Kentaro mixed 3.5 gallons of cranberry juice with 3 quarts of orange juice to make a punch.1 gallon = 4 quarts1 gallon = 16 cups1 cup = 8 fluid OuncesHow many fluid ounces of punch did Kentaro make? Enter the answer in the box.

The simplification of the expression ab³/a⁴b  +  (c²)³ is determined as b²/a³  +  c⁶.

The given expression is simplified as follows;

The given expression is written as;

ab³/a⁴b  +  (c²)³

To simplify the expression given above, we will divide the fraction with the common factor as follows;

From the numerator; ab³, we will factor out "ab"

From denominator; a⁴b, we will factor out "ab"

The resulting expression becomes;

ab³/a⁴b  +  (c²)³

= b²/a³  +  c⁶

Note: for the power of c, we simplify by multiplying 2 and 3 = 6

Thus, the simplification of the expression ab³/a⁴b  +  (c²)³ is determined as b²/a³  +  c⁶.

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Answer:

The last choice

Answer (Please vote me Brainliest if this helps!):

The answer is D

Step-by-step explanation:

Lets start off with the square roots:

\(\sqrt{16}\) = 4

\(\sqrt{18}\) = \(3\sqrt{2}\) = 4.24264...

Mixed fraction:

\(4\frac{2}{3}\) = 4.667

Therefore the answer is D.

9514 1404 393

Answer:

  d. √16, 4.23_23, √18, 4 2/3

Step-by-step explanation:

There are a couple of different ways to compare these numbers. Maybe one of the most straightforward is to find the decimal equivalent, rounded to hundredths.

  4.23_23 ≈ 4.23

  4 2/3 ≈ 4.67

  √18 ≈ 4.24

  √16 = 4.00

These can be sorted least-to-greatest by putting the first number (4.23) between the last two (4.00, 4.24) and reading the new list last-to-first.

  4.00, 4.23, 4.24, 4.67   ⇔   √16, 4.23..., √18, 4 2/3

_____

Additional comment

Another way to work this problem is to square the numbers not under a radical. 4.23...² ≈ 17.91 and (4 2/3)² ≈ 21.78. The ordering of the squares is the same as the ordering of their square roots.

  16 < 17.91 < 18 < 21.78   ⇔   √16 < 4.23... < √18 < 4 2/3

Using the normal distribution, the upper boundary, in inches, of a symmetric and centered interval of the sample averages with n = 167 that are within 0.92 standard deviation s of the mean is of:

67.21 inches.

The z-score of a measure X of a normally distributed variable that has mean represented by \(\mu\) and standard deviation represented by \(\sigma\) is given as follows:

\(Z = \frac{X - \mu}{\sigma}\)

Considering samples of 167, with the mean and standard deviation of the population given in the problem, the parameters are given as follows:

\(\mu = 66.9, \sigma = 4.33, n = 167, s = \frac{4.33}{\sqrt{167}} = 0.335\)

The desired height is X when Z = 0.92, because it is 0.92 standard deviations from the mean and we want the upper limit, hence:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

0.92 = (X - 66.9)/0.335

X - 66.9 = 0.92 x 0.335

X = 67.21 inches.

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Answer:

31

Step-by-step explanation:

replace the values of a and b in the given term

=2a x 3 + b

2(5) x 3 + (1)

2x5 x 3 + 1

10 x 3 + 1

30 + 1

31

Answer:

The car is 10 miles from parking lot.

Step-by-step explanation:

Given that:

The car travels 6 miles north and 8 miles east.

This forms the two legs of a right angled triangle.

The distance from car to parking lot will be hypotenuse.

Using Pythagorean theorem;

\(a^2+b^2=c^2\\(6)^2+(8)^2= c^2\\c^2 = 36 + 64 \\c^2 = 100\)

Taking square root on both sides

\(\sqrt{c^2}=\sqrt{100}\\c=10\)

Hence,

The car is 10 miles from parking lot.

There were 5 1/4 bags of popcorn left after eating 4 bags.

To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.

Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:

9 1/4 = (4 * 9 + 1) / 4 = 37/4

Now, let's subtract the 4 bags eaten from the total:

37/4 - 4

To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:

37/4 - 4/1

Now, let's find a common denominator and subtract the fractions:

37/4 - 16/4 = (37 - 16) / 4 = 21/4

The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:

21/4 = 5 1/4

Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.

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Hey there! :)

Answer:

y = 7/2x - 11

Step-by-step explanation:

Use the slope formula to calculate the slope:

\(m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}\)

Plug in the coordinates:

\(m = \frac{10-(-4)}{6-2}\)

Simplify:

\(m= \frac{14}{4}\)

\(m = \frac{7}{2}\)

Slope-intercept form is y = mx + b. Plug in the slope, as well as the coordinates of a point given to solve for b:

10 = 7/2(6) + b

10 = 42/2 + b

10 = 21 + b

10 - 21 = b

b = -11.

Write the equation:

y = 7/2x - 11

Answer:

f(x) = - 2x + 4

Step-by-step explanation:

Since we are only trying to move the graph up 3 units, the slope does not change. So, it would be -2.

We also know that the 1 in f(x)= -2x + 1 is the y-intercept (y=mx+b). But again, we are moving the graph 3 units up, so we have to add 3. That makes it 4 (3+1=4).

So, the new equation would be f(x) = -2x + 4

Step-by-step explanation:

it simply means that g(x) is f(x) just shifted 3 units upwards.

that means nothing else changes, only whatever y result f(x) produces is increased by 3.

so,

g(x) = f(x) + 3 = -2x + 1 + 3 = -2x + 4

therefore, as domain and range were the whole set of real numbers, the addition of 3 does not make any difference in relation to infinity. so, they remain unchanged.

the slope stays the same (g(x) is simply a parallel line to f(x)).

the y-intercept (the y-value when x = 0) also increases by 3, and is 4.

the x-intercept (the x-value when y = 0) changes :

0 = -2x + 4

2x = 4

x = 2

the x-intercept is 2.

Answer:

1 = 1 or 2x-4 = 2x-4

Step-by-step explanation:

Answer:

Infinite Solution

Step-by-step explanation:

Use distributive property

2x-4=2x-4

subtract 2x from 2x

-4=-4

Answer:

sept one

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

10x - 20 + 6x + 8 = 180

Supplementary angles

Answer:

x = 12

Step-by-step explanation:

The two given angles create a straight line (Definition of Straight Line). This means that:

\((10x - 20) + (6x + 8) = 180\)

First, combine like terms. Like terms are terms that share the same amount of the same variables:

\((10x + 6x) + (8 - 20) = 180\\(16x) + (-12) = 180\\16x - 12 = 180\\\)

Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, add 12 to both sides of the equation:

\(16x - 12 = 180\\16x - 12 (+12) = 180 (+12)\\16x = 180 + 12\\16x = 192\)

Next, divide 16 from both sides of the equation:

\(\frac{16x}{16} = \frac{192}{16} \\x = \frac{192}{16}\\ x = 12\)

12 is your answer.

~

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Answer:

Step-by-step explanation:

23/40 = 0.575

It is said that the rural landscape has been replaced by the urban landscape because rural landscapes have been transformed into urban ones.

We have to:

At present, more and more rural spaces become urban, which is why it is indicated that the urban landscape is replacing the rural one.

¡Hope this helped!

Answer:

All are true except C. CPR is not a guarantee to keep someone alive till help arrives. Unfortunately some people die before help gets there regardless of the CPR.

The line segment's slope represents the period during which the speed decreases is b. The slope is -10.

The slope of a line segment measures the steepness of the line segment.

The slope is the ratio of the rise (the change in vertical height, y, between the endpoints) over the run (the difference in horizontal length, x, between the endpoints.

Elapsed Time (sec)     Speed (mph)

1                                        45

2                                       35

3                                       25

4                                       15

5                                       15

6                                       15

The Slope of the line segment during speed decreases = y₂ - y₁ ÷ x₂ - x₁.

= (35 - 45) / (2 - 1)

= -10/1

= -10

Thus, b. The slope is -10.

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Answer:

n = 55/8

Step-by-step explanation:

You can solve it by cross multiplying. Where you multiply the denominator of the fraction on the left side with the numerator on the right side, and vice versa.

11/n = 8/5

n x 8 = 11 x 5

8n = 55

n = 55/8

(or 6.875)

Answer:

\(\boxed{\pink{n = 7 \frac{3}{8} }}\)

Step-by-step explanation:

\( \frac{11}{n} = \frac{8}{5} \\ \)

Use cross multiplication

\(11 \times 5 = 8 \times n \\ 55 = 8n \\ \frac{55}{8} = \frac{8n}{8} \\ n = 7 \frac{3}{8} \)

The steps to create a bar graph are explained below.

To match the two-way table to the segmented bar graph, we need to create a segmented bar graph that represents the data in the table. The table shows the percentage of students in each grade who voted for each mascot option.

Here is how we can match the two-way table to the segmented bar graph:

By creating a segmented bar graph that represents the data in the two-way table, we can visually compare the percentage of students who voted for each mascot option across different grade levels.

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The speed of the ball after one second is given as follows:

9.175 m/s.

The speed function is the derivative of the position function, which is graphed in this problem.

The position function, in meters, for a projectile's height, is given as follows:

h(t) = -4.9t² + v(0)t + h(0).

In which:

From the graph, the initial height is given as follows:

h(0) = 6.

When t = 4, h = 2.5, hence the initial velocity is obtained as follows:

2.5 = -4.9(4)² + 4v(0) + 6

4v(0) = 2.5 - 5 + 4.9(4)²

4v(0) = 75.9

v(0) = 75.9/4

v(0) = 18.975.

Then the position function is of:

h(t) = -4.9t² + 18.975t + 6.

The velocity function is the derivative of the position, hence:

v(t) = -9.8t + 18.975.

Then the velocity after one second is of:

v(1) = -9.8 + 18.975 = 9.175 m/s.

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If Matt and Jan each create 10 gallons of punch, Jan uses 2 liters more orange juice as a result than Matt.

Using the unitary approach, an issue can be resolved by first figuring out the value of a single unit, then multiplying that value by the number of units needed to solve the problem. The unitary technique is sometimes useful for multiplying and dividing by fractions because it makes sense immediately and can be done mentally if the numbers add up. This makes it a good method for defending or explaining frequently employed written fractional algorithms, like division by a fraction. The unitary technique has a formula that involves finding the value of a single unit, multiplying it by the quantity of units, and then finding the desired value.

given

For his 10-gallon punch, Matt uses gallons of orange juice, which adds up to 3x=3*2 = 6.

Using the formula Jan uses gallons of orange juice to create 10 gallons of punch and Matt uses gallons of orange juice to make 10 gallons of punch, we can calculate that Jan uses 2 gallons more orange juice than Matt.

If Matt and Jan each create 10 gallons of punch, Jan uses 2 liters more orange juice as a result than Matt.

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After the raise, Tyler's brother will make $14 x 1.05 = $14.70 per hour.

Answer:

14 x 1.05 = 14.70

Step-by-step explanation:

Answer:

Given Figure has set of Stacked cubes.

To Draw the Base Plan, lets see its right side, Left Side and Front side view.

Right side:

It has 3 cubes in base.

2 cubes in 2nd layer clearly seen in figure and only 1 cube in 3rd layer.

Left Side:

It has 2 Cubes in base.

Both Cubes attached to 1st and 2nd cube of right side cubes.

Front Side:

It can be seen that, here base only has 2 rows of cubes.

Therefore,  1st Figure is correct Base Plan (or enclosed figure)

Note: Numbers in enclosed figure just shows the total no. of cubes in that stack.

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Answer:

y=-1/3|x+2|+5 is upside down compared to y=|x|, and the slope 1/3 that of y=|x|, the vertex is also shifted left by two units and up by 5.

Step-by-step explanation:

Answer:

18h - 3hk

Step-by-step explanation:

3h(6 - k)

= 3h(6) + 3h(-k)

= 18h + -3hk

= 18h - 3hk

The simplified for of the expression 2.3h(6 - k) can be written as 13.8h - 2.3hk

Given the expression :

2.3h(6 - k)

Open the bracket ; multiply values in the bracket by 2.3h

13.8h - 2.3hk

Since there is no other way to reduce the expression further, then the simplified form of the expression would be expressed as 13.8h - 2.3hk

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Answer:

k

Step-by-step explanation:

Answer: 4 pages

Step-by-step explanation:

To solve this problem, we need to use the formula:

Rate = Output/Time

Let's use "p" to represent the number of pages Ethan can type and "t" to represent the time he has before the meeting starts.

Rate = 2 pages/(1/8 hour) = 16 pages/hour

Since the meeting starts 3/4 hour later than the scheduled time, Ethan has t = 1 - 3/4 = 1/4 hour to type pages before the meeting starts.

Output = Rate * Timep = (16 pages/hour) * (1/4 hour) = 4 pages

Therefore, Ethan can type 4 pages before the meeting starts.

Answer: 4 pages

Answer:

C. The slope is 1/2.

Step-by-step explanation:

When looking for the slope of a graph you can either use the formula y=mx+b (and find m) OR you can find the rise and the run. The rise is how many units up or down, and the run is how many units left or right until the graph intersects at a given point on the line. From the y-intercept of the given graph, the rise over run would be up 1, right 2 (1/2).