5 friends share 3 bags of trail mix equally. What fraction of a bag of trail mix does each friend get?

Answer:

[tex]\large\boxed{A.\ 0}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}ax+by=c\\dx+ey=f\end{array}\right\\\\D=\left|\begin{array}{ccc}a&b\\d&e\end{array}\right|=ae-bd\\\\D_x=\left|\begin{array}{ccc}c&b\\f&e\end{array}\right|=ce-fb\\\\D_y=\left|\begin{array}{ccc}a&c\\d&f\end{array}\right|=fa-cd\\\\\text{If}\ D\neq 0\ \text{then the system of equations has one solution}\ x=\dfrac{D_x}{D}\ and\ y=\dfrac{D_y}{D}\\\\\text{If}\ D=0\ \text{and}\ D_x=0\ \text{and}\ D_y=0\ \text{then the system of equations has}\\\text{infinitely many solutions.}\\\\\text{If}\ D=0\ \text{and}\ D_x\neq0\ \text{or}\ D_y\neq0\ \text{then the system of equations has}\\\text{no solutions.}[/tex]

[tex]\text{We have}\\\\\left\{\begin{array}{ccc}3x+4y=12\\x-6y=-18\end{array}\right\\\\D=\left|\begin{array}{ccc}3&4\\1&-6\end{array}\right|=(3)(-6)+(1)(4)=-18+4=-14\\\\D_x=\left|\begin{array}{ccc}12&4\\-18&-6\end{array}\right|=(12)(-6)-(-18)(4)=-72+72=0\\\\x=\dfrac{D_x}{D}\to x=\dfrac{0}{-14}=0[/tex]

Using Cramer's Rule, the value of x in the given system of linear equations is approximately -5.09.

To solve the system of linear equations using Cramer's Rule, we need to find the determinants of the coefficient matrix and the matrices obtained by replacing the corresponding column of the coefficient matrix with the constant matrix. Let's find the determinants:

Determinant of the coefficient matrix = |3 -4| = (3)(-6) - (4)(1) = -18 - 4 = -22

Determinant of the matrix obtained by replacing the x column = |-18 -4| = (-18)(-6) - (-4)(1) = 108 - (-4) = 112

Now, using Cramer's Rule:

x = Determinant of the matrix obtained by replacing the x column / Determinant of the coefficient matrix

x = 112 / -22 = -5.09

Therefore, the value of x in the given system of linear equations is approximately -5.09.

Answer:

1.85 gallons

Step-by-step explanation:

1 gallon = 3.785 liters

(7 liters)/(3.785 liters/gallon) = 1.85 gallons

Answer:

1.8492

Step-by-step explanation:

for an approximate result, divide the volume value by 3.785

Answer:

51°

Step-by-step explanation:

The sum of all exterior angles of any polygon is always 360°.

To find the measure of one of these angles, divide 360° by the number of sides of the polygon

In this case, we have 7 sides, so

m = 360°/7 = 51.42°, or 51° rounded to the nearest degree

Answer:

for ape x its 51

Step-by-step explanation:

45.00x +17.99 = 422.99 (Setup Equation)

45.00x = 405 (Subtract 17.99 from both sides)

x = 9 (Divide both sides by 45.00)

Answer:

9

Step-by-step explanation:

First, you write out the equation. We don't know how many tickets Eva bought, so it can be represented by x. Each ticket costs 45 dollars. The amount of tickets times 45 plus the fee will equal 422.99, so the equation will look like this:

45x + 17.99 = 422.99

Subtract 17.99 from both sides:

45x = 405

Divide 45 on both sides:

x = 9

Eva bought 9 tickets

hope this helps :)

Answer:

See below.

Step-by-step explanation:

15 - -5

= 15 - 1(-5)

= 15 + 5

= 20.

Answer:

15--5

add the negatives so its positive.

15+5=20

Step-by-step explanation:

Answer:

The least number of pizza make deal 1 better than deal 2 is 4

The cost of deal 1 is $53.99 and the cost of deal 2 is $60

The cost per pizza of deal 1 is $5.399

The better deal is deal 1

Step-by-step explanation:

* Deal 1 becomes better if it costs less than deal 2

- Assume that the number of pizza are n

* Deal 1:

∵ The cost of one large pizza = $8.99 for first 1 and = $5 for each

   additional one

∵ They ordered n large pizza

∴ The cost = 8.99 + 5(n - 1)

- Multiply the bracket by 5

∴ The cost = 8.99 + 5n - 5

- Add like terms

∴ The cost = 3.99 + 5n

∴ The cost of deal 1 = 3.99 + 5n

* Deal 2:

∵ The cost of any large pizza is $6

∵ They ordered n large pizza

∴ The cost = 6 × n = 6n

∴ The cost of deal 2 = 6n

- We need Deal 1 better than deal 2

- Then, put the cost of deal 1 < the cost of deal 2

∵ 3.99 + 5n < 6n

- Subtract 5n from both sides

∴ 3.99 < n

∴ n > 3.99

∴ n = 4

* The least number of pizza make deal 1 better than deal 2 is 4

∵ n = 10

∴ The cost of deal 1 = 3.99 + 5(10) = 53.99

∴ The cost of deal 2 = 6(10) = 60

* The cost of deal 1 is $53.99 and the cost of deal 2 is $60

∵ The cost per one pizza = total cost ÷ the number of pizza

∴ The cost per pizza of deal 1 = 53.99 ÷ 10 = 5.399

* The cost per pizza of deal 1 is $5.399

∵ The unit price of deal 1 is $5.399

∵ The unit price of deal 2 is $6

∵ $5.399 < $6

∴ The unit rate of deal 1 is less than the unit price of deal 2

* The better deal is deal 1

Deal #1 becomes a better deal at 4 pizzas. The cost of 10 pizzas for Deal #1 is $43.99, and for Deal #2 is $60.00. The cost per pizza in Deal #1 is $8.99 for the first pizza and $5 for each additional pizza. Deal #1 is the better deal when ordering 4 or more pizzas because the cost per pizza decreases as more pizzas are added to the order.

To determine at what number of pizzas Deal #1 becomes a better deal than Deal #2, we need to compare the total cost of pizzas under each deal.

For Deal #1, the cost structure is as follows:

The first pizza costs $8.99.

Each additional large pizza on the same order costs $5.

For Deal #2, the cost is a flat rate of $6.00 per large pizza.

Let's first find out at what point the total cost of pizzas under Deal #1 equals the total cost under Deal #2. We'll denote the number of additional pizzas (after the first one) as 'n'.

The total cost for Deal #1 can be expressed as:

[tex]\[ C_1 = 8.99 + 5n \][/tex]

The total cost for Deal #2 is:

[tex]\[ C_2 = 6(n + 1) \][/tex]

We set [tex]\( C_1 \) equal to \( C_2 \)[/tex]  to find the break-even point:

[tex]\[ 8.99 + 5n = 6(n + 1) \][/tex]

[tex]\[ 8.99 + 5n = 6n + 6 \][/tex]

[tex]\[ 8.99 - 6 = 6n - 5n \][/tex]

[tex]\[ 2.99 = n \][/tex]

Now let's calculate the cost of 10 pizzas for each deal:

For Deal #1:

[tex]\[ C_{10} = 8.99 + 5(10 - 1) \][/tex]

[tex]\[ C_{10} = 8.99 + 5 \times 9 \][/tex]

[tex]\[ C_{10} = 8.99 + 45 \][/tex]

[tex]\[ C_{10} = \$43.99 \][/tex]

For Deal #2:

[tex]\[ C_{20} = 6 \times 10 \][/tex]

[tex]\[ C_{20} = \$60.00 \][/tex]

The cost per pizza in Deal #1 is $8.99 for the first pizza and $5 for each additional pizza. As the number of pizzas increases, the average cost per pizza decreases.

b. 0.9 million dollars

Answer:

Option a

Step-by-step explanation:

Given that in the first week of its release, the latest video game sold $4.5 million dollars in games.

[tex]P_t=P_0e^{-0.4t}[/tex]

To find out the predicted game sales to the nearest $0.1 million for the fifth week of this game’s release we have to substitute t =5

P0 = initial sales of games = 4.5 million

Thus substitute to get

[tex]P(5) =4.5 e^{-0.4*5} =0.609[/tex] million

Hence when rounded off to 0.1 million we have

0.6 million dollars

Option a

Answer:

V =64 cm^3

Step-by-step explanation:

The volume of a cube is given by

V =s^3

We know the side length is s=4

V =4^3

V =64 cm^3

V = 64 cm ^ 3

V = s 3   x

s = 4

V = 4 ^ 3

V = 64 cm x  3

Answer:

the interest rate is $183.89 =~ $ 184

Step-by-step explanation:

In this question, Antuan deposited $2590 into a 3 year CD (Certificate of Deposit)  at an interest rate of 2.3% compounded quarterly. We need to find the interest account earned after 3 years.

Formula used will be :

[tex] Interest = P ( 1 + r/n) ^ n ^ t - P[/tex]

Where

P= Principal amount

r= interest rate (in decimals)

n= no of times the interest is compounded

t = no of years

Here we are subtracting P because we only need interest amount and not the future value.

Using this formula and finding the value will be:

P= $2590

r = 2.3 % or 0.023

n = 4

t = 3

[tex]Interest = 2590 * ( 1 - 0.023 / 4) ^ 4^ * ^ 3 - 2590[/tex]

[tex]Interest= 2590 (1.071) -2590\\Interest= 2773.89 - 2590\\Interest= 183.89[/tex]

So the interest rate is $183.89 =~ $ 184

The new price is $15.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Original Price: $20.

Discount Rate: 25%.

The discount amount,

= 25% of 20

= 5

The price,

= 20 - 5 = $15

Therefore, $15 is the new price.

To learn more about the percentage;

https://brainly.com/question/24159063

#SPJ2

Answer:

a = 102.05

b = 393.76

B = 93°

Step-by-step explanation:

The law of sines tells you ...

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

Since the sum of angles in a triangle is 180°, angle B must be ...

B = 180° -72° -15° = 93°

and the unknown sides must be ...

a = c/sin(C)·sin(A) = 375·sin(15°)/sin(72°) ≈ 102.05192

B = 93°

b = 375·sin(93°)/sin(72°) ≈ 393.75796

_____

The rounding requirement got cut out of your picture, so we can't help you with that.

Answer: 1,340 :)

Step-by-step explanation:

44*13= 572

96*8=768

572+768=1,340

Final answer:

The expression to calculate the total number of beads Lola used to make 13 bracelets and 8 necklaces is 13 × 44 + 8 × 96, with the total being 1340 beads.

Explanation:

To calculate the total number of beads Lola used to make 13 bracelets and 8 necklaces, we need to consider the number of beads used for one bracelet and one necklace individually. For one bracelet, Lola uses 44 beads, and for one necklace, she uses 96 beads.

Now, we add the two quantities together to get the total number of beads used:

572 beads (for bracelets) + 768 beads (for necklaces) = 1340 beads

Therefore, the expression to calculate the total number of beads used is 13 × 44 + 8 × 96.

Answer: -13

j(5)=11

k(5)=24

11-24=-13

Your answer is (C) !

The correct equation to find the amount of time they spent swimming laps is:

[tex]c. \( \frac{1}{2} \times 1 \frac{1}{2} \)[/tex]

To find the amount of time Paul and Krystal spent swimming laps, we need to determine what half of 1 1/2 hours is. This can be calculated by multiplying 1 1/2 by 1/2.

Let's look at the options:

a. [tex]\( 1 \frac{1}{2} - \frac{1}{2} \):[/tex] This would subtract 1/2 hour from 1 1/2 hours, which is not what we need.

b. [tex]\( 1 \frac{1}{2} \div \frac{1}{2} \):[/tex]This would divide 1 1/2 hours by 1/2, which is not what we need.

c. [tex]\( \frac{1}{2} \times 1 \frac{1}{2} \):[/tex]This is the correct operation, as it multiplies 1 1/2 hours by 1/2 to find half of the time.

d.[tex]\( \frac{1}{2} + 1 \frac{1}{2} \):[/tex] This would add 1/2 hour to 1 1/2 hours, which is not what we need.

So, the correct equation to find the amount of time they spent swimming laps is:

[tex]c. \( \frac{1}{2} \times 1 \frac{1}{2} \)[/tex]

Let's calculate it:

[tex]\[\frac{1}{2} \times 1 \frac{1}{2} = \frac{1}{2} \times \frac{3}{2} = \frac{3}{4} \text{ hours}\][/tex]

Therefore, Paul and Krystal spent [tex]\( \frac{3}{4} \)[/tex] hours (or 45 minutes) swimming laps.

Answer:

Step-by-step explanation:

The difference between double the first purchase and the second purchase is $7 and 2 pounds of jelly beans. Hence a pound of jelly beans is $3.50.

  (4t +8j) -2(2t +3j) = (33) -2(13) . . . . . let t and j represent pounds of trail mix and jelly beans, respectively

  2j = 7 . . . . . . . . . . simplify

  j = 7/2 = 3.50

Using that value in the first purchase, we get ...

  2t +3(3.50) = 13

  2t = 13 -10.50

  t = 2.50/2 = 1.25

A pound of trail mix is $1.25.

Answer:

The dimensions ⇒ 3 × 4

Step-by-step explanation:

* Any matrix has two dimensions

- Raw and column

- The dimensions very important in the operations on matrices

- We called the number of raw m and the number of column n

- We must write the number of raw before the number of column

- m × n is the dimensions of the matrix

* Example : If the dimension of a matrix is 2 × 3, that

  means the matrix has 2 raw and 3 column

* Now lets look to our problem

∵  It has 3 raw and 4 column

∴ Its dimensions is 3 × 4

Answer:

Size of matrix = 3 × 4

Step-by-step explanation:

We are given the following matrix and we are to determine its dimensions:

[tex] \left [ \begin {array}{cccc} 1&-3&8&4\\7&5&3&0\\9&6&-2&-1 \end { array } \right ] [/tex]

We know that the dimension of a matrix is written in the form:

rows × columns

Here we have 3 rows and 4 columns. Therefore, the size of this matrix is 3 × 4.

Answer:

The new points would be (-7, -1), (-3, -2) and (-8, 1). The angle would not change

Step-by-step explanation:

When you rotate points by 180 degrees, you simply change the sign on the ordered pairs. This will give you the new points.

Also, spinning the points will not change the angle between them. Therefore it stays the same.

Answer:

D p^2 +3p -10

Step-by-step explanation:

(p+5) (p-2)

FOIL

First  p*p = p^2

Outer  -2*p = -2p

Inner  5*p = 5p

Last  -2 *5= -10

Add them together

p^2 -2p+5p -10

p^2 +3p -10

Answer:

Their answer is correct.

Step-by-step explanation:

Answer:

1/4 of the pan

Step-by-step explanation:

1/3 of 3/4 = 1/4

Answer:   [tex]\bold{\dfrac{41}{80}}[/tex]

Step-by-step explanation:

[tex]\dfrac{puppies}{total}+\dfrac{kittens}{total}+\dfrac{unicorns}{total}\\\\\\=\dfrac{15}{80}+\dfrac{16}{80}+\dfrac{10}{80}\\\\\\=\large\boxed{\dfrac{41}{80}}[/tex]

Answer:

  length: 10 ft; width: 7 ft.

Step-by-step explanation:

Factorizations of 70 are ...

  70 = 1·70 = 2·35 = 5·14 = 7·10

The last pair of numbers has the relation that 2·7 -10 = 4, so the numbers 7 and 10 can be used for width and length.

The length is 10 ft; the width is 7 ft.

ANSWER

8π ft

EXPLANATION

The circumference of a circle is calculated using the formula C=πd.

Where d=8 is the diameter of the circle.

We substitute d=8 into the formula to obtain,

C=8π ft.

Because we are looking for the exact circumference, we leave the answer in terms of π.

Answer:

The correct answer is,

circumference = 8π feet

Step-by-step explanation:

Formula:-

Circumference of a circle = 2πr

Or circumference = πd

Where 'r' is the radius of circle and 'd' is the diameter of circle

It is given that, diameter of circle is 8 feet

To find the circumference

Here d= 8 feet

Circumference = πd = π * 8 = 8π feet

7 inches best 7 x 2 = 14 / 2 = 7 inches

Answer:

  17.  37 2/7

  20.  3.4

Step-by-step explanation:

17.  The scale factor of the smaller triangle PQR to the larger triangle LMN is given by the ratio of corresponding sides:

  RP : NL = 18 : 28 = 9 : 14

The perimeter of LMN is the sum of the lengths of its sides:

  16 + 14 + 28 = 58

So, the perimeter of PQR is ...

  (9/14)×58 = 261/7 = 37 2/7 . . . . units

__

20. By the same reasoning as above, the sides of triangle RQP are 25/40 = 5/8 of those of triangle MNP. Then ...

  RQ = (5/8)·MN

  5x -2 = (5/8)·24 = 15 . . . . substitute the measures shown

  5x = 17 . . . . . add 2

  x = 17/5 = 3.4 . . . . . . divide by 5

The value of x is 3.4.

Answer:

260 cm

Step-by-step explanation:

formula for finding volume:

l x w x h = v

l=length   w=width    h=height    v=volume

[tex]10\frac{2}{5}[/tex] × 3 × [tex]8\frac{1}{3}[/tex]

[tex]10\frac{2}{5}[/tex] = [tex]\frac{52}{5}[/tex]

how did i do that?

cross multiply the whole number and the denominator together and add the product by the numerator.

[tex]8\frac{1}{3}[/tex] = [tex]\frac{25}{3}[/tex]

so, [tex]\frac{52}{5}[/tex] × [tex]\frac{25}{3}[/tex] × [tex]\frac{3}{1}[/tex]

cross simplify(dont have to do it just makes everything easier)

and you get:

[tex]\frac{52}{1}[/tex] × [tex]\frac{5}{1}[/tex] × [tex]\frac{1}{1}[/tex]

and you get [tex]\frac{260}{1}[/tex]

[tex]\frac{260}{1}[/tex] = 260 cm

plz give me a brainliesttttt

Answer:

Step-by-step explanation:

52/5 x 3/1 x 25/3= 3900/15= 260 cm^3

Answer:

they became "roamin' numerals"

Step-by-step explanation:

ANSWER

D) 4n

EXPLANATION

You can observe the following pattern from the table.

For the first term, we have,

[tex]1\to 4(1)[/tex]

For the second term, we have,

[tex]2\to 4(2) = 8[/tex]

For the third term, we have,

[tex]3\to 4(3) = 12[/tex]

For the fourth term,

[tex]4\to 4(4) = 16[/tex]

For the nth term, we will have,

[tex]n\to 4(n)[/tex]

The correct choice is D.

Answer:

Yo ________ en el mar.

A. nadó

b. nadé

c. nadamos

Step-by-step explanation:

Explanation:

The first determinant is that of the matrix of coefficients:

[tex]|A|=\left|\begin{array}{cc}5&2\\-3&-5\end{array}\right|=(5)(-5)-(-3)(2)=-19[/tex]

The second determinant is the same as the above but with the constants substituted for the x-coefficients.

[tex]|A_x|=\left|\begin{array}{cc}14&2\\3&-5\end{array}\right|=(14)(-5)-(3)(2) =-76[/tex]

The third determinant is the same as the first but with the constants substituted for the y-coefficients.

[tex]|A_y|=\left|\begin{array}{cc}5&14\\-3&3\end{array}\right|=(5)(3)-(-3)(14)=57[/tex]

_____

The solution to the system of equations is then ...

[tex]x=\dfrac{|A_x|}{|A|}=\dfrac{-76}{-19} =4\\\\y=\dfrac{|A_y|}{|A|}=\dfrac{57}{-19} =-3[/tex]

Answer:

the exterior angles of a polygon sum to 360

so the number of sides is 360/45

-PlushDna

Answer:

The difference in number of sides from one park to the next is 7

Step-by-step explanation:

For all polygon's the exterior angles combine to measure to 360 degrees. So to find the number of sides of each gazebo, we simply divide 360 by the measure of each individual exterior angle. We'll start with Logan Park.

360/22.5 = 16 sides

Now we can do the same with Cerro Park.

360/15.65 = 23 sides

Therefore, the difference in sides would be 7

23 - 16 = 7