Jessica and Riley are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping
paper or holiday wrapping paper. Jessica solf 5 rolls of plain and 13 rolls of holiday wrapping paper for a total
$272. Ryan solf 11 rolls of plain and 16 rolls of holiday wrapping paper for a total $359. What is the cost of one
roll of plain wrapping paper and one roll of holiday wrapping paper?

To divide 120.4 by 602, place the decimal point in the quotient above the decimal point in the dividend. Divide the whole numbers and then bring down the next digit.
The result is 0.2 (rounded to one decimal place).

To divide 120.4 by 602, follow these steps:

Therefore, 120.4 divided by 602 is equal to 0.2 (rounded to one decimal place).

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Answer:

18

Step-by-step explanation:

18 x 8.3 = 149.4

Answer:

B:18 as you divide the 149.4 by 8.3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Law of sines is:

(sin A) / a = (sin B) / b = (sin C) / c

Law of cosines is:

c² = a² + b² − 2ab cos C

Note that a, b, and c are interchangeable, so long as the angle in the cosine corresponds to the side on the left of the equation (for example, angle C is opposite of side c).

Also, angles of a triangle add up to 180° or π.

(i) sin(B−C) / sin(B+C)

Since A+B+C = π, B+C = π−A:

sin(B−C) / sin(π−A)

Using angle shift property:

sin(B−C) / sin A

Using angle sum/difference identity:

(sin B cos C − cos B sin C) / sin A

Distribute:

(sin B cos C) / sin A − (cos B sin C) / sin A

From law of sines, sin B / sin A = b / a, and sin C / sin A = c / a.

(b/a) cos C − (c/a) cos B

From law of cosines:

c² = a² + b² − 2ab cos C

(c/a)² = 1 + (b/a)² − 2(b/a) cos C

2(b/a) cos C = 1 + (b/a)² − (c/a)²

(b/a) cos C = ½ + ½ (b/a)² − ½ (c/a)²

Similarly:

b² = a² + c² − 2ac cos B

(b/a)² = 1 + (c/a)² − 2(c/a) cos B

2(c/a) cos B = 1 + (c/a)² − (b/a)²

(c/a) cos B = ½ + ½ (c/a)² − ½ (b/a)²

Substituting:

[ ½ + ½ (b/a)² − ½ (c/a)² ] − [ ½ + ½ (c/a)² − ½ (b/a)² ]

½ + ½ (b/a)² − ½ (c/a)² − ½ − ½ (c/a)² + ½ (b/a)²

(b/a)² − (c/a)²

(b² − c²) / a²

(ii) a (cos B + cos C)

a cos B + a cos C

From law of cosines, we know:

b² = a² + c² − 2ac cos B

2ac cos B = a² + c² − b²

a cos B = 1/(2c) (a² + c² − b²)

Similarly:

c² = a² + b² − 2ab cos C

2ab cos C = a² + b² − c²

a cos C = 1/(2b) (a² + b² − c²)

Substituting:

1/(2c) (a² + c² − b²) + 1/(2b) (a² + b² − c²)

Common denominator:

1/(2bc) (a²b + bc² − b³) + 1/(2bc) (a²c + b²c − c³)

1/(2bc) (a²b + bc² − b³ + a²c + b²c − c³)

Rearrange:

1/(2bc) [a²b + a²c + bc² + b²c − (b³ + c³)]

Factor (use sum of cubes):

1/(2bc) [a² (b + c) + bc (b + c) − (b + c)(b² − bc + c²)]

(b + c)/(2bc) [a² + bc − (b² − bc + c²)]

(b + c)/(2bc) (a² + bc − b² + bc − c²)

(b + c)/(2bc) (2bc + a² − b² − c²)

Distribute:

(b + c)/(2bc) (2bc) + (b + c)/(2bc) (a² − b² − c²)

(b + c) + (b + c)/(2bc) (a² − b² − c²)

From law of cosines, we know:

a² = b² + c² − 2bc cos A

2bc cos A = b² + c² − a²

cos A = (b² + c² − a²) / (2bc)

-cos A = (a² − b² − c²) / (2bc)

Substituting:

(b + c) + (b + c)(-cos A)

(b + c)(1 − cos A)

From half angle formula, we can rewrite this as:

2(b + c) sin²(A/2)

(iii) (b + c) cos A + (a + c) cos B + (a + b) cos C

From law of cosines, we know:

cos A = (b² + c² − a²) / (2bc)

cos B = (a² + c² − b²) / (2ac)

cos C = (a² + b² − c²) / (2ab)

Substituting:

(b + c) (b² + c² − a²) / (2bc) + (a + c) (a² + c² − b²) / (2ac) + (a + b) (a² + b² − c²) / (2ab)

Common denominator:

(ab + ac) (b² + c² − a²) / (2abc) + (ab + bc) (a² + c² − b²) / (2abc) + (ac + bc) (a² + b² − c²) / (2abc)

[(ab + ac) (b² + c² − a²) + (ab + bc) (a² + c² − b²) + (ac + bc) (a² + b² − c²)] / (2abc)

We have to distribute, which is messy.  To keep things neat, let's do this one at a time.  First, let's look at the a² terms.

-a² (ab + ac) + a² (ab + bc) + a² (ac + bc)

a² (-ab − ac + ab + bc + ac + bc)

2a²bc

Repeating for the b² terms:

b² (ab + ac) − b² (ab + bc) + b² (ac + bc)

b² (ab + ac − ab − bc + ac + bc)

2ab²c

And the c² terms:

c² (ab + ac) + c² (ab + bc) − c² (ac + bc)

c² (ab + ac + ab + bc − ac − bc)

2abc²

Substituting:

(2a²bc + 2ab²c + 2abc²) / (2abc)

2abc (a + b + c) / (2abc)

a + b + c

Answer:

A19

Step-by-step explanation:

Answer:

-16/8 or -16÷8 equals -2 which is a whole number

an integer is a whole number that is positive ,negative or zero

Examples of integers: 1, 2, -5, -18, 20

Not Integers: 0.2, 9.15, 2/3

Final answer:

The division of -16 by 8 results in -2, which is an integer because it has no decimal component. Therefore, -16/8 is an integer.

Explanation:

The question is whether -16/8 is an integer. To determine this, we simply perform the division: -16 divided by 8 equals -2. Since -2 has no decimal component, it is indeed an integer. Integers are whole numbers that can be positive, negative, or zero, but do not include fractions or decimals. Examples of integers include -8, -6, -2, 0, 4, and 12. In this case, -16/8 simplifies precisely to -2, which is an integer.

Answer:

Associative  

Step-by-step explanation:

The associative property of addition states that you can add numbers however they are grouped inside parentheses.  

It doesn't matter where you put the parentheses. You will always get the same answer.

For example,

[tex]\begin{array}{rcl}(5 + 3) + 7 & = & 5 + (3 + 7)\\8 + 7& = & 5 + 10\\15 & = & 15\\\end{array}[/tex]

The expression with the greatest value among the options is |-14|, which equals 14. This is because absolute value operation gives always a positive result and ignores the negative sign in front of the number.

This is a question about absolute value, which is a mathematical operation that measures distance from zero on the number line. Regardless of direction, an absolute value always yields a positive result. In the absolute value operation | -14 |, the negative sign is disregarded and the result is 14. Similarly, | -8 | equals 8, | 3 | equals 3, and | 12 | equals 12. Thus, the greatest value among these options is | -14 |, which equals 14.

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The product of 2 and the sum of a number and 8 is equivalent to 16 is 2(n + 8) = 16 which is the correct answer would be an option (B)

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

To determine the product of 2 and the sum of a number and 8 is equivalent to 16

Let the number n

According to the problem,

The sum of a number and 8 is

⇒ n + 8

So,  n + 8

Now, the product of 2 and the sum of a number and 8 is

⇒ 2*(n + 8)

Now, the product of 2 and the sum of a number and 8 is equivalent to 16

So,  2(n + 8) = 16

Hence, the product of 2 and the sum of a number and 8 is equivalent to 16 is 2(n + 8) = 16

Learn more about Arithmetic operations here:

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The correct equation modeling the problem is B. 2(n + 8) = 16. This represents the product of 2 and the sum of a number and 8 being equivalent to 16.

The problem states: 'The product of 2 and the sum of a number and 8 is equivalent to 16.' To model this sentence mathematically, consider the steps involved:

Hence, the correct equation that models this sentence is B. 2(n + 8) = 16.

Answer:

You would do $1.25 multiplied by 2.4 and the answer will be $3.

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

okay first you multiply 1.25*2.4

1.25*2.4

Now you solve it

3

Answer:

144

Step-by-step explanation:

Data:

Emily's age : 46 years old

Find Colin's age

Colin's age: 11 years older than Emily

                    Emily's age + 11

                    46 + 11 = 57 years old

Find Dan's age

Dan's age: 5 years younger than Emily

                  Emily's age - 5

                  46 - 5 = 41 years old

Find their combined ages

Combined ages: Emily's age + Colin's age + Dan's age

Combined ages = 46 + 57 + 41

Total = 144

Therefore, the total of their combined ages is 144.

Answer:

36/5

Step-by-step explanation:

x/3 + 6 -2x = -6

multiply the whole equation by 3 to get rid of the denominator of the first x term.

x+18-6x = -18

move x terms to one side and numerical terms to the other, subtract 18 from both sides in this case

x+18-6x-18=-18-18

x-6x = -36

simplify

-5x = -36

divide both sides by -5 to isolate x

x = -36/-5

=36/5

Answer:X = 2

Step-by-step explanation:

Apply the distributive property.

2x+2⋅5+4(x−9)=−142x+2⋅5+4(x-9)=-14

Multiply 22 by 55.

2x+10+4(x−9)=−142x+10+4(x-9)=-14

Apply the distributive property.

2x+10+4x+4⋅−9=−142x+10+4x+4⋅-9=-14

Multiply 44 by −9-9.

2x+10+4x−36=−142x+10+4x-36=-14

Simplify by adding terms.

6x−26=−146x-26=-14

Move all terms not containing xx to the right side of the equation.

Add 2626 to both sides of the equation.

6x=−14+266x=-14+26

Add −14-14 and 2626.

6x=126x=12

Divide each term by 66 and simplify.

Divide each term in 6x=126x=12 by 66.

6x6=1266x6=126

Cancel the common factor of 66.

x=126x=126

Divide 1212 by 66.

x=2

Answer:

(-1, -1.5)

Step-by-step explanation:

A coordinate is a point (a single place) on a graph. Coordinates can be recorded as (#, #).

The first number is the one on the x-axis (left/right) and the second number is the one on the y-axis (up/down). (x, y) The middle point, where the x-axis and y-axis meet is called the origin, and is at (0,0).

The point that marks the campground is at -1 on the x-axis and -1.5 on the y axis.

Because the y-axis has two lines for every whole number, the line in between is the halfway mark and counts as a 0.5 increment.

Answer:

15 students

Step-by-step explanation:

5 DIVIDED by 8

You then multiply by 24

The method i just explained is known as cross multiplication

By multiplying the total number of students (24) by the fraction (5/8), we find that 15 students earned an A on their geometric unit assessment in Mr. Bonogofsky's class.

In Mr. Bonogofsky's math class, there are 24 students. If 5/8 of the students earned an A on the geometric unit assessment, we would need to multiply the total number of students by 5/8 to determine how many got an A.

Here's how to do it: 5/8 * 24 = 15

So, 15 students in Mr. Bonogofsky's class earned an A on the geometric unit assessment.

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Answer:832,719

Step-by-step explanation:

For this problem it wants you to subtract 10,000 from 842,719, or 842,719-10,000, which gives you 832,719.

Answer:

9

Step-by-step explanation:

its difficult to explain but I found that there is a 10.3%Tax so 10.3% of 93 is 9

The sales tax on the second item, which cost $93 before tax, would be approximately $8.99 based on the tax rate of the first item.

To determine the amount of sales tax on the second item, we first need to understand the rate of sales tax applied to the first item. The sales tax on the first item was $21 on a pre-tax cost of $217. So, the tax rate would be 21 divided by 217, which is approximately 0.0967, or 9.67%.

If we apply this tax rate to the second item, which costs $93 before tax, we get 93 times 0.0967, or $8.99. Therefore, the amount of sales tax on the second item would be approximately $8.99.

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Answer: 1 hour and 45 min

Step-by-step explanation:

From 5:30 to 6 is 30 min

From 6 to 7 is 1 hour

And finally from 7 to 7:15 if 15 min

If we add all of the times up, we get 1 hour and 45 min, so it took them an hour and 45 min to eat dinner

Answer:

9/4

Step-by-step explanation:

Answer:

undefined

Step-by-step explanation:

The formula for a slope is m=[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

Let's say (8,1) represents [tex]x_{1}[/tex] and [tex]y_{1}[/tex],

and (8,-6) represents [tex]x_{2}[/tex] and [tex]y_{2}[/tex]

m= [tex]\frac{(-6)-1}{8-8}[/tex]

m= [tex]\frac{-7}{0}[/tex]

A number can't be divided by 0, so the answer would be undefined.

m= undefined

Answer:

111.25 ft.

Step-by-step explanation:

Answer:

7000 - 24x = y(the amount he can sell the car for)

Step-by-step explanation:

Answer:

7000 - 24x

Step-by-step explanation:

Johnny bought a car for $7000  about 2 years ago.

He wants to sell his car now.

The monthly depreciation amount = $x

2 years = 2 x 12 = 24 months.

The amount of depreciation for 2 years = 24x.

The expression that shows how much money he can get now by selling the car = Amount paid 2 years ago - depreciation for 2 years

= 7000 - 24x

Therefore, the answer is 7000 - 24x

Answer:

5.9

Step-by-step explanation:

The answer should be 5.9, is it multiple choose or type in your answer? But it should be 5.9

Answer:

4/9.1

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

10x = 4x + 66

10x - 4x = 66

 6x = 66

 x = 66/6

 x= 11

Answer:

x=11

Step-by-step explanation:

10(11)=4(11)+66

110=44+66

110=110

CAN EXPLAIN FURTHER

WOULD GREATLY APPRECIATE BRAINLIEST ANSWER

Answer:

Mean = 93.3 ( to nearest tenth).

Median = 97.

Mode = 97.

Step-by-step explanation:

Arrange the data in ascending order:

79 82 87 91 93 97 97 98 99 101 102

There are 11 numbers.

The Median is the center value (= the 6th number) = 97.

The mode = highest occurring value = 97.

The mean = sum / 11 = 93.3.

now, let's notice that 23 days is not even a month let alone a year, assuming there are 365 days in a year, then 23 days is really 23/365 of a year.

[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill&\$11.88\\ P=\textit{original amount deposited}\dotfill & \$1200\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &\frac{23}{365} \end{cases}[/tex]

[tex]\bf 11.88=(1200)(r)\left(\cfrac{23}{365} \right)\implies 11.88=\cfrac{(1200)(23)r}{365}\implies 11.88=\cfrac{27600r}{365} \\\\\\ 4336.2=27600r\implies \cfrac{4336.2}{27600}=r\implies 0.157\approx r \\\\\\ \stackrel{\textit{converting that to a percentage}}{0.157\cdot 100 \approx r}\implies \stackrel{\%}{15.7}\approx r[/tex]

Step-by-step explanation:

6 is divisible by 2 and 3 (6 = 2 · 3).

257 is not divisible by 2 and 3 (257 is a prime number).

Therefore 257 is't divisible by 6.

Final answer:

257 is not divisible by 6 because it is not even.

A number must be even and the sum of its digits divisible by 3 to be divisible by 6.

Explanation:

To determine if 257 is divisible by 6, we need to check if it satisfies the criteria for divisibility by 6.

A number is divisible by 6 if it is divisible by both 2 and 3.

Examining 257, we see that it ends with a 7, which is not an even number.

So it does not meet the criterion for divisibility by 2.

Therefore, 257 is not divisible by 6.

Answer:

y - 2 = [tex]\frac{1}{3}[/tex](x - 3)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = [tex]\frac{1}{3}[/tex] and (a, b) = (3, 2), thus

y - 2 = [tex]\frac{1}{3}[/tex](x - 3) ← in point- slope form

We want to find the equation of a line in the point-slope form, such that we know the slope and a point on the line.

The line will be: y - 2 = (1/3)*(x - 3)

Let's see how to find that line:

We know that our line has a slope equal to 1/3, and that it passes through the point (3, 2).

First, a general line in the point-slope form is:

y - y₁ = a*(x - x₁)

Where a is the slope and (x₁, y₁) is the point on the line.

Then, by using that general form and the given information, we can see that our line is:

y - 2 = (1/3)*(x - 3)

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Answer:

Step-by-step explanation:

so what your gonna do is you are going to add 81 to 360 and then sum it up. after you are going to divide it by 3.5.

This might be wrong but there is always a point where you have to try :)

Answer:

This is how you could anwser

283.5 or 283 1/2

Answer:

Step-by-step explanation:

Lines are considered to be perpendicular if the angle between at the point they intersect is 90°, or a right angle.

If you have the equations of two lines, you can determine if they are perpendicular by looking at their slope. For the slope-intercept form of a line,

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

[tex]m[/tex] is the slope of the line.

Two lines are considered perpendicular, if the slope of one line is [tex]m[/tex], and the slope of the other line is [tex]\frac{1}{-m}[/tex].

For example, if a line had a slope of 4, say [tex]y = 4x + 2[/tex], then a line that would be perpendicular to this line would have a slope of [tex]\frac{-1}{4}[/tex], say [tex]y = \frac{-1}{4} + 7[/tex].

The expression is simplified by dividing each term and exponent separately. After simplification, the expression becomes [tex]\(2x^{10}y^{12}\)[/tex], corresponding to option b.

To simplify the given expression [tex]\(\frac{60x^{20}y^{24}}{30x^{10}y^{12}}\)[/tex], we can simplify the numerator and denominator separately, then divide.

First, let's simplify the numerator:

[tex]\[ \text{Numerator: } 60x^{20}y^{24} \][/tex]

Now, let's simplify the denominator:

[tex]\[ \text{Denominator: } 30x^{10}y^{12} \][/tex]

Now, we divide the simplified numerator by the simplified denominator:

[tex]\[ \frac{60x^{20}y^{24}}{30x^{10}y^{12}} = \frac{60}{30} \times \frac{x^{20}}{x^{10}} \times \frac{y^{24}}{y^{12}} \\\[ = 2 \times x^{20-10} \times y^{24-12} \\\[ = 2 \times x^{10} \times y^{12} \][/tex]

[tex]\[ = 2x^{10}y^{12} \][/tex]

So, the expression equivalent to [tex]\( \frac{60x^{20}y^{24}}{30x^{10}y^{12}} \)[/tex] is:

b. [tex]\( 2x^{10}y^{12} \)[/tex]

The probable question may be:

Which expression is equivalent to 60x^(20)y^(24)/30x^(10)y^(12)?

a. 2x^2y^2

b. 2x^(10)y^(12)

c. 30x^2y^2

d. 30x^(10)y^(12)