The Advanced Drama Club is selling tickets for Annie. Pre-registered tickets cost $6 and tickets at the door cost $8.50. The total number of tickets sold was 355. The total amount received was $2,580. Write a system to determine how many of each type of ticket was sold. Use p for pre-registerd and d for tickets purchased at the door. Solution: (pre-registered tickets, door tickets)

Answer:

Step-by-step explanation:

The perimeter of a rectangle is 2x+2y.

The perimeter of a triangle is a+b+c.

Set these equal to each other and you have this equation:

2(8) +2(x+2) = 8+2x+ (2x+4)

16+2x+4 = 8+2x+2x+4

2x+20=4x+12

8=2x

x=4

Now that you know x=4, you can plug it back into your perimeter equations.

For the rectangle: 16 +2(2+4)

= 16+2(6) = 16+12= 28

The perimeter of the rectangle is 28 inches.

For the triangle: 8+ 2(4) + (2(4) + 4)

= 8+ 8+ (8+4)

= 16 +12 = 28

The perimeter of the triangle is 28 inches.

Since the perimeters are equal, x=4.

The credit card issuer will receive $\(0\) less after both items are returned.

A credit card's biggest feature is that it's not connected to a checking account. Hence, rather than taking money out of your bank account when you swipe you credit card, your credit or debit card limit is used instead.

For individuals with bad credit or no credit, secured credit card will probably be the simplest to obtain. This is due to the fact that they demand collateral in the form of a deposit, which is ordinarily equivalent to your credit limit and minimizes the danger to the card company in the event that you fail to make your payment.

\(269 + 375 = 644\)

The credit card issuer will reimburse the whole amount spent if Karana's mother returns both products, hence the revised sum payable to a credit card provider is as follows:

\(644 - 644 = 0\)

Therefore, the change in the amount owed to the credit card company from returning both items is $\(0\).

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the length of both pairs of adjacent sides AB and BC are not equal, so ABCD is not a rectangle.

To prove that the quadrilateral ABCD is not a rectangle when A(0, -4), B(8, -3), C(4, 4), D(-4, 3), we need to use the distance formula and check the length of all four sides of the quadrilateral.Let's first find out the length sides  of the given quadrilateral ABCD:AB = sqrt [(8 - 0)^2 + (-3 - (-4))^2] = sqrt(64 + 1) = sqrt(65)BC = sqrt [(4 - 8)^2 + (4 - (-3))^2] = sqrt(16 + 49) = sqrt(65)CD = sqrt [(-4 - 4)^2 + (3 - 4)^2] = sqrt(64 + 1) = sqrt(65)DA = sqrt [(-4 - 0)^2 + (3 - (-4))^2] = sqrt(16 + 49) = sqrt(65)We can see that all four sides of the given quadrilateral are equal to the same value of sqrt(65).Therefore, we can say that ABCD is not a rectangle, because if it were a rectangle, it would have opposite sides equal and the adjacent sides would be equal.

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The opposite sides of the quadrilateral have different slopes, they are not parallel and thus, the quadrilateral ABCD is not a rectangle.

To prove that the quadrilateral ABCD is not a rectangle, we need to show that the opposite sides are not parallel or the diagonals are not congruent.

Here are the coordinates of the given quadrilateral:

A(0,-4), B(8,-3), C(4,4), D(-4,3).

Now, let us find the slopes of the lines using the given coordinates and then compare them to determine whether opposite sides are parallel or not.

Slope of AB using A(0,-4) and B(8,-3):

Slope = (y2-y1) / (x2-x1)

Slope= (-3-(-4)) / (8-0)

Slope= 1/8

Slope of CD using C(4,4) and D(-4,3):

Slope = (y2-y1) / (x2-x1)

Slope= (3-4) / (-4-4)

Slope= -1/4

The slopes being unequal , hence the opposite sides of this quadrilateral are not parallel & hence this quadrilateral is not a rectangle.

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Answer:

Rs. 1250

Step-by-step explanation:

\(x\) is the cost of the video-game without VAT.

VAT is 162.5 at the rate of 13%.

13% of \(x\) is the VAT.

\(13/100 \times x = 162.5\)

\(0.13 \times x =162.5\)

\(x=162.5 \div 0.13\)

\(x=1250\)

The obtained value must be compared against the critical value. Hence, the correct option is b.

In hypothesis testing, the critical value is a threshold or cutoff point that is determined based on the chosen significance level (alpha level) and the distribution of the test statistic. It helps in determining whether to reject or fail to reject the null hypothesis.

After calculating the test statistic (such as z-score or t-statistic) from the observed data, it is compared to the critical value associated with the chosen significance level.

If the test statistic exceeds the critical value, it falls into the critical region, leading to the rejection of the null hypothesis.

If the test statistic is less than or equal to the critical value, it falls into the non-critical region, resulting in a failure to reject the null hypothesis.

Therefore, the obtained value must be compared against the critical value to make a decision in hypothesis testing. Hence, the correct answer is option b.

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Answer:

9

Step-by-step explanation:

triangle AEB is similar to triangle ADC so their sides are proportional.  AE/AD = AB/AC .

Answer:

Step-by-step explanation:

The meaning of the translation (x + 6, y + 10) is that all points in a coordinate plane are moved 6 units to the right and 10 units up.

In other words, for any point (x, y) in the original position, after the translation, the new coordinates would be (x + 6, y + 10). This means that the x-coordinate of each point is increased by 6 units, resulting in a shift to the right, and the y-coordinate is increased by 10 units, resulting in a shift upwards.

Answer:

y=2x+1

Step-by-step explanation:

Hi there!

We are given the slope (m), which is 2, as well as the point (5,11).

We need to find the equation of the line.

There are 3 ways to write the equation of the line, but the most common type is slope-intercept form, or y=mx+b, where m is the slope and b is the y intercept

We're already given the slope (2), so we can substitute it into the equation right away

here's the equation so far:

y=2x+b

now we need to find b.

We can do this by plugging (5,11) into the equation, as the line passes through that point.

Substitute x as 5 and 11 as y

11=2(5)+b

multiply

11=10+b

subtract 10 from both sides

1=b

substitute 1 as b into the equation

y=2x+1

Hope this helps! :)

Answer:

  $20

Step-by-step explanation:

You want the amount of the overdraft fee if an $89 check written against a balance of $41 resulted in an account balance of -$68.

The new balance in James's account is ...

  old balance - check written - overdraft fee = new balance

  41 - 89 - fee = -68

  fee = 68 + 41 - 89 = 20

James was charged an overdraft fee of $20.

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Answer:

5. 8

6. 5

7. 7

8. 6

9. 3

10. 4

Step-by-step explanation:

The unknown number is the the larger number divided by 10.

Like in #5 : 80 ÷ 10 = 8

In your test plan, include the number of repetitions you will perform and a method for analyzing the data to account for random errors.

A test plan should account for the presence of systematic and random errors through the following steps:

1. Calibration: Calibration ensures that the instruments used in the experiment are accurate and consistent. By calibrating the equipment, you can minimize the impact of systematic errors on your results. Start your test plan by ensuring all instruments are calibrated and their measurements are reliable.

2. Randomization: Randomization is the process of randomly assigning subjects or samples to different experimental conditions. This helps to eliminate any potential bias or systematic errors caused by the arrangement of the experiment. In your test plan, make sure to include a method for randomizing the experiment to minimize the effect of systematic errors.

3. Repetition: Repeating the experiment multiple times can help reduce the impact of random errors. By performing the experiment multiple times and averaging the results, you can minimize the influence of random errors on your findings.

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Answer:

X=7

Step-by-step explanation:

Both are equal angles( the little 2 arrows prove that) so we set up the equation like this

75=11x-2

We need to isolate x to solve for it so we add 2 to both side since it's the opposite of subtraction.

our equation will then look like this

77=11x

last but not least, we divide 11 to both sides since it's the opposite of multiplication which 11 and X are doing

the answer is 7

At least 10 people or guests could go to a party and the second caterer is $250 cheaper to hire.

In the question we can use the equation :

  Y = mx + b ,  which is the slope-intercept form of the equation of a straight line. Here, m is the slope of the line and b is the intercept, x and y represent the distance of the line from the x-axis and y-axis, respectively.

For caterer A, the cost per guest is $15. This is the m value. The b value is the additional fee for setting up the tables, $100.

Here, the equation will be  y = 15x + 100     -------------------------(1)

For Caterer B, the cost per guest is $20. The b value is the additional fee for setting up the tables $50.

For this the equation will be : Y = 20X + 50.  --------------------- (2)

To find the number of guests that will result in an equal cost, set the equations equal to one another. Solve for x.

                    15x + 100 = 20x + 50        ---------------------- (3)

solving the equation (3),

   15x - 20x = 50 - 100

⇒ -5x = - 50

⇒ x = 10

Putting x = 10 in equation (1),

   15 × 10 + $100 = $250

Therefore, the cost of 10 people or guest will attend the party and the second caterer is $250 cheaper then the first caterer.  

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Answer:

Step-by-step explanation:

The total of their account balances is equal to the total spent plus the remaining amount. The given relations tell us ...

__

Solving this equation, we can find Mark's withdrawal and his initial deposit.

  145 +1.6d = 265

  1.6d = 120 . . . . . . . the amount Mark withdrew

  d = 120/1.6 = 75 . . . . the amount Mark deposited

Mark put $75 into his savings account.

__

Had Mark put $100 into his savings account, the total of withdrawals would have been ...

  Trisha + Mark = $100 × 145% +$100 ×160% = $145 +160 = $305

After spending $225 of this amount, they would have had a leftover amount of ...

  $305 -225 = $80

Trisha is not correct in her thinking that there would be more than $100 left over.

Given:

Total number of students = 147

Number of students taking math = 95

Number of students taking science = 73

Number of students taking both = 52

To find:

The theoretical probability of randomly choosing a student who is taking math.

Solution:

We have,

Total number of students = 147

Number of students taking math = 95

Now, the theoretical probability of randomly choosing a student who is taking math is

\(P(M)=\dfrac{\text{Number of students taking math}}{\text{Total number of students}}\times 100\)

\(P(M)=\dfrac{95}{147}\times 100\%\)

\(P(M)=64.62585\%\)

\(P(M)\approx 64.6\%\)

The theoretical probability of randomly choosing a student who is taking math is 64.6%.

Therefore, the correct option is C.

In the last basketball game, the ratio of baskets made to the total shots taken was 4:7 and if the team shot a total of 56 baskets in the game then the total basket they made is 40.

The ratio is 4:7, this means that for every 7 shots taken, 4 of them were made. If the team shot a total of 56 shots in the last game, then they made

(4/7) ×56 = 40 baskets.

This calculation can be broken down into simpler terms. For every 7 shots, 4 shots were made. Therefore, for 56 shots, 40 shots were made. Therefore, the team made 40 baskets in the last game.

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Data defines a claim that has been verified, examined, and backed up by numerous pieces of evidence.

Data is information that has been transformed into a format that is useful for transfer or processing in computing. Information that has been converted into binary digital form for usage with contemporary computers and communication channels is referred to as data.

As the volume of data being collected and stored increases, so do the units used to measure it. For instance, the relatively new concept of a "brontobyte" refers to a unit of data storage that is 10 to the 27th power of bytes.

File formats can be used to store data, such as ISAM and VSAM in mainframe systems. Another file format for storing, converting, and processing data is comma-separated values.

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The coordinates of triangle RST after it is translated four units right and three units up are (0, 5), (7, 8) and (0, -1)

From the figure, the coordinates of the triangle RST are:

R = (-4, 2)

S = (3, 5)

T = (-4, -4)

The rule of translation is given as:

This is represented as:

(x, y) = (x + 4, y + 3)

So, we have:

R' = (-4 + 4, 2 + 3) = (0, 5)

S' = (3 + 4, 5 + 3) = (7, 8)

T = (-4 + 4, -4 + 3) = (0, -1)

Hence, the coordinates of triangle RST after it is translated four units right and three units up are (0, 5), (7, 8) and (0, -1)

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Answer: a prediction of the number of hot cocoas sold when the temperature is 0F

Step-by-step explanation: i did it on delta math

The line's y-intercept represent ''Number of hot cocoas sold''.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Chloe has a part-time job at an ice skating rink selling hot cocoa.

She decided to plot the number of hot cocoas she sold relative to the day's high temperature and then draw the line of best fit.

Now,

Since, She decided to plot the number of hot cocoas she sold relative to the day's high temperature and then draw the line of best fit.

Hence, By the graph we have;

The line's x - intercept represent ''Temperature''.

And, The line's y-intercept represent ''Number of hot cocoas sold''.

Thus, The line's y-intercept represent ''Number of hot cocoas sold''.

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Answer:

6,7,8,9

Step-by-step explanation:

To find the partial derivatives of U with respect to T and T with respect to U, we will use the implicit differentiation technique. First, we differentiate both sides of the equation with respect to T:

2(TU-V)(U dT + T dU) ln(W - UV) + (TU - V)^2 (1/(W - UV))(-U dT + V dU) = 0

Simplifying this equation and plugging in the values at (T,U,V,W) = (2,3,7,28), we get:

12ln(19) dT - 21ln(19) dU = 0

Next, we differentiate both sides of the equation with respect to U:

2(TU-V)(T dU - U dT) ln(W - UV) + (TU - V)^2 (1/(W - UV))(-T dU + U dV) = 0

Simplifying this equation and plugging in the values at (T,U,V,W) = (2,3,7,28), we get:

-8ln(19) dT + 9ln(19) dU = 0

Solving these two equations, we get:

dT/dU = 21/12 = 1.75

dU/dT = -8/9 = -0.8888 (rounded to 4 decimal places)

Therefore, the partial derivative of U with respect to T is approximately -0.8888 and the partial derivative of T with respect to U is approximately 1.75.

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ΔM N O and ΔQ R S are congruent triangles because all three sides of ΔM N O are equal in length to the corresponding sides of ΔQ R S. Therefore, we can say that ΔM N O ≅ ΔQ R S.

To determine whether ΔM N O ≅ ΔQ R S, we need to compare the corresponding sides and angles of the two triangles.

Let's start by finding the lengths of the sides of each triangle. Using the distance formula, we can calculate the lengths as follows:

ΔM N O:
- Side MN: √[(5-2)^2 + (2-5)^2] = √[9 + 9] = √18
- Side NO: √[(1-5)^2 + (1-2)^2] = √[16 + 1] = √17
- Side MO: √[(1-2)^2 + (1-5)^2] = √[1 + 16] = √17

ΔQ R S:
- Side QR: √[(-7+4)^2 + (1-4)^2] = √[9 + 9] = √18
- Side RS: √[(-3+7)^2 + (0-1)^2] = √[16 + 1] = √17
- Side QS: √[(-3+4)^2 + (0-4)^2] = √[1 + 16] = √17

From the lengths of the sides, we can see that all three sides of ΔM N O are equal in length to the corresponding sides of ΔQ R S. Hence, we can say that ΔM N O ≅ ΔQ R S by the side-side-side (SSS) congruence criterion.

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In the big bucks lottery, there are chances that 10 out of 1000 people will win the lottery.

If there are 1000 people in the Big Bucks lottery and there is a 1 percent chance of winning 10 dollars prize if all 1000 people buy the lottery ticket of 10 dollars. If every person buys 10 dollar lottery ticket, then the chances of winning people would be calculated as follows:

Total number of People = 1000

Chances of winning the lottery = 1%

How many people would win 10 dollar lottery = 1000 * 1%

= 1000 * 0.01

= 10 People.

So there are chances that 10 out of 1000 people will win the lottery.

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It is most important to have a random sample in inferential statistics, particularly in making statistical inferences about a population based on the sample data.

Random sampling is a critical component of inferential statistics because it helps to ensure that the sample is representative of the population. When a sample is randomly selected, each member of the population has an equal chance of being included in the sample, which reduces the risk of bias in the results. Without a random sample, the results of statistical analyses may not be accurate or generalizable to the population, and the conclusions drawn from the data may be flawed or misleading.

Therefore, random sampling is crucial in making valid statistical inferences about a population.

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On solving the provided question, we can say that the - by solving algebraic equation x= 0 and y= 4.

A mathematical statement in which two expressions are rendered equal to one another is known as an algebraic equation. A variable, coefficients, and constants make up an algebraic equation in most cases. Check out algebraic expressions as well. Equations, or the equal sign, simply indicate equality. With mathematics, and algebraic expression is one that is constructed using variables, constant algebraic numbers, and algebraic operations. An algebraic expression is, for instance, 3x2 2xy + c.

y+ (2/3)x = 4

12—3y

3y +6x 12

2x+3y=12

by subtracting2frorn1.

4x=o

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Answer:Yes, the Boolean sum is represented as a Boolean product.

Step-by-step explanation:Problem 2. Let A be a 3 × 3 zero-one matrix. Let I be a 3 × 3 identity matrix. Show that A ⊙ I = I ⊙ A = A. Solution. Let. Show that a Boolean function can be represented as a Boolean product of maxterms. This representation is called the product-of-sums expansion or conjunctive normal form of the function. (Hint: Include one maxterm in this product for each combination of the variables where the function has the value 0.)

Step 1: Definition.

The complements of an elements 0=1 and 1=0.

.

The Boolean sum + or OR is 1 if either term is 1.

The Boolean product (.) or AND is 1 if both term are 1.

Step 2: Show the Boolean function can be represented as a Boolean product.

The Boolean sum is

where

or

, has the value 0 for exactly one combination of the values of the variables, namely, when

if

and

if

. This Boolean sum is called a maxterm.

For each combination of the values of the variables for which the Boolean function F is 0.

The Boolean product of maxterms is 0 if and only if at least one of the maxterm is 0. Thus, the Boolean function F can be represented as a Boolean product of the maxterm.

Therefore, the Boolean sum is represented as Boolean products.

To find the Boolean product of A and B, we need to perform a logical AND operation between each corresponding pair of bits in A and B.

Starting with the rightmost bit in B, we have:

1 AND 0 = 0

Next, we have:

1 AND 1 = 1

Then:

1 AND 1 = 1

And finally:

0 AND 1 = 0

So the result of the first column is:

0110

Moving on to the next column, we have:

1 AND 0 = 0

0 AND 1 = 0

1 AND 1 = 1

1 AND 0 = 0

So the result of the second column is:

0000

Continuing on to the third column, we have:

0 AND 0 = 0

1 AND 1 = 1

1 AND 1 = 1

1 AND 1 = 1

So the result of the third column is:

1111

Finally, we have:

1 AND 1 = 1

0 AND 0 = 0

0 AND 1 = 0

1 AND 0 = 0

So the result of the fourth column is:

0000

Putting it all together, the Boolean product of A and B is:

0110
0000
1111
0000

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