A case of Mountain Dew (24 cans) cost $7.68. What is the unit price?

Answer:

Brian has 12 apples. How many more apples does he need to have 30 apples in all?

Step-by-step explanation:

In this case "a" is the number of apples he needs to have 30 in all, and adding that to 12 results in the equation a + 12 = 30.

Hope this helps!

Let's consider each of the options and evaluate whether the given number is rational or not. Remember, a rational number is any number that can be expressed as the quotient or fraction of two integers (where the denominator is not zero).
1. **3•π**: This number is not rational because π (pi) is an irrational number. An irrational number is a number that cannot be expressed as a simple fraction - its decimal goes on forever without repeating. When you multiply an irrational number by an integer (in this case 3), the result is still irrational.
2. **2/3 + 9.26**: To determine if this sum is rational, we can evaluate each addend. The fraction 2/3 is clearly rational, as it is already expressed as a quotient of two integers. The decimal 9.26 can be expressed as a fraction because it is a terminating decimal; in fraction form, it is \( \frac{926}{100} \) which simplifies to \( \frac{463}{50} \) when reduced to lowest terms. The sum of two rational numbers is also rational (since both can be written as fractions, and the sum of two fractions is a fraction), so this number is indeed rational.
3. **45 + 36**: Both 45 and 36 are integers and the sum of two integers is also an integer. Integers are a subset of rational numbers, because they can be expressed as a fraction with a denominator of 1 (e.g., \( \frac{45}{1} + \frac{36}{1} \)). Thus, this number is rational.
4. **14.3 + 5.78765239**: The number 14.3 is a terminating decimal and can be represented as a fraction (\( \frac{143}{10} \)). However, 5.78765239 is given without any indication that it is a repeating or terminating decimal. If it is a non-repeating and non-terminating decimal, then it cannot be expressed as a fraction and would be considered irrational. Without further information, we cannot determine if this number is rational or not. Therefore, we can neither confirm nor deny that the sum is rational.
Given these considerations, the rational option from the given choices is **45 + 36**.

Answer:

the Answer is 60 miles.

Step-by-step explanation:

The current of the river is towards city B; hence, the reason the ferry moves faster from town A to B than when coming back from town B to A. The distance between both towns is 60m.

Let

[tex]s \to[/tex] speed in still water

[tex]d \to[/tex] distance between both cities

The given parameters are:

[tex]t_{AB} =2[/tex] -- from A to B

[tex]t_{BA} =1.5[/tex] -- from B to A

[tex]s_c = 5mph[/tex] -- speed of the current

Speed is calculated as:

[tex]Speed = \frac{Distance}{Time}[/tex]

The speed (s) from town A to town B is:

[tex]s = s_c + \frac{d}{t_{AB}}[/tex] --- i.e. speed of the current + speed in still water from A to B

[tex]s = 5 + \frac{d}{2}[/tex]

Multiply through by 2

[tex]2s = 10 + d[/tex]

Make d the subject

[tex]d = 2s - 10[/tex]

The speed (s) from town B to town Ais:

[tex]s = -s_c + \frac{d}{t_{BA}}[/tex] --- i.e speed in still water from B to A - . speed of the current

[tex]s = -5 + \frac{d}{1.5}[/tex]

Multiply through by 1.5

[tex]1.5s = -7.5 + d[/tex]

Make d the subject

[tex]d = 1.5s + 7.5[/tex]

So, we have:

[tex]d = 1.5s + 7.5[/tex] and [tex]d = 2s - 10[/tex]

Equate both values of d

[tex]2s - 10 = 1.5s + 7.5[/tex]

Collect like terms

[tex]2s - 1.5s= 10 + 7.5[/tex]

[tex]0.5s= 17.5[/tex]

Divide both sides by 0.5

[tex]s = 35[/tex]

Substitute [tex]s = 35[/tex] in [tex]d = 1.5s + 7.5[/tex] to calculate distance (d)

[tex]d =1.5 *35 + 7.5[/tex]

[tex]d =52.5 + 7.5[/tex]

[tex]d =60[/tex]

The distance between town A and B is 60m.

Read more about speed at

https://brainly.com/question/14750228

Answer:

11: 136 people

12: 55 Cherries

Answer:

You will use this formula x= -b +

[tex] x = - b + \sqrt{ { \: - 4ac}^{?} } [/tex]

Step-by-step explanation:

4n

[tex] {?}^{?} [/tex]

so you want to do n to the second power minus and minus 39 equals 0 so you using the quadratic formula

Answer:

5

Step-by-step explanation:

To solve with calculus, distance is the integral of speed:

d = ∫ |v| dt

d = ∫₀⁴ |t − 3| dt

d = -∫₀³ (t − 3) dt + ∫₃⁴ (t − 3) dt

d = ∫₀³ (3 − t) dt + ∫₃⁴ (t − 3) dt

d = (3t − ½ t²) |₀³ + (½ t² − 3t) |₃⁴

d = [ (9 − 9/2 ) − (0 − 0) ] + [ (8 − 12) − (9/2 − 9) ]

d = 9/2 + 1/2

d = 5

You can also find this geometrically.  Graph y = |x − 3|, then find the area under the curve.  You will find it's the area of two triangles.

d = ½ (3)(3) + ½ (1)(1)

d = 5

It's important to note that distance is not the same thing as displacement.  Displacement is the difference between where you start and where you stop.  Distance is length of the path you take.

Answer:

Sinx= 1(maximum value)

Step-by-step explanation:

Answer:

The maximum is 1

Step-by-step explanation:

-1<_sin(x)<_1

Range of sin(x)= [-1,1]

sin(x)= 1

Given

106 + (147x + 92)

Combine like terms

106 + 92 = 198

Simplify

147x + 198

Answer

147x + 198

106 + (147x + 92) = what

To solve this expression, you need to apply the distributive property, which states that a(b + c) = ab + ac.

Therefore, 106 + (147x + 92) = 106 + 147x + 92, which simplifies to 239 + 147x.

Answer:

Advance=15$

Same-day=20$

Step-by-step explanation:

Advance=15 Same-day=20

15*35=525

20*30=600

525+600=1125

Answer:

Step-by-step explanation:

The first thing you have to do is look at the mother curve. That curve is y = 1/x

It becomes undefined at x = 0 (I will show both curves below).

That is not what has been given. The graph you have been given becomes undefined at x = - 1 , so the equation of the curve (so far) y = 1/(x + 1)

Now we have to worry about the y intercept. When x = 0, y = 4. That can be accomplished in two ways

A. y = 4/(x + 1) or

B.  y = 2/(x + 1) + 2 or

C.  y = 1/(x + 1) + 3

All three of these will give a value of y = 4 when x = 0. But you have 1 problem left. What happens as x goes to say 5.

The value of A will give y = 4/(5 + 1)=4/6 = 2/3. Which does not work.

The value of C will give y = 1/(5 + 1) + 3 which gives 3 1/5 which also does not work.

Only B works. y = 2/(5+1) + 2 = 2/6 + 2 = 2 1/3 which is a little above the horizontal asymptote.

Red: y = 1/x

Blue: y = 2/(x + 1) + 2

The value at the end is never going to change. y will always be just a bit

Answer:

2w -8

Step-by-step explanation:

-4(w+2)+6w

Distribute the -4

-4w -8 +6w

Combine like terms

-4w  +6w   -8

2w -8

Answer:

Step-by-step explanation:

-4w-8+6w=0

8+2w=0

2w= -8

w= -4

Answer:

9

Step-by-step explanation:

Answer:

9 months

Step-by-step explanation:

There are 12 months in a year

Multiply 12 months by 3/4

12 *3/4

36/4

9

There are 9 months in 3/4 of a year

Answer:

=x/4 - 2 (the third choice.

Step-by-step explanation:

Letting the number be x, the phrase two less than a number divided by four is expressed using the following steps:

We first take the the number x then divide by four then subtract 2.

The expression becomes:

(x/4) - 2

To solve an algebraic expression such as the one you described – "two less than a number divided by four" – you can follow these steps:
1. Start by identifying the variable, which is typically represented by "x." In this case, "a number" will be our variable "x."
2. The phrase "two less than" indicates a subtraction of two from a certain value. In algebraic terms, "two less than x" would be written as "x - 2."
3. Finally, the phrase "divided by four" tells us to take our result from step 2 and divide it by 4. So, we place the expression "(x - 2)" over 4, indicating division.
Putting it all together, the algebraic expression that represents the phrase "two less than a number divided by four" is:
(x - 2) / 4
To evaluate this expression for a particular value of x, you would substitute the value of x into the expression and then perform the calculation.
For example, if x is 10, you would evaluate the expression as:
(10 - 2) / 4
= 8 / 4
= 2
So, when x is 10, the value of the expression "two less than a number divided by four" is 2.

Answer:

260 degrees is coterminal with -100 degrees.

Step-by-step explanation:

So a full rotation about a circle is 360 degrees.

So if we do 360+(-100) we get 260.

They will share the same terminal ray because if we go 100 clockwise from the initial ray that will be an angle coming counterclockwise 260 from the initial ray.

100+260=360.

Answer:

260°

Step-by-step explanation:

Co terminal angles are angle ± 360°n where n = 0, 1, 2, 3, ....

The least positive = - 100° + 360° = 260°

Answer:

[tex]\large\boxed{a_n=6\left(\dfrac{1}{10}\right)^{n-1}}[/tex]

Step-by-step explanation:

Check:

[tex]n=1\\\\a_1=6\left(\dfrac{1}{10}\right)^{1-1}=6\left(\dfrac{1}{10}\right)^0=6(1)=6\qquad\bold{CORRECT}\ (1,\ 6)\\\\n=2\\\\a_2=6\left(\dfrac{1}{10}\right)^{2-1}=6\left(\dfrac{1}{10}\right)^1=6\left(\dfrac{1}{10}\right)=\dfrac{6}{10}=0.6\qquad\bold{CORRECT}\ (2,\ 0.6)\\\\n=3\\\\a_3=6\left(\dfrac{1}{10}\right)^{3-1}=6\left(\dfrac{1}{10}\right)^2=6\left(\dfrac{1}{100}\right)=\dfrac{6}{100}=0.06\qquad\bold{CORRECT}\ (3,\ 0.06)[/tex]

Answer:

[tex]a_n=6\left(\frac{1}{10}\right)^{n-1}[/tex]

Option 3 is correct

Step-by-step explanation:

The coordinates are (1,6) (2,0.6) and (3,0.06)

If we make table of given coordinate:

x   :    1          2         3  

y   :   6        0.6     0.06

[tex]a_1=6,a_2=0.6,a_3=0.06[/tex]

Ratio of the sequence:

[tex]r=\dfrac{a_2}{a_1}=\dfrac{0.6}{6}=0.1[/tex]

Formula of geometric sequence:

[tex]a_n=ar^{n-1}[/tex]

[tex]a_n=6\cdot 0.1^{n-1}[/tex]

[tex]a_n=6\left(\frac{1}{10}\right)^{n-1}[/tex]

Hence, The sequence model by [tex]a_n=6\left(\frac{1}{10}\right)^{n-1}[/tex]

Answer:

y=4

Step-by-step explanation:

-9x - 3y = 6

Let x =-2

-9(-2) -3y =6

18 -3y =6

Subtract 18 from each side

18-18-3y = 6-18

-3y = -12

Divide each side by -3

-3y/-3 =-12/-3

y=4

Answer:

2.106 liters

Step-by-step explanation:

24 * 84 mL = 2016 mL = 2.106 L

Answer: 84*24=2016

You multiply 84 by 24 to get 2016.

Answer:

if the length, width and height of a cube quadruple, then the volume of the cube will be multiplied by 64.

Step-by-step explanation:

Given a cube of width W, height H and length L, the volume of the cube will be: Volume = W*H*L

If all the three parameters quadruple, then:

New Width = 4W

New Height = 4H

New Length = 4L

New Volume = 4W*4H*4L = 64WHL

Therefore, if the length, width and height of a cube quadruple, then the volume of the cube will be multiplied by 64.

Answer:

Volume will be multiplied by 64.

Step-by-step explanation:

We are to find the effect of quadrupling the length, width and height of a cube on its volume.

Since the length, width and height of a cube are all of the same dimension, let us represent it was a variable [tex] S [/tex].

[tex] V o l u m e = S ^ 3 [/tex]

[tex]New Volume = (4S)^3 =64S^3[/tex]

Therefore, if the length width and height of a cube all are quadrupled, the volume will be 64 times.

Conner's work is correct. To combine and make it simple, you Multiply:

(3^5+9)+(6^8+10) which will equal 3^14 6^18.

But Jane's work, instead of adding, Jane multiplies. So, Conner is correct.

Hope that helped!

Answer:

Flip a fair coin. It has a 50% chance of landing heads up and a 50% chance of landing tails up. Therefore, the person who will do the dishes will be chosen at random.

Answer:

B: Put each person's name on a separate piece of paper in a bag.  Randomly draw a name. The person whose name is chosen does the dishes.

D: Roll a number cube. If the number rolled is even, Alexa does the dishes. If the number is odd, Bart does the dishes.

Step-by-step explanation:

I got it right:)

Final answer:

Melody drove approximately 56.57 miles in total on her trip from her grandparents' house to her cousin's house by traveling in a straight line.

Explanation:

Melody drove a distance of 40 miles in a straight line from her grandparents house to her cousin's house. To find the total distance she drove, we can use the Pythagorean theorem as she traveled in a right-angled triangle.

Distance due south = 40 miles

Distance due west = 40 miles

Total distance driven = √(40² + 40²)

Total distance driven = √(1600 + 1600) = √3200

Total distance driven ≈ 56.57 miles

Answer: y=2x

Step-by-step explanation: A perpendicular line is the opposite reciprocal of the slope. The opposite reciprocal of -1/2 is 2.

The equation of the second line is y=2x

Answer:

C) h(x)=-1.3-1.75x

Step-by-step explanation:

f(x)=3.7-2x  

g(x) = 0.25x-5

f(x) + g(x) =3.7-2x   + 0.25x-5

Combine like terms

              = -1.75x - 1.3

Answer:

The answer is C.) h(x)=-1.3-1.75x

Step-by-step explanation:

Answer:

a. 1/13

b. 1/78

c. 1/4

d. 1/12

e. 1/6

f. 1/4

Step-by-step explanation:

First, lets write some basic data

a. result is a queen

Each set has one queen; 1 of spade, 1 of clubs, 1 of heart, 1 of heart

There are total 4 queens

Total number of cards is 52

Probability = Number of favourable outcomes/total number of outcomes

Probability = 4/52

Probability = 1/13

b. result is a queen result is a face card

From my understanding, this question is result is a queen given that result is a face card.

Queen: 4 cards

Face card means King, Queen and Jack

Each set has one King, one Queen and one Jack

There are total 4 sets

Therefore, there are 4 Kings, 4 Queens and 4 Jacks

Face cards: 12-4 (because 4 queens have already been taken out) = 8

Total number of cards: 52-4 (because 4 queens have already been taken out) = 48

Probability (A|B) = P(A) * P(A|B)

P(A) = result is a queen = 4/52 = 1/13

P(A|B) = result is a face card = 8/48 = 1/6

Probability (A|B) = P(A) * P(A|B)

Probability (A|B) = 1/13 * 1/6

Probability (A|B) = 1/78 or 0.01282

c. result is a heart

Out of the 52 cards, there are 26 red cards and out of the 26 red cards, there are 13 cards of heart

Heart = 13 cards

Total number of cards = 52 cards

Probability = Number of favourable outcomes/total number of outcomes

Probability = 13/52

Probability = 1/4

d. result is a heart | result is a red card

Result is a heart = P(A) = 13/52 = 1/4

Result is a red card=26/52 Total number of red cards is 26 but 13 cards (heart) are already taken out so 13 will be subtracted from the numerator and denominator

= 13/39 = 1/3

Result is a heart given that result is a red card P(A|B) = 1/3

Probability (A|B) = P(A) * P(A|B)

Probability (A|B) = 1/4 * 1/3

Probability (A|B) = 1/12

e. result is a heart result is a black card

Result is a heart = P(A) = 13/52 = 1/4

Result is a black card=26/52 Total number of cards is 52 but 13 cards (heart) are already taken out so 13 will be subtracted from the denominator

= 26/39 = 2/3

Result is a heart given that result is a black card P(A|B) = 2/3

Probability (A|B) = P(A) * P(A|B)

Probability (A|B) = 1/4 * 2/3 = 1/6

f. result is a heart result is not a diamond

Result is a heart = P(A) = 13/52 = 1/4

Result is not a diamond = there are 13 diamonds in a deck so cards that are not diamond are 52-13 = 39

Total cards = 52 - 13 (because hearts are already taken out) = 39

= 39/39 = 1

Probability (A|B) = P(A) * P(A|B)

Probability (A|B) = 1/4 * 1 = 1/4

!!

The probabilities of the given result in each subpart for deck of 52 cards can be given as following:
a. 1/13

b. 1/3

c. 1/4

d. 1/2

e. 0

f. 1/3

Following are the basics points need to know to solve this question:

a. Probability that the result is a queen

There are 4 queens in a standard deck of 52 cards. So the probability:

[tex]P(Queen) = \frac{ Number \ of \ Queens }{Total \ Cards} = \frac{4}{52} = \frac{1}{13}[/tex]

b. Probability that the result is a queen given the result is a face card

There are 12 face cards in a deck (3 face cards each for 4 suits: Jack, Queen, King). So, conditional probability:

[tex]P(Queen | Face Card) = \frac{ Number \ of \ Queens }{Total \ Face \ Cards} = \frac{4}{12} = \frac{1}{3}[/tex]

c. Probability that the result is a heart

There are 13 hearts in a deck. So the probability:

[tex]P(Heart) = \frac{ Number \ of \ Hearts }{Total \ Cards} = \frac{13}{52} = \frac{1}{4}[/tex]

d. Probability that the result is a heart given the result is a red card

Red cards consist of hearts and diamonds. There are 26 red cards, and half of them are hearts. So, conditional probability:

[tex]P(Heart | Red \ Card) = \frac{ Number \ of \ Hearts }{Number \ of \ Red \ Hearts} = \frac{13}{26} = \frac{1}{2}[/tex]

e. Probability that the result is a heart given the result is a black card

Black cards consist of spades and clubs. There are no hearts in black cards. So:

[tex]P(Heart | Black \ Card) = 0[/tex]

f. Probability that the result is a heart given the result is not a diamond

If the card drawn is not a diamond, it must be either a heart, club, or spade. There are 39 such cards. So:

[tex]P(Heart |Not \ a \ Diamond) = \frac{ Number \ of \ Hearts }{Number \ of \ Non-Diamond \ Cards} = \frac{13}{39} = \frac{1}{3}[/tex]

The first step in finding the equation of the line would be to find the slope of the points.

The slope-intercept form of a line is given by:

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

where:

- [tex]\( m \)[/tex] is the slope of the line, and

- [tex]\( b \)[/tex] is the y-intercept.

To find the equation of the line that passes through the points (5, -4) and (-1, 8) in slope-intercept form, you need to follow these steps:

1. Find the slope [tex](\( m \))[/tex]:

  The slope [tex](\( m \))[/tex] is given by the formula:

  [tex]\[ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} \][/tex]

  Pick two points, let's say (x1, y1) = (5, -4) and (x2, y2) = (-1, 8), and substitute them into the formula to find [tex]\( m \)[/tex].

 [tex]\[ m = \frac{{8 - (-4)}}{{-1 - 5}} \][/tex]

  Simplify the expression to find [tex]\( m \)[/tex].

2. Use the slope and one of the points to find the y-intercept [tex](\( b \))[/tex]:

  Substitute the slope [tex](\( m \))[/tex] and one of the points (let's use (5, -4)) into the slope-intercept form equation and solve for [tex]\( b \)[/tex].

  [tex]\[ -4 = m \cdot 5 + b \][/tex]

  Substitute the value of [tex]\( m \)[/tex] that you found in step 1 and solve for [tex]\( b \)[/tex].

3. Write the equation in slope-intercept form:

  Once you have the values of [tex]\( m \) and \( b \)[/tex], substitute them into the slope-intercept form equation.

  [tex]\[ y = mx + b \][/tex]

  Write the final equation.

By following these steps, you can find the equation of the line passing through the given points in slope-intercept form.

To find the equation of the line passing through (5,-4) and (-1,8), calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1), which results in a slope of -2.

The first step in finding the equation of the line that passes through the points (5,-4) and (-1,8) in slope-intercept form is to calculate the slope (m) of the line. The slope of a line is determined by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, we would use the following calculation:

With the slope, you can then use the point-slope form or directly the slope-intercept form (y = mx + b) to find the equation, using either of the two points to solve for b, the y-intercept.

Answer:

it would take roughly 6 and a half minutes i think

Answer:

4.DH

Step-by-step explanation:

let's assume the point P to be the point that X will be after it is  dilated.

we know that after dilation the length of PM should be two two times the length of XY

PM = 2.XY ===>[tex]\frac{PM}{XY}[/tex] = 2

and from proportionality theorem we now that:

[tex]\frac{PM}{XY}[/tex] = [tex]\frac{MX}{MP}[/tex] = 2

So we know XY should be half the size of MP  and we can see the only line matching is DH thus the answer is DH

Rectangles and squares always have congruent diagonals due to their geometrical properties, making option c (rectangle, square) the correct answer.

The question asks which of the given sets of quadrilaterals must have congruent diagonals. The key to answering this question is understanding the properties of each kind of quadrilateral mentioned. Rectangles and squares always have congruent diagonals because their diagonals bisect each other and are of equal length due to the right angles at the corners of the shapes.

A rhombus, while having diagonals that bisect each other at right angles, does not necessarily have congruent diagonals because the angles between adjacent sides do not guarantee equal lengths of diagonals. As such, the correct answer is c.rectangle, square, where both of these shapes must have diagonals of equal length due to their geometrical properties.