Mathematics College

## Answers

**Answer 1**

**Answer:**

15% market price = 6000+900=6900

sale price=4600

discount given= 6900-4600=2300

**Step-by-step explanation:**

brainist pls?

**Answer 2**

The **percentage** discount given to the customer is approximately 33.33%.

To find the percentage discount given to the customer, we need to calculate the **difference** between the market price and the sale price, and then express it as a percentage of the market price.

The cost price of the article is given as Rs. 6,000. The market price is 15% above the cost price, which means it is calculated as 1.15 times the cost **price**:

Market price = 1.15 * Cost price = 1.15 * 6000 = Rs. 6,900.

The sale price of the article is given as Rs. 4,600.

To find the discount, we **subtract** the sale price from the market price:

Discount = Market price - Sale price = 6,900 - 4,600 = Rs. 2,300.

To calculate the percentage discount, we divide the discount by the market price and **multiply** by 100:

Percentage discount = (Discount / Market price) * 100 = (2300 / 6900) * 100 ≈ 33.33%.

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## Related Questions

Maya can fit 13 marbles in a small box and 50 marbles in a large box. She has 10 small boxes of marbles and would like to reorganize the marbles into large boxes. how many large boxes could she fill?

A: she could fill ___ box. Since 10 small boxes is __ marbles, Sha san fill __ large boxes with the __ marbles left.

### Answers

She could fill 10 boxes. Since 10 small boxes is 130 marbles, she can fill 2 large boxes with 30 marbles left.

Determine the smallest integer that makes -6x+3-2x<19 true.

### Answers

The **smallest integer** that would make the equation true is x < -2.

Given,

The equation; -6x + 3 - 2x < 19

We have to find the smallest integer that makes the** equation** true.

Integers;-

An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a** fraction.** Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.

Here,

Solve the equation for x.

That is,

-6x + 3 - 2x < 19

-8x + 3 < 19

-8x < 19 - 3

x < -16/8

x < -2

That is,

The smallest** integer** that would make the equation true is x < -2.

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Suppose that the local sales tax rate is 6% and you purchase a car for $25,500.

a. How much tax is paid?

### Answers

**Answer: $27,030**

**Sales Tax: $1,530**

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If P dollars is deposited in a savings account that pays interest at a rate r% per year compounded continuously, find the balance after t years. (Round your answer to the nearest cent)

P = 60, r = 4 1/2, t = 10

### Answers

**Answer:**

$94.09

**Step-by-step explanation:**

Use **continuous compound** equation:

[tex]A = P*e^{rt}[/tex], where A- future amount, P- invested amount, t- time, r- rate

Given

P = $60,r = 4 1/2% = 4.5% = 0.045,t = 10 years.

Plug in and calculate

[tex]A = 60*e^{0.045*10}=60*e^{0.45}=94.09[/tex]

**Answer:**

$90.10 (nearest cent)

**Step-by-step explanation:**

Continuous Compounding Formula

[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]

where:

A = Final amount.P = Principal amount.e = Euler's number (constant).r = Annual interest rate (in decimal form).t = Time (in years).

Given values:

P = $60r = 4.5% = 0.045t = 10 years

**Substitute **the given values into the **formula **and **solve for A**:

[tex]\implies \sf A=60 \cdot e^{0.045 \cdot 10}[/tex]

[tex]\implies \sf A=60 \cdot e^{0.45}[/tex]

[tex]\implies \sf A=60 \cdot 1.56831218...[/tex]

[tex]\implies \sf A=94.0987311...[/tex]

Therefore, the **balance **of the account after 10 years is **$90.10** (nearest cent).

The table shows the amount of flour needed for several servings in a recipe. Based on this table, how many cups of flour are needed for 36 servings?

cups of flour

2 8

4 16

6 24

Group of answer choices

18

8

12

9

### Answers

**Answer:**

18 cups.

**Step-by-step explanation:**

The cups of flour multiplied by two gives you the servings. Lets say cups of flour is represented by c and servings is represented by s. Therefore you have 2c = s. You can rearrange this equation to be s/2 = c. Plug in the servings, 36 into the equation to find c. 36/2 = c. This gives you 18 cups.

There are 27 Pennie’s on one pan of a pan balance and 18 Pennie’s in the other. To make the pans balance, Hillary thinks 5 Pennie’s should be added, Rachel thinks 9 Pennie’s should be added. Use the equation 27 = 18 + p to determine who is correct.

### Answers

The **person** that's correct based on the information is **Rachael**.

How to illustrate the information?

An **equation** is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation isa **mathematical** statement which is made up of two expressions that are connected by an equal sign.

From the information, there are 27 **Pennie’s** on one pan of a pan balance and 18 Pennie’s in the other.

In order to make the **pans** balance, Hillary thinks 5 Pennie’s should be added, **Rachel** thinks 9 Pennie’s should be added.

The **equation** will be:

27 = 18 + p

p = 27 - 18

p = 9

Therefore, **Rachael** is correct.

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You pick a card at random. 1 2 3 4 What is P(2 or less than 4)?

### Answers

In the event of **picking **a **card randomly **the **probability**, P(2 or less than 4) = 1

How to find the probability

To find the **required** **probability**, each to the probability is solved then added to get the required probability.

The probability can be separated as P(2) or P(less than 4)

**Probability **is solved by = required outcome / possible outcome

the **possible outcome** is the number of sample space.

S = {1, 2, 3, 4}

n(S) = 4

In this case the number of sample space is 4

P(2):

**required outcome **= 1

possible outcome = 4

P(2) = 1/4

P(less than 4)

= 1 - P(4)

P(4) = 1/4

P(less than 4) = 1 - 1/4 = 3/4

P(2 or less than 4)

= P(2) + P(less than 4)

= 1/4 + 3/4

= 1

Therefore the probability of 2 or less than 4 is 1

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The volume of a cylindrical can is 3.08 litre. If the area of its base is 154 cm², find its curved surface area

### Answers

**Answer:**

879.8 cm² (nearest tenth)

**Step-by-step explanation:**

Given:

Volume = 3.08 LArea of base = 154 cm²

**Convert **the given **volume **to **cubic centimeters**:

[tex]\boxed{\begin{aligned}1\; \sf L&=1000\; \sf cm^3\\\\\implies 3.08\; \sf L&=3.08 \times 1000\\&=3080\; \sf cm^3\end{aligned}}[/tex]

Substitute the volume and base area into the formula for the **volume of a cylinder** and **solve for** **height**, h:

[tex]\boxed{\begin{aligned}\textsf{Volume of a cylinder}&= \sf area\;of\;base \times height\\\\\implies 3080&=154h\\h&=\dfrac{3080}{154}\\h&=20\;\; \sf cm\end{aligned}}[/tex]

The **base **of a **cylinder **is a **circle**.

Substitute the given area of the base into the formula** **for the **area of a circle** and **solve for** **radius**, r:

[tex]\boxed{\begin{aligned}\textsf{Area of a circle}&= \pi r^2\\\\\implies 154&=\pi r^2\\r^2&=\dfrac{154}{\pi}\\r&=\sqrt{\dfrac{154}{\pi}}\;\; \sf cm\end{aligned}}[/tex]

The curved surface area of a cylinder is called the** Lateral Surface Area **(LSA).

Substitute the found **radius **and **height **into the formula for LSA of a cylinder:

[tex]\boxed{\begin{aligned}\textsf{LSA of a cylinder}&=2\pi r h\\\\\implies \sf LSA&=2 \pi \left(\sqrt{\dfrac{154}{\pi}}\right) (20)\\& = 879.8229537...\\&=879.8\;\; \sf cm^2\end{aligned}}[/tex]

Express the pair of fractions using the least common denominator of the two. 5/12, 7/16

### Answers

The possible **pair** of fractions using the **least common **denominator are 15/32 and 14/32

How to determine the possible fractions using the least common denominator?

From the question, we have the following **statement **that can be used in our computation:

Pair of fractions using the least common **denominator** of the two

Also, we have the **fractions **to be

5/12 and 7/16

These **fractions **can be represented by n

So, we have

n = 5/12 and 7/16

The fractions 5/12 and 7/16 can be rewritten as

5/12 = 15/32

7/16 = 14/32

This means that

5/12 and 7/16 = 15/32 and 14/32

So, the **possible **fractions are 15/32 and 14/32

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The standard deviation of the scores on a skill evaluation test is 354 points with a mean of 1458 points. If 313 tests are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 40 points? Round your answer to four decimal places.

### Answers

And we can find this probability with this difference and using the normal standard distribution or excel and we got:

0.977-0.0228 = 0.9542

Hope this help! :)

9. Amaia purchased the DVD

player shown in the sign on

the right. Find the percent

markdown rounded to the

nearest percent.

SALE!

WAS $175.90

NOW

$153.77

Answer?

### Answers

**Answer:**

The percent markdown for the cost of DVD player for considered case is 14.4% approx.

How do you graph a dilated image?

### Answers

**To graph a dilated image** you need a **center of dilation **and the **scale factor **

**Dilation **means changing the size of an object without changing its shape. The size of the object may be** increased or decreased** based on the scale factor

When we dilate shapes on a grid, we need to know the center of dilation and **the scale factor.**

**The center of dilation** is like the fixed projector

The scale factor determines how much smaller or larger the dilated image will be.

To graph a dilated image follow the following steps:

Step 1. Identify the **center of dilation**

Step 2. Identify the **original** points of the polygon.

Step 3. Identify the **scale factor** .

Step 4**. Multiply **each original point of the polygon by the scale factor to get the new points.

Step 5.** Plot the new points** and connect the dots to get your dilated shape.

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A mathematics teacher wanted to see the correlation between test scores and homework. The homework grade (x) and test grade (y) are given in the accompanying table. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the projected test grade, to the nearest integer, for a student with a homework grade of 35.

### Answers

The **regression equation** that models the relationship between homework grade and test grade and the predicted homework grade are :

y = 1.20x - 14.32

Predicted, x = 69

How to find the regression equation?

Using technology, the linear model can be obtained using either excel or a linear **regression** calculator. Using a linear regression calculator which gives the linear **equation** in the form :

y = bx + c

y = 1.20x - 14.32

y = Test grade ;

x = homework grade

Slope, b = 1.20 ;

intercept, c = - 14.32

Using the model equation obtained :

Test **grade**, y = 68

Homework grade, x

y = 1.20x - 14.32

68 = 1.20x - 14.32

68 + 14.32 = 1.20x

82.32 = 1.20x

x = (82.32 ÷ 1.20)

x = 68.6

x = 69 (nearest integer)

Therefore, the estimated **homework** grade for a test score of 68 is 69.

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Complete question

A mathematics teacher wanted to see the correlation between test scores and homework. The homework grade (x) and test grade (y) are given in the accompanying table. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, estimate the homework grade, to the nearest integer, for a student with a test grade of 68.

Homework Grade (x) Test Grade (y)

X | Y

88 | 90

55 | 55

89 | 91

85 | 88

61 | 52

76 | 76

76 | 81

61 | 59

Savannah deposits $280.00 each month into a savings account that earns annual simple interest of 1.8% on the current principal balance of $4,778.00. In two years, what will the difference be between the balance at the current savings amount versus adding an additional $65.00 each month? (2 points)

### Answers

The **difference** between the balance at the current **savings** amount versus adding an **additional** $65.00 each month is $1560.

Given that, principal = $4,778.00 and annual simple interest = 1.8%

What is the simple interest?

**Simple interest **is a method to calculate the amount of interest charged on a sum at a given **rate** and for a given period of time.

Simple interest is calculated with the following formula: S.I. = (P × R × T)/100.

First, find the **simple** annual **interest** earned:

Now, simple interest = (4,778.00×1.8×2)/100

= 17200.8/100

= $172.008

The total amount in the savings account at a **savings** rate of $280 per month is:

= **Principal** + Simple interest + total monthly deposit

= 4,778.00 + 172.008 + ( 280 × 12 months per year × 2 years)

= 4,778.00 + 172.008 + 6720

= $11670.008

The **total amount** in the savings account at a savings rate of (280 + 65) per month is:

= 4,778.00 + 172.008 + ( 345 × 12 months per year × 2 years)

= 4,778.00 + 172.008 + 8280

= 13230.008

So, the difference is

= 13230.008 - 11670.008

= $1560

Therefore, the **difference** between the balance at the current **savings** amount versus adding an **additional** $65.00 each month is $1560.

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Wich statement is true about the product 0f 7 ×2/3

### Answers

The **true **statement of the product **expression **7 x 2/3 is (2) The product is **greater **than 2/3 and less than 7.

How to determine the true statement of the product?

The complete question is added at the end of the **solution**

From the question, the **product** expression is given as

7 x 2/3

Evaluate the product in the above expression

So, we have the following **representation**

7 x 2/3 = 14/3

Evaluate the **quotient **in the above expression

So, we have the following representation

7 x 2/3 = 4.7

The result in the above **computation **is **greater than **2/3

However, the result in the above computation is **less than **7

Hence, the true statement is (2)

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Complete question

Which is true about the product of 7 x 2/3.

1.The product is less than 2/3.

2.The product is greater than 2/3 and less than 7.

3.The product is greater than 7

pls help me fast rapidly is of khan academy:

### Answers

**Answer:**

508.231

**Step-by-step explanation:**

500+8+0.2+0.03+0.001

=508.231

When we make inferences about ONE POPULATION PROPORTION, what assumptions do we need to make? Mark all that apply.

A. Data must be from a simple random sample.

B. The data must have a Normal Distribution.

C. Counts of successes and failures at least 15 each.

D. Counts of successes and failures at least 5 each.

E. Sample Size is 30 or more.

F. Data is categorical.

G. Data is quantitative.

### Answers

In making **inferences** about a **population** using a sample of the subject from the **population**, the following **assumptions** need to be made :

*Data is quantitative**The sample Size is 30 or more**Data must be from a simple random sample**The data must have a Normal Distribution*

The data must be from a** randomly** distributed **sample** in other to ensure that it can be generalized well.

Based on the **central limit theorem**, the **sample size** must be **at least** 30 or **more.**

**Quantitative** data in which **statistical** deductions can be made such as mean and **standard deviation**.

The distribution should not be **skewed **to avoid **bias** or rather increase the **sample** to be as large as possible.

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If a drug has a concentration of 4.258 mg per 3.433 mL, how many mL are needed to give 9.208 gram of the drug?

### Answers

The **number **of mL for 9.208 gram of the **drug** is 7423.9 mL

How to determine the number of mL?

The given parameters can be represented as

**Concentration **of 4.258 mg per 3.433 mL

This can be rewritten as

**Concentration **= 4.258 mg/3.433 mL

For 9.208 gram of the drug, we have the number of mL to be

Number of mL = 9.208 gram/(4.258 mg/3.433 mL)

Cancel out the **units**

Number of mL = 9208/(4.258/3.433) mL

Evaluate

Number of mL = 7423.9 mL

Hence, the number of mL is 7423.9 mL

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Multiply 3x (2x-1) by the following steps:

### Answers

**Answer:**

[tex]6x^{2} -3x[/tex]

**Step-by-step explanation:**

3x(2x-1)

3x(2x)-(3x)(1)

6x^2-3x

Hopes this helps please mark brainliest

Check the photo for the full answer

how do you graph 1/3x - 1/6y=-2/3

### Answers

**Answer:** See attached and view below.

**Step-by-step explanation:**

First, we will turn this **equation **into **slope-intercept form**.

**Given**:

1/3x - 1/6y = -2/3

**Add **1/6y and 2/3 to both sides of the equation:

1/6y = 1/3x + 2/3

**Divide **both sides of the equation by 1/6"

y = 2x + 4

Looking at our **equation**, we see we have a **slope **of 2 and a **y-intercept** of 4.

Mrs. Bell's class is working together to earn enough money for a field trip. The total cost for the class to go to the observatory is $910. The students want to have the money for their field trip in 5 months - How much do they need to earn each month in order to accomplish their goal? Explain.

### Answers

$182 they need to **earn **each month in order to accomplish their goal

What is Division?

A division is a process of **splitting **a specific amount into equal parts.

Given,

Mrs. Bell's class is **working **together to earn enough money for a field trip.

The** total cost **for the class to go to the observatory is $910

The students want to have the **money** for their field trip in 5 months

We need to find how much they has to earn in each **month **in order to accomplish their goal.

We need to **split** 910 by 5

910/5

182

Hence $182 they need to **earn **each month in order to accomplish their goal

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Students need to **earn **$182 per month to accomplish the goal.

What is ratio?

**Ratio **basically compares quantities, that means it shows the **value **of one quantity with respect to the other quantity.

If a and b are two **values**, their ratio will be a:b,

Given that,

Total **cost **for the class to go to the observatory = $910.

Since, students want to have money for field trip in 5 months,

To find earning of each month to accomplish the goal, use **ratio **property,

5 months = $910

⇒1 month = $910/5

⇒1 month = $182

So, $182 needs to earn each month in order to **accomplish **the goal.

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4. The temperature on Monday was -11° C. The temperature on

Thursday was -7° C. How many degrees did the temperature

change from Monday to Thursday?

### Answers

**Answer:**

The temperature increased 4 degrees

**Step-by-step explanation:**

-7 - -11

-7 + 11

4

dont know the answer to last question

### Answers

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the line AB.... hmmm wait a second!!!, you found it already, well, we know AB has a slope of -1/3.

so we're really looking for the equation of a line whose slope is -1/3 and that it passes through (0 , -5)

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{-5})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{- \cfrac{1}{3}}(x-\stackrel{x_1}{0}) \implies y +5= -\cfrac{1}{3} (x -0) \\\\\\ y+5=-\cfrac{1}{3}x\implies {\Large \begin{array}{llll} y=-\cfrac{1}{3}x-5 \end{array}}[/tex]

In a sporting event, the scoring area (shown here) consists of four concentric circles on the ice with radii of 3 inches, 2 feet,

3 feet, and 4 feet. If a team member lands a (43-pound) stone randomly within the scoring area, find the probability that it

ends up centered on the given color.

(a) red

(b) white

(c) blue

### Answers

Answer:

Step-by-step explanation:

The **probability **of the stone landing in the **center **of the red circle is 0.16.

What is the probability?

**Probability **can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an **event **= Number of favourable outcomes/Total number of outcomes.

Given that, the scoring area consists of four concentric circles on the ice with radii of 3 inches, 2 feet, 3 feet, and 4 feet.

To calculate the probability of the stone landing in the center of the red, white, or blue circle, we must first calculate the area of each circle.

The **area **of the red circle = π× (3 inches)²= 28.27 in²

The area of the white circle = π× (2 feet)² = 50.27 ft²

The area of the blue circle = π× (3 feet)² = 113.09 ft²

Now, we can calculate the probability of the stone landing in the center of the red, white, or blue circle.

The probability of the stone landing in the center of the red circle = 28.27 in² / (28.27 in² + 50.27 ft² + 113.09 ft²) = 0.16

The probability of the stone landing in the center of the white circle = 50.27 ft² / (28.27 in² + 50.27 ft² + 113.09 ft²) = 0.27

The **probability **of the stone landing in the center of the blue circle = 113.09 ft² / (28.27 in² + 50.27 ft² + 113.09 ft²) = 0.57

Therefore, the probability of the stone landing in the center of the red circle is 0.16.

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Giving brainliest to who ever answers this question right

### Answers

The required **equation **of the line in **slope intercept **form is given as y = -6x - 4.

What is the slope of the line?

The **slope **of the **line **is a **tangent angle **made by line with horizontal. i.e. m =tanx where x in degrees.

Here,

Consider two **points **on the line,

(-1, 2) and (0, -4)

The **standard equation **of the **line **is given as

y -y₁ =(y₂ - y₁) / (x₂ - x₁) (x - x₁)

Substitute points in the above equation,

y - 2 = [(-4 - 2)/ (0+ 1)] (x +1)

y = [-6](x + 1) + 2

y = -6x -6 + 2

y = -6x - 4

Thus, the required equation of the line in **slope intercept form **is given as y = -6x - 4.

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Each package holds 72 markers:

Mr. Alvarez has 4 packages. Write

and solve an equation that can be

used to find the number of markers

Mr. Alvarez has.

72

72

m

72

72

M

### Answers

**Answer:**

288

**Step-by-step explanation:**

72×4=288

she has 72 in each package so you multiply them

A community theater has two acting troupes that each have 9 members. The theater plans to put on a play that requires seven actors. Three of the actors will come from the first troupe and four of the actors will come from the second troupe.

Use the template below to show the notation for calculating the total number of possible ways the seven actors can be chosen.

### Answers

The **expression **that gives the total number of possible ways to choose the **seven actors** is given as follows:

[tex]C_{9,3} \times C_{9,4}[/tex]

How to obtain the expression for the number of actors?

The first step towards obtaining the expression for the number of actors is defining if the **permutation **formula or if the **combination **formula is used.

The order in which the authors are chosen is not important, hence the **combination **formula is used to obtain the expression.

The **number **of** different combination**s of x objects from a set of n elements is obtained with the equation presented as follows, which uses factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, the actors are **chosen** as follows:

First troupe: 3 actors from a set of 9 actors -> Combination of 3 actors from a set of 9.Second troupe: 4 actors from a set of 9 actors -> Combination of 4 actors from a set of 9.

Then the two combinations are multiplied to give the **expression**.

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A farmer has enough grass to feed 50 cows for 10 days. If the sell 10 cows. If how many days will the grass last?

### Answers

**Answer:**

20 days

**Step-by-step explanation:**

0.03÷0.2

100 Points pls full solution

### Answers

**Answer:**

0.15

**Step-by-step explanation:**

Picture 0.03 and 0.2 as whole numbers. [tex]3\div 2[/tex]Whenever you divide a number by 2, you're dividing it in half, right? So we know that half of 3 is 1.5. Use this information and shift the decimal place one unit left because we are multiplying by hundredths. [tex]= 0.15[/tex]

Hope this helps!

**Answer: 0.15**

**Step-by-step explanation:**

Lets not worry about the zero's for now, first lets divide 3 by 2 and you get 1 with a remainder of 1. If you divide 1 by 2 you get .5. This is when the zeros come in an if you put it together, you get 0.15.

Solve for

k

kk.

4.5

+

1.5

k

=

18

−

3

k

4.5+1.5k=18−3k

### Answers

The **value** of k from the given **equation** is 53.

The given equation is 4.5+1.5k=18−3k.

What is an equation?

In mathematics, an **equation** is a formula that expresses the **equality** of two **expressions**, by connecting them with the equals sign =.

The given **equation** is can be solved as follows

4.5+1.5k=18−3k

⇒ 1.5k+3k=18-4.5

⇒ 4.5k=13.5

⇒ k=13.5/4.5

⇒ k=3

Hence, the **value** of k from the given **equation** is 53.

To learn more about an **equation** visit:

https://brainly.com/question/14686792.

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