At one store, a 2-liter bottle of soda costs $2.12. At another store, a 3-liter bottle costs $3.15. Which bottle is a better deal?

Answer:

\(360 \times 678 = 244,080\)

Hope it helps you

ignore my answer sorry I got it wrong

Answer: Add 40 to both sides to collect like terms on each side of the equation

Step-by-step explanation: That's the first step

The correct response is c. 8√2 . The length of the diagonal if the side of the square is 8√2.

A polygon's opposed vertices (or corners) are connected by a line segment known as a diagonal. Or to put it another way, a diagonal is a line segment joining two polygonal vertices that are not neighbouring. With the exception of the figure's edges, it connects a polygon's vertices. For instance, a diagonal line or movement runs slopingly from one corner of a square to the other corner. a type of straight line called a diagonal. Straight up, down, or across are not possible on a diagonal line. It is a line that joins the corners of a form at two points. Instead of running straight up or across, a diagonal is formed by a straight line that is positioned at an angle.

Right isosceles triangles with both legs 8 feet long would make up each half.

The hypotenuse that both of those triangles would share is the diagonal.

We must determine the hypotenuse's length, d, in feet.

According to the Pythagorean theorem, the lengths of the legs' squares sum up to the length of the hypotenuse's square, so

\(8^{2} +8^{2} =8\sqrt{2}\)

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A gardener wants to divide a square piece of lawn in half diagonally. What is the length of the diagonal if the side of the square is 8ft? Leave your answer in simplest radical form.

a. 16√8

b. 2√8

c. 8√2

d. 4

Answer:

8.75 hours for 2 builders so complete it

Step-by-step explanation:

its right because im smart and i say its right

If it takes 5 builders \(3\frac{1}{2}\) hours to build a wall, it will take 2 builders  \(8\frac{3}{4}\) hours to build an identical wall

The time taken for 5 builders to build the wall = \(3\frac{1}{2}\) hours

The time take for 5 builders to build the wall = 3.5 hours

Time taken for 1 builder to build an identical wall =

5 x  (Time taken for 5 builders to build the wall)

Time taken for 1 builder to build the wall = 5  x  3.5

Time taken for 1 builder to build the wall = 17.5 hours

Time taken for 2 builders to build an identical wall = (Time taken for 1 builder)/2

Time taken for 2 builders to build an identical wall = 17.5/2

Time taken for 2 builders to build an identical wall =  8.75 hours

Time taken for 2 builders to build an identical wall = \(8\frac{3}{4}\) hours

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Answer:

10w

Step-by-step explanation:

→ Work out the length

4 × w = 4w

→ State width

w

→ Find perimeter

4w + 4w + w + w = 10w

Answer:

he got 5000 rands for it

Step-by-step explanation:

you multiply it

500 x 10 = 5000

Answer:

Ranika should have known since the series of letters and numbers Radhika gave her don't make out to be a legal phone number.

Step-by-step explanation:

Answer:

No pic srry

Step-by-step explanation:

Answer:

whats the question?

Step-by-step explanation:

Ok, what is your question.

The angle between 0 degrees and 360 degrees that is coterminal with the following angle 0=-1625 degrees is 175.

Angles on the same side of the same quadrant are said to be coterminal angles. We repeatedly add or subtract a 360° full revolution from the supplied angle in order to discover an angle that is coterminal with it.

To determine a coterminal angle with the provided angle between 0tp 360 we add 360 to the given angle:

-1625 + 360(5) = 175

Hence, the angle between 0 degrees and 360 degrees that is coterminal with the following angle 0=-1625 degrees is 175.

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The angle of rotation at the point \(\(z_0 = 2i + 1\)\) when \(\(w = z^2\)\) is \(\(2\arctan(2)\),\) which is approximately 1.107 radians or 63.43 degrees.

To determine the angle of rotation at the point \(\(z_0 = 2i + 1\)\) when \(\(w = z^2\),\) we can follow these steps:

1. Express \(\(z_0\)\) in polar form: To find the polar form of \(\(z_0\)\), we need to calculate its magnitude \((\(r_0\))\) and argument \((\(\theta_0\))\). The magnitude can be obtained using the formula \(\(r_0 = |z_0| = \sqrt{\text{Re}(z_0)^2 + \text{Im}(z_0)^2}\)\):

\(\[r_0 = |2i + 1| = \sqrt{0^2 + 2^2 + 1^2} = \sqrt{5}\]\)

  The argument \(\(\theta_0\)\) can be found using the formula \(\(\theta_0 = \text{arg}(z_0) = \arctan\left(\frac{\text{Im}(z_0)}{\text{Re}(z_0)}\right)\)\):

\(\[\theta_0 = \text{arg}(2i + 1) = \arctan\left(\frac{2}{1}\right) = \arctan(2)\]\)

2. Find the polar form of \(\(w\)\): The polar form of \(w\) can be expressed as \(\(w = |w|e^{i\theta}\)\), where \(\(|w|\)\) is the magnitude of \(\(|w|\)\) and \(\(\theta\)\) is its argument. Since \((w = z^2\)\), we can substitute z with \(\(z_0\)\) and calculate the polar form of \(\(w_0\)\)using the values we obtained earlier for \(\(z_0\)\):

 \(\[w_0 = |z_0|^2e^{2i\theta_0} = \sqrt{5}^2e^{2i\arctan(2)} = 5e^{2i\arctan(2)}\]\)

3. Determine the argument of \(\(w_0\):\) To find the argument \(\(\theta_w\)\) of \(\(w_0\)\), we can simply multiply the exponent of \(e\) by 2:

  \(\[\theta_w = 2\theta_0 = 2\arctan(2)\]\)= 1.107 radians

Therefore, the angle of rotation at the point \(\(z_0 = 2i + 1\)\) when \(\(w = z^2\)\) is \(\(2\arctan(2)\).\)

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The complete question is:

"Determine the angle of rotation, in radians and degrees, at the point z0 = 2i + 1 when w = z^2."

The only solution to the equation is (6, 5).

Linear equation can be represented in slope intercept form as follows;

y = mx + b

where

Therefore, the linear equation is y = 2 / 3 x + 1 .

Therefore, let's check if  (6, 5) and (9, 8) are solution to the linear equation. We have to insert the x values in the equation to know whether we will get the y values

y = 2 / 3 x + 1 .

5 = 2 / 3(6) + 1

5 = 4 + 1

5  = 5

let's check (9, 8)

y = 2 / 3 x + 1

8 = 2 / 3 (9) + 1

8 = 6 + 1

8 ≠ 7

Therefore, only (6, 5) is a solution

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The distance of the foot of the ladder from the wall is approximately 4.6 cm.In the given scenario, the ladder of length 6cm is leaning against a vertical wall and making an angle of 40° with the wall. We need to find the distance of the foot of the ladder from the wall, correct to one decimal place.

Let the distance of the foot of the ladder from the wall be x cm.

Using trigonometry, we know that:

cos(40°) = adjacent/hypotenuse

cos(40°) = x/6

x = 6*cos(40°)

Using a scientific calculator, we can find the value of cos(40°) as approximately 0.766.

Substituting this value, we get:

x = 6*0.766

x = 4.596 cm (rounded to one decimal place).

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Answer:

a. P= 5000( 1.016)^x

b. $ 6344.18

Step-by-step explanation:

The equation for finding the compound interest annually is

P = P_1 ( 1 +r)^t

Here

P = the amount after the interest has been added or the new balance

P_1= the principal amount

r= rate at which interest is charged

t= time in years

So we have

P = the new balance

P_1= the principal amount= $ 5000

r= rate at which interest is charged= 1.6 %

t= time in years= x

Putting the values in the above equation

P = P_1 ( 1 +r)^t

P = 5000 ( 1+ 1.6/100) ^x

P= 5000( 1.016)^x

b) When t= 15

Again

Putting the values in the above equation

P = P_1 ( 1 +r)^t

P = 5000 ( 1+ 1.6/100)^15

P = 5000( 1.26883637) = 6344.18185= $ 6344.18

The expression √180 * 2√30 is equivalent to the expression 60√6

An equation is an expression that shows the relationship between two numbers and variables.

The square root is a factor of a number that, when multiplied by itself, gives the original number.

Given the expression √180 * 2√30

Collecting like terms give:

= 2√(180 * 30)

Simplifying:

= 60√6

The expression √180 * 2√30 is equivalent to the expression 60√6

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~~—☆☆☆——☆☆☆——☆☆☆——☆☆☆——☆☆☆—~~

Answer:

Hello! I hope I’m correct!! :)

Step-by-step explanation:

#7.   7 x 7 ( = 49 )

#8.   8 x 8 x 8 x 8 ( = 4096 )

#9.    2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 ( = 256 )

#10.  4 x 4 x 4 ( = 64 )

#11.   5 x 5 x 5 x 5 x 5 ( = 3125 )

#12.  7 x 7 x 7 ( = 343 )

______________________________

Hope this helps! If you have any questions about this, feel free to ask! Have a wonderful day! ^-^

#Thank you so much for using brainly!

Best regard! :D

~By, BrainlyAnime~

~~—☆☆☆——☆☆☆——☆☆☆——☆☆☆——☆☆☆—~~

The bicycle wheel turns around 23 times while traveling 100 feet. The first step in solving this problem is to find the circumference of the bicycle wheel.

The formula for circumference is C = πd, where d is the diameter of the wheel. In this case, the diameter is 22 inches, so we can plug that into the formula: C = π(22) = 69.115 inches.

Next, we need to convert the distance traveled by the bicycle (100 feet) into inches, since we're working with the circumference of the wheel in inches. There are 12 inches in a foot, so 100 feet is equal to 1200 inches.

Now we can use the circumference to find how many revolutions the wheel makes. We know that one revolution of the wheel covers the circumference, so we can divide the total distance traveled by the circumference to get the number of revolutions: 1200 ÷ 69.115 ≈ 17.364.

However, we need to round our answer to the nearest whole number, so the final answer is 23 revolutions.

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Answer:

the angle of depression is approx 22 degrees

Step-by-step explanation:

Model drawn below to visualize

I represented the angle of depression as x

Since two side lengths are given, we can use tangent to find the angle of depression

tan x= 3/7.5

We then use inverse tangent to find the angle measure:

m<x=\(tan^{-1}\)(3/7.5)

m<x is approx 21.8 or 22 when rounded to the nearest degree

(when using tan, inverse tan, sin, cos, inv... use deg on calculator when finding angle of depression, solving triangles, etc.)

Answer:

x^2

Step-by-step explanation:

The greatest common factor of 5x^2, 10x^3, 6x^5:

For the numbers, there is no greatest common factor except for 1.

For the variables, the furthest we can go is x^2.

In conclusion, the greatest common factor of 5x^2, 10x^3, 6x^5 is x^2.

Answer:

20

Step-by-step explanation:

200-180=20

Pro tip:

Next time you should asd what you want us to answer.

Answer:

815.76 is your answer

Step-by-step explanation:

For the current is rate of charge flows through a surface, \( \frac{ dQ}{dt} = I \), the charge passes through the surface after 9 seconds is equals to 2052 C.

There is amount of charge passing through a surface, by a function Q(t) is measured in coulombs C. The modeled current function, I(t) = 9t²- 4t + 3 --(1)

where t denotes the time in second. We have to determine the charge passes through the surface after 9 seconds. As we know current is defined as a rate at which charge flows through a surface, i.e., \( \frac{ dQ}{dt} = I \). The units used for current is Ampere, A. From equation (1) and (2), \(\frac{ dQ}{dt} = 9t² - 4t + 3\)

So, for determining the charge we integrate, the previous equation with respect to the time t, \(\int \frac{ dQ}{dt} dt = \int_{0}^{t} I(t) dt = \int_{0}^{9} ( 9t² - 4t + 3) dt\)

\(Q =[\frac{9t³}{3} - \frac{ 4t²}{2} + 3t]_{0}^{9}\)

\( = 3× 9³ + 27 - 2× 9²\)

= 2052

Hence, required value is 2052 coulombs.

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Complete question:

The amount of charge passing through a surface, given by a function Q(t), is measured in coulombs C. The current is the rate at which charge flows through a surface. This function is I(t) and is measured in amperes, A, or coulombs per second, C/s. If a current for a certain surface is modeled by the function I(t)=9t² −4t + 3 for t≥0, how much charge passes through the surface after 9 seconds? ______________coulombs

Answer:

33.3 is your answer

Step-by-step explanation:

The surface area of the smaller cone A₁ is approximately 33.3 cm² when rounded to the nearest tenth.

A cone is a three-dimensional geometric form with a flat base and a smooth, tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that link the base's points to the apex, which is a common point on a plane that does not include the base.

Two cones A₁ and A₂ are similar.

The radius of A₁ = 2 cm

radius of A₂ = 3 cm

The surface area of A₁ = ? cm²

surface area of A₂ = 75 cm²

Since the cones A₁ and A₂ are similar, their corresponding sides are proportional.

Specifically, the ratio of their radii is the same as the ratio of their surface areas. That is,

(radius of A₁) / (radius of A₂) = (surface area of A₁) / (surface area of A₂)

We can use this relationship to solve for the surface area of A₁:

(surface area of A₁) = (radius of A₁ / radius of A₂)^2 × (surface area of A₂)

Substituting the given values, we get:

(surface area of A₁) = (2/3)² × 75

(surface area of A₁) = 4/9 × 75

(surface area of A₁) ≈ 33.3 cm²

Therefore, (surface area of A₁) ≈ 33.3 cm²

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Answer:

1) Words learned=15x+75

2) 15 is the slope

3) 270 words

4) 21 weeks

Step-by-step explanation:

Let x be equal to the number of weeks that pass.

Let y be equal to the number of words we learn.

1) We're told that we learn 15 words per week. Therefore, 15x would equal the number of words we learn. However, because we already know 75, we add that to 15x, giving us this equation:

y=15x+75

2) The slope is the same thing as the rate of change in a situation. In this scenario, every week, we learn 15 words. Therefore, the rate of change, or the slope, is 15.

3) To find this, plug 13 into our equation as x and solve for y.

y=15x+75

y=15(13)+75

y=195+75

y=270

Therefore, we would learn 270 vocabulary words in total in 13 weeks.

4) To find this, plug 390 into our equation as y and solve for x.

y=15x+75

390=15x+75

Subtract 75 on both sides to isolate x

390-75=15x+75-75

315=15x

Divide both sides by 15

315/15=15x/15

21=x

Therefore, it would take 21 weeks to learn 390 new vocabulary words.

I hope this helps!

Answer:

6 3/5+ 3 2/5 =10

Step-by-step explanation:

EZ 6+3 3/5+2/5 10

The value of Absolute maximum are (a) 8, (b) -30.36, (c) -10 and the Absolute minimum are (a) -10, (b) -362.39, (c) -362.39.

We are given a function:f(x) = x³ - 12x² - 27x + 8We need to find the absolute maximum and absolute minimum values of the function f(x) over each of the indicated intervals. The intervals are:

a) Interval = [-2, 0]

b) Interval = [1, 10]

c) Interval = [-2, 10]

Let's begin:

(a) Interval = [-2, 0]

To find the absolute max/min, we need to find the critical points in the interval and then plug them in the function to see which one produces the highest or lowest value.

To find the critical points, we need to differentiate the function:f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:f'(x) = 0Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)x = (24 ± √(888)) / 6x = (24 ± 6√37) / 6x = 4 ± √37

We need to check which critical point lies in the interval [-2, 0].

Checking for x = 4 + √37:f(-2) = -10f(0) = 8

Checking for x = 4 - √37:f(-2) = -10f(0) = 8

Therefore, the absolute max is 8 and the absolute min is -10.(b) Interval = [1, 10]

We will follow the same method as above to find the absolute max/min.

We differentiate the function:f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:f'(x) = 0Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)

x = (24 ± √(888)) / 6

x = (24 ± 6√37) / 6

x = 4 ± √37

We need to check which critical point lies in the interval [1, 10].

Checking for x = 4 + √37:f(1) = -30.36f(10) = -362.39

Checking for x = 4 - √37:f(1) = -30.36f(10) = -362.39

Therefore, the absolute max is -30.36 and the absolute min is -362.39.

(c) Interval = [-2, 10]

We will follow the same method as above to find the absolute max/min. We differentiate the function:

f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:

f'(x) = 0

Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)x = (24 ± √(888)) / 6x = (24 ± 6√37) / 6x = 4 ± √37

We need to check which critical point lies in the interval [-2, 10].

Checking for x = 4 + √37:f(-2) = -10f(10) = -362.39

Checking for x = 4 - √37:f(-2) = -10f(10) = -362.39

Therefore, the absolute max is -10 and the absolute min is -362.39.

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By the end of week 52, Westway Company deducted $8,857.60 for Social Security and $2,426.48 for Medicare from Suzle Chan's earnings.

To calculate the deductions made by Westway Company, we'll need to consider the Social Security and Medicare taxes.

Social Security tax:

The Social Security tax rate is 6.2% on income up to $142,800.

Since Suzle Chan earns $3,220 per week, their annual income is $3,220 * 52 = $167,440.

However, the maximum taxable income for Social Security is $142,800.

Therefore, the Social Security tax deduction is $142,800 * 0.062 = $8,857.60.

Medicare tax:

The Medicare tax rate is 1.45% on all income.

The Medicare tax deduction is $167,440 * 0.0145 = $2,426.48.

By the end of week 52, Westway Company would have deducted a total of $8,857.60 for Social Security and $2,426.48 for Medicare from Suzle Chan's earnings.

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Answer:

Step-by-step explanation:

If you drew out the bell curve and put the values where they go, this would be a no-brainer that doesn't even need math to solve. However, we will use the formula and then the table for z-scores to find this answer.

We are looking for the probability that the number of calls falls between 19 and 67. The standard deviation is 8 and the mean is 43. The probability we are looking for is P(19 < x < 67), therefore we look for the probability first that number of calls is greater than 19:

\(z=\frac{19-43}{8}=-3\) and from the table and to the right of the z-score, the probability that the number of calls is greater than 19 is .99865 (or 99.8%). Likewise,

\(z=\frac{67-43}{8}=3\) and from the table and to the right of the z-score, the probability that the number of calls is greater than 67 is .00315.

Take the difference of these to get the probability that the number of calls falls between these 2:

.99865 - .00135 = .9973 or 99.7%