Elena went to a store where you can scoop your own popcorn and buy as much as you want. She bought 10 ounces of spicy popcorn for $2.50 (before taxes).

How much popcorn can you buy per dollar?

Answer:

first option is correct

Step-by-step explanation:

finding area for upper rectangle

length = 16 miles

breadth = (2x - 1) miles

area of rectangle = l*b

=16 *(2x - 1)

16*2x - 16*1

=32x - 16

finding area for another rectangle

length = (5x + 5) miles

breadth = 4 miles

area of rectangle = l*b

= (5x + 5) * 4

=5x*4 + 5*4

=20x + 20

area of the figure = area of upper rectangle + area of another rectangle

=32x - 16 + 20x + 20

= (52x + 4) sq mi

Answer:

He can buy up to 2 outfits.

Step-by-step explanation:

440.12 + 2(12.86) + 19.26 + 53.96o ≤ 620

53.96o + 485.10 ≤ 620

53.96o ≤ 134.9

o ≤ 2.5

He can buy up to 2 outfits.

The probability that a randomly selected student is taking a math class or an English class is 0.79.

Using the formula for the union of two events, P(A or B) = P(A) + P(B) - P(A and B), where A is the event "taking a math class" and B is the event "taking an English class", we can find the desired probability:

P(A or B) = 0.76 + 0.75 - 0.72 = 0.79

So,  "0.79" (which is given in upto two decimal places) is the probability that a randomly selected student is taking a math class or an English class.

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Answer:

48

Step-by-step explanation:

The given parameters are;

The activities in which the students of the school participate = 1) Debate, 2) Music, and 3) Community services

The number of students that do all three activities = 3

The number of students that do two or more activities = 21

The number of the students that participate in music = Half of the students

The ratio of the students that take part in debate, music, and community service = 5 : 4 : 3

Let x represent a common number factor of participants in each of the given three activities, we have;

5·x participate in debate, A

4·x participate in music, B

3·x participate in community service, C

We get;

The sum of the students in the school = A∪B∪C = A + B + C - A∩B - A∩C - B∩C + A∩B∩C

Given that the number of students that do two or ore activities = 21, we have;

(A∩B)∪(A∩C)∪(B∩C) = 21

However, we have;

(A∩B)∪(A∩C)∪(B∩C) = (A∩B) + (A∩C) + (B∩C) - A∩B∩C - B∩A∩C - C∩B∩A + A∩B∩C

∴ 21 = (A∩B) + (A∩C) + (B∩C) - 3 - 3 - 3 + 3

(A∩B) + (A∩C) + (B∩C) = 21 + 3 + 3 + 3 - 3 = 21 + 6 = 27

∴ -(A∩B) - (A∩C) - (B∩C) = -27

Therefore;

A + B + C - A∩B - A∩C - B∩C + A∩B∩C = 5·x + 4·x + 3·x - 27 + 3

5·x + 4·x + 3·x - 27 + 3 = 12·x - 24

The total number of students = A∪B∪C = 12·x - 24

The number of students participating in music, B = 4·x = Half the total number of students = (12·x - 24)/2

∴ 4·x = (12·x - 24)/2

8·x = 12·x - 24

12·x - 8·x = 24

4·x = 24

x = 24/4 = 6

The total number of students at the school = 12·x - 24 = 12 × 6 - 24 = 48

Answer:

7

Step-by-step explanation:

use the distance formula which is (the pic down below)

so then plug in the numbers:

the sqaure root of  (3-(-4)^2 + (-6-(-6)^2

then you get the sqaure root of (7)^2+ (0)^2

then add the numbers

you get sqaure root of 49

and the square root of 49 is 7 (because 7*7=49)

Hope this helps!

Answer: 7

Step-by-step explanation:

use this equation \(\sqrt{(x2-x1)^{2} + (y2-y1)^{2}\)

your points are (-4, -6) and (3, -6)

i recommend plugging this into your calculator: (3+4)^2 + (-6+6)^2

you get 49 (second part cancels out so (7)^2=49

now bring the root sign down \(\sqrt{49}\) =7

Answer:

The answer would be $6,700

Hence, if a cricket chirps 70 times, a good estimate of the outside temperature is 5.49 degrees Celsius.

A scatterplot is a particular kind of graphical display that uses a collection of dots on a this double coordinate plane to represent a collection of information values. A pair of values, often a variable shown on the horizontally (x) axis and a predictor variables plotted just on vertical (y) axis, are represented by each figure on the plot. Each point's location provides information about both variables' values, and the arrangement of the points can show any relationships between the two factors. Scatterplots are frequently used to spot patterns, correlations, or other connections between different data sets.

given

According to the scatterplot, a logical line of greatest fit would go via the points (15, 57) and (90, 89). We must first determine the slope of this line in order to determine its equation:

slope = (89 - 57) / (90 - 15) = 0.53

The equation of the line can therefore be expressed in the point-slope form of a linear equation as follows:

y - 57 = 0.53(x - 15) (x - 15)

If we simplify this equation, we get:

y = 0.53x - 30.11

If a cricket chirps 70 times, what will the outside temperature be? We may solve for y by substituting 70 for x and making the following prediction:

y = 0.53(70) - 30.11 = 5.49

Hence, if a cricket chirps 70 times, a good estimate of the outside temperature is 5.49 degrees Celsius.

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Answer: 30 degrees

Step-by-step explanation:

1 hour = 60 min = 360 degree

1 min = 360/60 degree

1 min = 6 degree

and the gap of hour hand and minute hand at 1pm, is of 5 min

therefore acute angle formed is 5 X 6 = 30 degrees.

:-)

Answer:

30 degrees

Step-by-step explanation:

1 hour = 60 min = 360 degree

1 min = 360/60 degree

1 min = 6 degree

and the gap of hour hand and minute hand at 1pm, is of 5 min

therefore acute angle formed is 5 X 6 = 30 degrees.

The tree is 10 meters tall.

To find the height of the tree, we can use the concept of similar triangles. The ratio of the height of the tree to the length of its shadow should be equal to the ratio of the height of the post to the length of its shadow, since they are both located in the same plane and are being illuminated by the same light source.

Let's use proportions to solve this problem. We can set up the proportion:

height of tree / length of tree's shadow = height of post / length of post's shadow

Let h be the height of the tree. Then we have:

h / 15 = 2 / 3

Cross-multiplying, we get:

3h = 30

h = 10

Therefore, the tree is 10 meters tall.

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On the arranged survey, the statistical margin of error is supposed to be 14.73 SEK.

In a large consumer survey, 610 randomly selected customers are interviewed in a large grocery store. They are asked, among other things, how much they have shopped for. On average, they have shopped for 412 SEK with a standard deviation of 181 SEK .

Estimate with a 95% confidence interval the average purchase amount in the entire population. The formula for finding the margin of error is given as;

Margin of Error = z * (σ/√n)

Where:

σ is the standard deviation

n is the sample size

z is the Z-score for the desired confidence level, which is 95%.

Z-score corresponding to 95% confidence level is 1.96

Margin of Error = 1.96 * (181/√610) = 14.73

The statistical margin of error is 14.73 SEK.

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The task requires analyzing a list of departments and performing several tasks related to relationship codes, activity relationship diagrams, reason codes, a worksheet, and a dimensionless block diagram.

We need to consider the number of departments. Since we have 7 departments listed, the number of relationship codes can be calculated using the formula: (n * (n-1)) / 2, where n is the number of departments.

Substituting the value of n = 7, we get:

Relationship Codes = (7 * (7-1)) / 2

= (7 * 6) / 2

= 42 / 2

= 21

Therefore, there will be 21 relationship codes in the chart.

Create an activity relationship diagram:

An activity relationship diagram visually represents the relationships between departments. Here is a basic diagram representing the given departments:

Receiving --+

           +-- Assembly & Shipping -- Offices

Fabrication--+

           +-- Painting -- Stores

Restrooms & Lockers

Populate the diagram with codes for all the relationships:

To populate the diagram with codes, we can assign a unique code to each relationship. Here's an example of assigning codes to the relationships in the diagram:

Receiving (R) --+

               +-- Assembly & Shipping (AS) -- Offices (O)

Fabrication (F)--+

               +-- Painting (P) -- Stores (S)

Restrooms & Lockers (RL)

What is the percentage of codes in each category? Does it follow the standard percentages?

To determine the percentage of codes in each category, we need to count the number of codes in each category and calculate the percentage relative to the total number of codes (21).

In this case, we have the following categories and their respective codes:

Production: R, F, AS, P (4 codes)

Administration: O, S (2 codes)

Support: RL (1 code)

Percentage of Production codes = (4 / 21) * 100 ≈ 19.05%

Percentage of Administration codes = (2 / 21) * 100 ≈ 9.52%

Percentage of Support codes = (1 / 21) * 100 ≈ 4.76%

These percentages do not necessarily follow any standard percentages. The distribution of codes among categories can vary depending on the specific organization or context.

Provide at least 3 reason codes for the chart:

Reason codes are used to provide explanations or justifications for the relationships depicted in the chart. Here are three example reason codes for the given chart:

R01: Receiving department receives raw materials and supplies from external sources.

AS01: Assembly & Shipping department assembles products and prepares them for shipment.

O01: Offices department provides administrative support and management functions for the organization.

Create a worksheet to assist in the creation of the dimensionless block diagram:

Here's an example of a worksheet that can assist in creating the dimensionless block diagram:

Relationship Code From Department To Department

R Receiving Fabrication

F Fabrication Painting

AS Assembly & Shipping Offices

P Painting Stores

RL Restrooms & Lockers -

O Offices -

S Stores -

This worksheet lists the relationship codes along with the corresponding "From" and "To" departments.

Create a dimensionless block diagram for your data B. Show the flow through the dimensionless block diagram:

A dimensionless block diagram represents the flow of activities or information between different departments. Here's an example of a dimensionless block diagram based on the given data:

Receiving --> Fabrication --> Painting --> Stores

                  |

                  v

        Assembly & Shipping --> Offices

                  |

                  v

       Restrooms & Lockers

The arrows indicate the flow of activities or information from one department to another.

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Answer:

3.66666666667

or

3.67(rounded to the nearest tenth)

Step-by-step explanation:

2x 1/2 x3 2/3 = 3.66666666667

Ace Carlos

Developer

Answer:

=3 2/3

Step-by-step explanation:

2 x 1/2 x 3 2/3

2 x 1/2 = 2/2 = 1

1 x 3 2/3

=3 2/3

The equation represents a circle with the same radius as the circle shown but with a center at (-1, 1) is (x + 1)² + (y - 1)² = 16.

We know that, the center of a circle is (-1, 1).

We know that, the standard form for an equation of a circle is

(x - h)² + (y - k)² = r²

The (h, k) are co-ordinate of your Centre of circle, which in this case is (-1,1) and r is the radius of circle.

As we can see in the figure radius = 4units

From Centre (1,-2) to (1,-2)

Put these into the equation

(x + 1)² + (y - 1)² = 4²

(x + 1)² + (y - 1)² = 16

Therefore, option D is the correct answer.

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The value of the investment after 3.5 years is approximately $2530.67.

The principal amount refers to the initial amount of money borrowed or invested, excluding any interest or additional fees. For example, if someone takes out a loan for $10,000, the principal amount is $10,000, and this is the amount that must be repaid to the lender, not including any interest that may accrue over time. Similarly, if someone invests $5,000 in a savings account, the principal amount is $5,000, and any interest earned on that amount will be calculated based on the principal amount. The principal amount is an important concept in finance and investing, as it determines the starting point for calculating interest, returns, and other financial transactions.

The formula for compound interest is:

\(A= P(1+\frac{r}{n} )^{nt}\)

Where:

A = the final amount

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years)

In this case, we have:

P = 2000

r = 0.04 (4% as a decimal)

n = 12 (compounded monthly, so 12 times per year)

t = 3.5 (3.5 years)

Plugging these values into the formula, we get:

\(A= 2000(\frac{1+0.04}{12})^{12*3.5}\)

A = 2000(1.00333333)⁴²

A ≈ 2530.67

Therefore, the value of the investment after 3.5 years is approximately $2530.67.

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Answer: Moe is wrong.

Step-by-step explanation:

Moe is incorrect because 25 divided by 5 equals 5 (constant of proportionality) but 12 divided by 3 does not equal 5 (it equals 4)

The eigenvalues of matrix A are λ₁ = 1.7 and λ₂ = -0.3. For each eigenvalue, the eigenspace basis is determined as follows: For λ₁ = 1.7, the eigenspace basis is {v₁ = [1 1]ᵀ}. For λ₂ = -0.3, the eigenspace basis is {v₂ = [-1 1]ᵀ}.

To find the eigenvalues of matrix A, we solve the characteristic equation det(A - λI) = 0, where A is the given matrix, λ is the eigenvalue, and I is the identity matrix. For the given matrix A, the characteristic equation becomes:

|1.6 - λ   -1.6 |

|-1.6       -0.2 - λ| = 0.

Simplifying and expanding the determinant, we have:

(1.6 - λ)(-0.2 - λ) - (-1.6)(-1.6) = 0,

-0.32 + 0.2λ + 1.6λ - λ² + 2.56 = 0,

λ² - 1.8λ + 2.88 = 0.

Solving this quadratic equation, we find the eigenvalues λ₁ = 1.7 and λ₂ = -0.3.

To find the basis for each eigenspace, we substitute each eigenvalue back into the equation (A - λI)v = 0 and solve for the corresponding eigenvector v.

For λ₁ = 1.7:

(A - 1.7I)v₁ = 0,

| -0.1  -1.6 | |x|   |0|,

| -1.6   1.5 | |y| = |0|.

Solving this system of equations, we get x = y. Therefore, v₁ = [1 1]ᵀ is a basis for the eigenspace corresponding to λ₁.

For λ₂ = -0.3:

(A + 0.3I)v₂ = 0,

| 1.9  -1.6 | |x|   |0|,

| -1.6   1.5 | |y| = |0|.

Solving this system of equations, we also get x = y. Therefore, v₂ = [-1 1]ᵀ is a basis for the eigenspace corresponding to λ₂.

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Answer:

x = 5

Step-by-step explanation:

Angles on a straight line add up to 180, so add up the angles and equate to 180:

9x + 85 + 10x = 180

Now we can solve for x by simplifying further:

19x + 85 = 180

Subtract 85 on both sides:

19x + 85 - 85 = 180 - 85

19x = 95

Divide 19 on both sides which cancels out the 19 on the left:

x = 95/19 = 5

Answer:

\(\frac{x-5}{\left(x-3\right)\left(x+2\right)}+\frac{2}{\left(x-3\right)\left(x+2\right)}=\frac{1}{2+x}\)

Step-by-step explanation:

\(\frac{x-5}{\left(x-3\right)\left(x+2\right)}+\frac{2}{\left(x-3\right)\left(x+2\right)}\)

\(\mathrm{Apply\:rule}\:\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\)

\(=\frac{x-5+2}{\left(x-3\right)\left(x+2\right)}\)

\(\mathrm{Add/Subtract\:the\:numbers:}\:-5+2=-3\)

\(=\frac{x-3}{\left(x-3\right)\left(x+2\right)}\)

\(\mathrm{Cancel\:the\:common\:factor:}\:x-3\)

\(=\frac{1}{2+x}\)

Since 1/4 is greater than 1/6 we can infer that Tiffany painted more of the room's wall.

Since most walls are square or rectangular, their surface area may be calculated by multiplying the width and height values, then taking out any spaces for doors or windows. However, unusual architecture and design might lead to the combination of the rectangle with triangular, round, or trapezoidal shapes. Using the fundamental formulas for estimating the area of two-dimensional forms is the key to accurately determining the surface area of a wall.

We must determine the precise dimensions of the parts Tiffany and Roberto painted in order to compare the quantity of each.

Assume for the moment that the wall is one unit in size. Tiffany then painted 1/4.

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The sales price of the item is $48.

The sale price of an item that costs 60% of its original price which is $80 is $48. The original price of the item is $80, and it costs 60% of the original price. The amount of money we'll be spending is calculated as follows: 60 per cent of $80 (60/100) × $80= $48 Therefore, the sales price is $48. The percentage discount for the item is calculated as follows:$80 - $48 = $32

$32 is the amount of money saved due to the discount, which is then divided by the original price, $32/$80 = 0.4 or 40%. Thus, there was a 40% discount on the original price.

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The applicants who are granted admission is 0.8413, The applicants who will score 860 or higher is 0.0228, and there will be 2023 applicants that are expected to be qualified to the university.

a) The scores in this problem are known to be normally distributed with a mean of 700 and a standard deviation of 80. To find the proportion of all applicants taking the exam who are granted admission, we must compute the Z-score of 620.

We then need to find the area under the normal curve to the right of this Z-score.1. Z-score of 620: (620 - 700)/80 = -1.00Therefore, P(X ≥ 620) = P(Z ≥ -1.00) = 0.8413 (using a standard normal table)

So, the proportion of all applicants taking the exam who are granted admission is approximately 0.8413.

b) To find the proportion of all applicants who will score 860 or higher on the exam, we must compute the Z-score of 860.

We then need to find the area under the normal curve to the right of this Z-score.2. Z-score of 860: (860 - 700)/80 = 2.00

Therefore, P(X ≥ 860) = P(Z ≥ 2.00) = 0.0228 (using a standard normal table)So, the proportion of all applicants who will score 860 or higher on the exam is approximately 0.0228.

c) Using the proportions calculated in parts (a) and (c), we can expect the following number of applicants to be qualified for admission to the university.

Qualified applicants = (2400)(0.8413) = 2023 (rounded to the nearest whole number)

Therefore, we expect 2023 applicants to be qualified for admission to the university.

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The volume of the pyramid with a square base which has an edge length of 2 cm and a measure of an angle BAC is 45° is equal to 4.8cm³.

A pyramid's edge length is 2cm.

The bottom is square.

Base area = (2)²

A is the center of the square base B is the apex of the right triangle BCA.

m ∠BAC = 45°

m ∠ABC = 45°

AC = BC

AC length = 3.6cm

BC height = 3.6cm

Volume (pyramid) = (1 ÷ 3) × base area × height

Volume (pyramid) = (1 ÷ 3) × (2)² × 3.6

Volume (pyramid) = 4.8cm³

As a consequence, the dimension of a pyramid with only a square base, a 2 cm edge length, and a BAC angle of 45° is 4.8cm³.

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The complete question is :

A solid oblique pyramid has a square base with an edge length of 2 cm. Angle bac measures 45°.

Point B is the apex and point A is the center of the square base. Line BC is the height of the pyramid. Triangle BCA is a right triangle. Base AC has a length of 3. 6 centimeters. What is the volume of the pyramid?

a. 2.4 cm³      b. 3.6 cm³      c.  4.8 cm³          d. 7.2 cm³.

Answer:

4.8cm^3

Step-by-step explanation:

Answer:

x = 13

Step-by-step explanation:

4x + 14 = 66

     -14     -14

---------------------

     4x = 52

     ----   ----

      4      4

      x = 13

The low end of a 95% confidence interval for the proportion of all BCTC students who say they would rather speak to animals is 0.3964.

The low end of a 95% confidence interval for the proportion of all BCTC students who say they would rather speak to animals is 0.3964.What is confidence interval?A confidence interval is a range of values, calculated from a data sample, that is used to estimate an unknown population parameter.The formula for the margin of error:margin of error = z* (standard deviation / sqrt(n))Wherez* = critical valueStandard deviation (σ) = Sample standard deviationn = Sample sizeHow to calculate the low end of a 95% confidence interval for the proportion of all BCTC students who say they would rather speak to animals?The formula for calculating the confidence interval for a proportion is:p ± z* (sqrt((p(1-p))/n))Here,Sample proportion (p) = 30/50 = 0.6Sample size (n) = 50Critical value for a 95% confidence interval (z*) = 1.96Put these values in the above formula to calculate the low end of the confidence interval:0.6 ± 1.96 * sqrt((0.6(1-0.6))/50)0.6 - 1.96 * 0.1143 = 0.3964 (rounded to 4 decimal places)Therefore, the low end of a 95% confidence interval for the proportion of all BCTC students who say they would rather speak to animals is 0.3964.

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Answer:

41.309 kg, 41.32 kg, 41.236 kg

Step-by-step explanation:

I think these are the correct answers.

Answer:

The data are at the nominal level of measurement

Step-by-step explanation:

Nominal Level of measurement is irrespective of orders or classes. In this survey we do not find out which game is ranked the most favorite.

Nominal; level is used just for counting.  Its cannot be used as a measure or for quantitative analysis.

Such data cannot give the mean of the sample. And the two means cannot be compared.

In the given question it only gives the number of likes  nothing more. The average cannot be calculated for such data.

Answer:

-7/9

Step-by-step explanation:

= (-4/9) x (7/4)

= -4/9 x 7/4

= -28/36 (simplifying gives -7/9)