Mrs. Williams has 1/4 gallon of juice left in a bottle. She pours an equal amount of
juice into 5 glasses to empty the bottle. Which model represents the fractional
amount of the gallon of juice in each glass?​

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

For more questions on trigonometric form

https://brainly.com/question/31744474

#SPJ8

Answer:

\(y = -7x + 22\)

Step-by-step explanation:

Given

\((x_1,y_1) = (4,-6)\)

\((x_2,y_2) = (2,8)\)

Required

Determine the line equation

This question will be answered using linear interpolation.

This is represented as thus:

\(\frac{y - y_1}{x - x_1} = \frac{y_2 - y_1}{x_2 - x_1}\)

Substitute values for x1,x2,y1 and y2

\(\frac{y - (-6)}{x - 4} = \frac{8 - (-6)}{2 - 4}\)

\(\frac{y +6}{x - 4} = \frac{8 +6}{2 - 4}\)

\(\frac{y +6}{x - 4} = \frac{14}{-2}\)

\(\frac{y +6}{x - 4} =-7\)

Cross Multiply

\(y + 6 = -7(x - 4)\)

\(y + 6 = -7x + 28\)

Make y the subject

\(y = -7x + 28-6\)

\(y = -7x + 22\)

We can match the amounts to their corresponding account descriptions as follows:

$92.40 to the account of $880 at 5.25% for 2 years

$94.50 to the account of $675 at 3.5% for 4 years

$94.23 to the account of $770 at 4.1% for 3 years

To calculate the interest earned on a simple interest account, we can use the following formula:

Interest = Principal x Rate x Time

where "Principal" is the initial amount of money invested, "Rate" is the annual interest rate as a decimal, and "Time" is the length of time in years that the money is invested.

Using this formula, we can calculate the interest earned on each of the accounts:

$880 at 5.25% for 2 years:

Interest = 880 x 0.0525 x 2 = $92.40

$675 at 3.5% for 4 years:

Interest = 675 x 0.035 x 4 = $94.50

$770 at 4.1% for 3 years:

Interest = 770 x 0.041 x 3 = $94.23

So the interest earned on each account is as follows:

$880 at 5.25% for 2 years: $92.40

$675 at 3.5% for 4 years: $94.50

$770 at 4.1% for 3 years: $94.23

Therefore, we can match the amounts to their corresponding account descriptions as follows:

$92.40 to the account of $880 at 5.25% for 2 years

$94.50 to the account of $675 at 3.5% for 4 years

$94.23 to the account of $770 at 4.1% for 3 years

for such more question on simple interest

https://brainly.com/question/1173061

#SPJ11

Answer:

A) P(T) = 30/120 = 1/4

B) P(T) = 50

Step-by-step explanation:

A) P(T) = 30/120 = 1/4

B) P(T) = 1/4 of 200 which is 50

a. Probability that the coin shows tails is  \(\frac{1}{4}\).

b. 50 number of times the coin shows tails.

Probability theory, a branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance.

Probability = \(\frac{Number \ of \ favorable \ outcomes}{Total \ number \ of \ favorable \ outcomes}\)

According to the question

a. John throws a biased coin 120 times. It shows heads 90 times.

Probability formula:

Probability = \(\frac{Number \ of \ favorable \ outcomes}{Total \ number \ of \ favorable \ outcomes}\)

Probability that the coin shows heads = \(\frac{90}{120}\) = \(\frac{3}{4}\)

Probability that the coin shows tails = 1 - \(\frac{3}{4}\) = \(\frac{1}{4}\)

b. Carly throws the same coin 200 times.

From a, we know the probability that the coin shows tails is  \(\frac{1}{4}\).

Number of times the coin shows tails = 200 × \(\frac{1}{4}\) = 50

Find out more information about probability here

brainly.com/question/13011617

#SPJ2

The function takes the trapezoid's area as input and returns as output the length of the other base is A(x)/7-5=x.

The function for the trapezoid area is:

A(x)=(B+b)*h/2

where B and b are the bases and h is the height.

Given height of 14 and one base length of 5 with the length of its other base

With the given data: h=14 B and b =5 and x (it may vary which one is bigger)

So that function becomes:

A(x)=(5+x)*14/2

A(x)=(5+x)*7

So if you want the inverse function, you have to operate to find x:

A(x)/7=5+x

A(x)/7-5=x

Learn more about area of trapezoid here:

brainly.com/question/4302947

#SPJ9

Answer:

No, Sam is not correct. The graph of a proportional relationship has the form y = kx, where k is the constant of proportionality. Sam added the constant of proportionality instead of using it as the coefficient of x. The correct equation is y = 6x. Sam’s graph would be a straight line, but it would not pass through the origin.

Step-by-step explanation:

on edge :)

Using the combination formula, it is found that these two positions can be filled in 780 ways.

The order in which the positions are filled is not important, for example, João and Elisa is the same outcome as Elisa and João, hence the combination formula is used to solve this question.

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by:

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this problem, two people are taken from a set of 40, hence the number of ways is given by:

\(C_{40,2} = \frac{40!}{2!38!} = 780\)

More can be learned about the combination formula at https://brainly.com/question/25821700

#SPJ1

Answer:

10

Step-by-step explanation:

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Answer: L = 10

Explanation:

The formula is L x W x H

We can do L * 0.5 * 11 = 55

L * 5.5 = 55

L  = 10

I hope this helped!

<!> Brainliest is appreciated! <!>

- Zack Slocum

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

9514 1404 393

Answer:

  A.  The volumes are equivalent.

Step-by-step explanation:

The volume of a pyramid can be found using the formula ...

  V = 1/3Bh

where B is the base area, and h is the height.

Both of these pyramids have the same height, so we can compare volumes by looking at the base area.

Prism X has a rectangular base with an area of A = LW = (6 cm)(5 cm) = 30 cm². Prism Y has a triangular base with an area of A = 1/2bh = 1/2(7.5 cm)(8 cm) = 30 cm².

The two base areas are the same, so the volumes are the same.

Answer:

\( ME = 1.64 \sqrt{\frac{0.32 (1-0.32)}{150}}= 0.0625\)

Step-by-step explanation:

For this case we have the following info given:

\( n = 150\) represent the sampel size selected

\( X = 48\) represent the number of households who relied strictly on cell phones for their service

The estimated proportion of households who relied strictly on cell phones for their service is given by:

\( \hat p =\frac{X}{n}= \frac{48}{150}= 0.32\)

And the margin of error would be given by:

\( ME = z_{\alpha/2} \sqrt{\hat p(1-\hat p)}{n}\)

The confidence is 90% so then the significance is \(\alpha=1-0.9=0.1\) and \( \alpha/2 =0.05\) the critical value for this case from the normal standard distribution is:

\( z_{\alpha/2}= 1.64\)

And the margin of error would be:

\( ME = 1.64 \sqrt{\frac{0.32 (1-0.32)}{150}}= 0.0625\)

a. The approximate value of the y-intercept is

b. The approximate value of the slope is

c. The expected number of cones of ice cream when the temperature is 30°C is 90°C.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (100 - 60)/(45 - 5)

Slope (m) = 40/40

Slope (m) = 1

At data point (5, 60) and a slope of 1, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 60 = 1(x - 5)  

y = x - 5 + 65

y = x + 60

Part a.

Based on the equation above, the y-intercept is equal to 60.

Part b.

Based on the equation above, the slope is equal to 1.

Part c.

In this scenario, the expected number of cones of ice cream when the temperature is 30°C;

y = x + 60

y = 30 + 60

y = 90°C.

Read more on point-slope here: brainly.com/question/24907633

#SPJ1

Answer:

$36570

Step-by-step explanation:

The original price is 34500, so the %given must be the increase in price :

34500x(1+6%)

=34500x1.06

=36570//

The scenarios that can be considered a seller-based discount are:

A. The offer by Wire and Cable

B. Carfna's Fine Foods

C. Mouser Electronics offer

E. Carchex Car Maintenance

A seller-based discount is a discount that is offered by a seller for the early purchase of a product. The goal of the seller in this case is to get cash as he or she is in an immediate need for cash.

The most outstanding example is that of Carchex Car Maintenance where an offer is made by the seller for the early purchase of products.

Learn more about the seller-based discount here:

https://brainly.com/question/30849708

#SPJ1

Answer:

False

Step-by-step explanation:

Answer:

A quadrilateral can't have 2 reflex angles

Step-by-step explanation:

A quadrilateral can't have 2 reflex angles because reflex angles > 180° so if you add two together, it is > 360°

The capacity of this swimming pool is between B. 500 gallons to 1,000 gallons.

Capacity refers to the product of the length, width, and height of a three-dimensional object or space.

The capacity of an object means the same as its volume.

Olympic-size swimming pools have the following standard dimensions:

Length = 50 m

Width = 25 m

Height = 2 m

Capacity of an Olympic swimming pool = 2,500 m³ (50 x 25 x 2)

= 660,000 gallons (2,500 x 1,000 ÷ 3.785)

An interval estimate shows the lower and upper limits.

6 x 105 gallons = 630 gallons

Thus, the capacity of the swimming pool is Option B.

Learn more about volume or capacity at https://brainly.com/question/463363

#SPJ1

A. 100 gallons to 500 gallons

B. 500 gallons to 1,000 gallons

C. 1,000 gallons to 1,500 gallons

D. 1,500 gallons to 2,000 gallons

Answer:

Expanded Notation Form:

500,000 = 500,000 + 0 + 0 + 0 + 0 + 0

Expanded Factors Form:

500,000 = 5 × 100,000 + 0 × 10,000 + 0 × 1,000 + 0 × 100 + 0 × 10 + 0 × 1

Expanded Exponential Form:

500,000 = 5 × 10⁵ + 0 × 10⁴ + 0 × 10³ + 0 × 10² + 0 × 10¹ + 0 × 10⁰

Word Form:

500,000 = Five hundred thousand

Step-by-step explanation:

Because math says so..

The length of the straw fitted in the box is 10.67 inches.

A cuboid is a solid three-dimensional object which has six faces that are rectangular with eight vertices, and twelve edges.

Given that, a straw is placed inside a rectangular box that is 5 inches by 5 inches by 8 inches, the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner,

Diagonal of a cuboid  = √ l² + w² + h²

Therefore, diagonal of the box = √ 5² + 5² + 8² = 10.67 in

Hence, The length of the straw fitted in the box is 10.67 inches.

For more references on cuboid, click;

https://brainly.com/question/19754639

#SPJ1

Answer:

24.08 miles/gallon

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

$13.35 is in Carla's piggy bank

Answer:

B

A

C

A

Step-by-step explanation:

The equation for the total cost of all adult tickets (a) and student tickets (s).

4a + 2.5s = 2,820  

a + s = 900

The number of adults ticket and student tickets is 380 and 520.

We have,

Adults ticket cost = $4

Student ticket cost = $2.5

Now,

Total amount earned = $2,820

The equation for the total cost of all adult tickets (a) and student tickets (s).

4a + 2.5s = 2,820   ______(1)

And,

The number of tickets sold = 900.

We can write as equation as:

a + s = 900 ______(2)

Now,

We have two equations.

4a + 2.5s = 2820

a + s = 900

Solving for s.

s = 900 - a

Substituting in (1)

4a + 2.5(900 - a) = 2820

Simplifying and solving for a.

4a + 2250 - 2.5a = 2820

1.5a = 570

a = 380

Now,

a + s = 900

380 + s = 900

s = 520

Therefore,

The number of adults ticket and student tickets is 380 and 520.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

Answer:

$839.20

Step-by-step explanation:

To find the finance charge, we need to first calculate the total amount financed, which is the price of the snow thrower minus the down payment.

The down payment is 20% of $1,501, which is:

0.20 x $1,501 = $300.20

So the total amount financed is:

$1,501 - $300.20 = $1,200.80

The total amount of the 12 monthly payments is:

12 x $170 = $2,040

The finance charge is the difference between the total amount of the payments and the amount financed:

$2,040 - $1,200.80 = $839.20

Therefore, the finance charge is $839.20.

Answer:

The top left option, with the equation y = -x + 7 and the line that goes down as it goes right.

Step-by-step explanation:

The equation for slope-intercept form is y = mx + b.

In order to turn the given equation x + y = 7, we need to isolate the y.

x + y = 7

subtract x from both sides:

x + y - x = 7 - x

y = 7 - x

The equation y = 7 - x can also be written as y = -x + 7.

If you were to graph this equation, the line would intersect the y-axis at point (0, 7). Since the slope of the line is negative, The line would go down as it goes right.

So, the correct choice is the first one, where the equation is y = -x + 7 and the line lowers as it goes right.