in the four atoms A, B,

C and D.

Atom

A

BCD

Protons

20

19

Neutrons

24

21

Electrons

20

Mass

40

45

44

### Answers

Based on the **given table**, the two particles that belong to the same element are: C. **2 and 3**.

What is a Neutron?

The neutron, symbol n or n0, is a subatomic particle with a neutral charge and slightly more mass than a proton. The nucleus of atoms consists of protons and neutrons.

Hence, an element always consists of the same number of protons and electrons.

The** number of neutrons** can be changed in an element based on its **isotropy**.

**Option C **is correct.

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protonsneutronselectronic structure

118222,8,8

219202,8,8

319212,8,8,1

420202,8,8,2

In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulas for the area of a triangle, such as half the base times the height. Use Heron's formula to find the area, in square meters, of ΔABC.

### Answers

The area of the **triangle **is A = 14.697 m²

What is Heron's formula?

**Heron**'s formula is used to calculate the area of a **triangle **in terms of the lengths of its sides. If a, b, and c are the lengths of the sides, then the area of the triangle is

Area of **Triangle **A = √ [ s(s - a) (s - b) (s - c) ]

where s is half the perimeter, or (a + b + c)/2

Given data ,

Let the area of the **triangle **be represented as A

Now , the value of A is

The measure of side AB , c = 6m

The measure of side AC , b = 5m

The measure of side BC , a = 7m

Now from the **Heron**'s formula ,

Area of **Triangle **A = √ [ s(s - a) (s - b) (s - c) ]

The perimeter of the triangle P = 6 + 7 + 5 = 18m

Now , the value of s = P/2 = 9m

Substituting the values in the equation , we get

Area of Triangle A = √ [ 9 ( 9 - 7 ) ( 9 - 5 ) ( 9 - 6 ) ]

On simplifying the equation , we get

Area of Triangle A = √ 9 ( 2 ) ( 4 ) ( 3 )

Area of Triangle A = √ 9 ( 24 )

Area of Triangle A = √216

Area of **Triangle **A = 14.697 m²

Hence , the area of **triangle **is 14.697 m²

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BIKING Talula got a new bicycle lock that has a four-number combination. Each number in the combination is from 0 to 9.

a. How many combinations are possible if there are no restrictions on the number of times Talula can use each number?

b. How many combinations are possible if Talula can use each number only once? Explain.

### Answers

a. With no restrictions on the number of times each number can be used, the number of combinations possible is 10 x 10 x 10 x 10 = 10,000. This is because for each digit in the combination, Talula has 10 choices (0 to 9).

b. If Talula can use each number only once, the number of combinations possible is calculated as follows:

For the first digit, Talula has 10 choices.

For the second digit, Talula has 9 choices (since 1 number has already been used).

For the third digit, Talula has 8 choices (since 2 numbers have already been used).

For the fourth digit, Talula has 7 choices (since 3 numbers have already been used).

Therefore, the total number of combinations possible is 10 x 9 x 8 x 7 = 5040. This is because for each subsequent digit, Talula has one less choice as each number can only be used once

hile watching a car move down the street, you close your eyes and count off 15 seconds. When you open your eyes again, the car is 144 feet further down the road from when you last saw it.WHAT IF the car traveled at a constant speed while your eyes were closed - how fast would it have had to travel?a. What constant speed would allow the car to travel exactly 144 feet in exactly 15 seconds?Select an answer second ft/sec feetb. If a car traveled at this speed for tt seconds, what formula would model its distance dd (in feet) from the starting point in terms of the time elapsed, tt (in seconds)? Recall that this does not necessarilly represent the actual relationship between the distance traveled and time elapsed for the real car. This represents the relationship for an imaginary car traveling at a constant speed.s = d/t

### Answers

**Answer:**

below

**Step-by-step explanation:**

A. To find the constant speed that allows the car to travel exactly 144 feet in exactly 15 seconds, we can use the formula: speed = distance / time.

So, speed = 144 feet / 15 seconds = 9.6 feet/second.

B. If a car traveled at a constant speed of 9.6 feet/second for t seconds, the formula for its distance dd (in feet) from the starting point in terms of the time elapsed, tt (in seconds) would be:

dd = 9.6 feet/second * t seconds = 9.6t feet.

Two planets are orbiting a star. Planet B can be seen from Planet A with the

eye, but as the figure shows, Planet could be located at either of two possible positions. Planet A is 65 million miles from the star and Planet B is 45 million miles from the star, as shown in the figure below. If the viewing angle between the star and Planet B is 19 , find the possible distances from Planet A to Planet B . Round your answers to the nearest tenth.

### Answers

**Answer:**

**Step-by-step explanation:**

Since the viewing angle between the star and Planet B is 19 degrees, we can use trigonometry to find the distances from Planet A to Planet B. Let's call these distances x and y, where x is the distance to the closer position of Planet B and y is the distance to the farther position of Planet B, as shown in the figure.

Using the Law of Cosines for the triangles with sides 65, x, and 45 (for the closer position) and 65, y, and 45 (for the farther position), we can write:

x^2 = 65^2 + 45^2 - 26545*cos(19) ≈ 2374.6

y^2 = 65^2 + 45^2 - 26545*cos(161) ≈ 10864.6

Taking the square roots of both sides, we get:

x ≈ 48.7 and y ≈ 104.2

Therefore, the possible distances from Planet A to Planet B are approximately 48.7 million miles (for the closer position of Planet B) and 104.2 million miles (for the farther position of Planet B), rounded to the nearest tenth.