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Mrs. Roslin has 32 students in her class. Of these students, 14 are girls. She chooses one boy and one girl at random to help pass out papers. Determine the total number of outcomes.
(Basically how many different outcomes can be made... no explanation needed.)

Answer:

There is no associative property of subtraction.

Step-by-step explanation:

Given:

x - (y - z) = 5 - (3 - 4) = 5 - (-1) = 5 + 1 = 6

(x - y) - z = (5 - 3) - 4 = 2 x -4 = -6

Therefore, there is no associative property of subtraction as 6 ≠ -6

Answer:

y minus 3 = 2x plus 1

Step-by-step explanation:

Answer:

Graph the line using a y-intercept -1 and slope 1.  

Graph the equation with vertex (0,0) and radius 2.

Answer:

1) y=2x-4

2) y=1/4x+2

Answer:

d. 4x+12

Step-by-step explanation:

distribute the 4

4*x =4x

4*3=12

therefore its

4x+12

Answer:

D

Step-by-step explanation:

4(x+3)

(4 times x) + (4 times 3)

4x + 12 = D

The Cartesian coordinates for point (c) are: (x, y) = (4.5, -7.794) which can be plotted on the graph using polar coordinates.

A system of describing points in a plane using a distance and an angle is known as polar coordinates. The angle is measured from a defined reference direction, typically the positive x-axis, and the distance is measured from a fixed reference point, known as the origin. In mathematics, physics, and engineering, polar coordinates are useful for defining circular and symmetric patterns.

(a) Polar coordinates (8, 4/3)
To convert to Cartesian coordinates, use the formulas:
x = r*\(cos(θ)\)
y = r*\(sin(θ)\)
For point (a):
x = 8 * \(cos(4/3)\)
y = 8 * \(sin(4/3)\)

Therefore, the Cartesian coordinates for point (a) are:
(x, y) = (-4, 6.928)

(b) Polar coordinates (-4, 3/4)
For point (b):
x = -4 * \(cos(3/4)\)
y = -4 * \(sin(3/4)\)

Therefore, the Cartesian coordinates for point (b) are:
(x, y) = (-2.828, -2.828)

(c) Polar coordinates (-9, \(-\pi /3\))
For point (c):
x = -9 * \(cos(-\pi /3)\)
y = -9 * \(sin(-\pi /3)\)

Therefore, the Cartesian coordinates for point (c) are:
(x, y) = (4.5, -7.794)

Now you have the Cartesian coordinates for each point, and you can plot them on a Cartesian coordinate plane.

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Density of water (ρ) = 1 g/cm³ Pressure at the tank (P1) = 1 atm (gauge) = 1 + 1 = 2 atm = 2 * 101.325 kPa Pressure at the surface of the lake (P2) = 1 atm (gauge) fric tion losses and Height difference between the lake and the tank (h) = 50 m Power delivered to the pump (P) = 2.5 hp = 2.5 * 745.7 W = 1864.25 WLet's solve the problem step by step.

Step 1: Calculate the pressure at the lake surface:Pressure at the lake surface = P2 + ρghHere, h = 50 m∴ Pressure at the lake surface (P2) = 1 atm (gauge) + 1 g/cm³ × 9.8 m/s² × 50 m = 601.8 kPa

Step 2: Determine the volume flow rate of water:Volume flow rate = Power / (ρgΔh)Here, Δh = h = 50 m∴ Volume flow rate = 1864.25 W / (1 g/cm³ × 9.8 m/s² × 50 m) = 3.784 m³/s

Step 3: Convert volume flow rate to mass flow rate:Mass flow rate = ρ × Volume flow rate= 1 g/cm³ × 3.784 m³/s= 3784 kg/s Therefore, the mass flow rate of water (in kg/s) is 3784.

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The transformations that can be used to map a triangle with vertices A(2, 2), B(4, 1), C(4, 5) to A’(–2, –2), B’(–1, –4), C’(–5, –4) is C. a 90 clockwise rotation about the origin and a reflection over the y-axis

This refers to the mathematical process where one figure or expression is changed from one form to another that has or contains a similar value.

Given the pair of points (x, y) in the original image, it has been transformed to (-y, -x).

If we allow ABC to be first transformed onto A"B"C" by a 90° clockwise rotation, this would result in:

B(4, 1) being mapped onto B''(1, -4).

Therefore, the rule mapping ABC to A"B"C"   is (x, y)→(y, -x)

With this, we can conclude that the transformation that maps (y, -x) to (-y, -x) is a reflection with respect to the y-axis

Option C is the correct transformation.

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Answer:

C

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Graph the two lines....where they intersect is the solution:

(-4,3)

OR sub in x = -4 into the first equation to find y = 3

Answer:

107 degrees

Step-by-step explanation:

since the two angles are on a straight line, and a straight line is 180 degrees,
180-73=x

x=107

Answer: a big number

Step-by-step explanation:

why do you even need to know the answer?? lol

Step-by-step explanation:

due to the rules of crossing lines and their angles, the 2 angles opposite of each other must be equal.

so,

7x + 7 = 112

7x = 105

x = 15

The balance in Adam's account at the end of June which has the credit card with an apr of 14.63% is $627.27.

Monthly payment is the payment which has to paid against the loan amount or the borrowed money calculated with interest rate.

The Adam’s credit card has an Apr of 14.63%,The table below shows his use of that credit card over three months.

For the purchase add the previous balance and for payment subtract the previous balance. I have mentioned another column for remaining balance in the above table.

The total of this transaction when multiplied with number of days, we get the total balance, 56498.48.

Now the monthly average balance is,

\(m=\dfrac{56498.48}{90}\\m=627.76\)

Thus, the balance in Adam's account at the end of June which has the credit card with an Apr of 14.63% is near to $627.27.

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Adam’s balance at the end of June is $629.42.

The adjusted balance method is an accounting method that bases finance charges on the amount(s) owed at the end of the current billing cycle after credits and payments post to the account.

Balance at the end of April = 626.45 + 37.41 + 44.50 = $708.36

Interest levied on $708.36= 708.36* (14.63/12) * 1/100

Interest levied on $708.36 = $8.64

So, balance on May 1st= 708.36+ 8.64 = $717

Balance at the end of May = 717-65.50+24.89-104.77 = $571.62

Interest levied on $571.62 = $571.62 * (14.63/12) * 1/100

Interest levied on  $571.62=$6.97

So, balance on June 1st = $578.59

Balance at the end of June = 578.59-23.60 + 15+51.85 = $621.84

Interest levied on $621.84 = $621.84* (14.63/12) * 1/100

Interest levied on $621.84 =$ 7.58

So balance at the end of the june = 621.84 + 7.58 = $629.42

Therefore, Adam’s balance at the end of June is $629.42.

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The Project Triangle is also known as the triple constraints model and consists of three elements: cost, time and scope.

The Project Triangle is also known as the Iron Triangle or Triple Constraints and is a graphical representation of the connection between project costs, schedule, and scope. It is one of the key principles of project management, and it is utilized to help organizations and project managers understand and handle trade-offs between different objectives of a project.

The three elements of the Project Triangle are:

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It could be slightly lower or higher, but we can be confident that it falls somewhere between 0.32 minutes and 1.47 minutes.

The most accurate interpretation of the given confidence interval is as follows:

We are 95% confident that the true difference in mean wait time between Facility A and Facility B falls within the range of 0.32 minutes to 1.47 minutes.

This means that if we were to repeat the study multiple times and calculate a new confidence interval each time, we would expect that approximately 95% of those intervals would contain the true difference in mean wait time between the two facilities.

Furthermore, based on the observed data and the calculated confidence interval, we can conclude that the difference in mean wait time between Facility A and Facility B is likely to be positive, with Facility B having a higher mean wait time than Facility A. However, we cannot say with certainty that the true difference is exactly within this specific range; it could be slightly lower or higher, but we can be confident that it falls somewhere between 0.32 minutes and 1.47 minutes.

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Answer

a) The system of two linear inequalities include

5x + 3y ≥ 15

3x + 4y > 12

b) Least number of times Sally needs to play only the ring toss in order to achieve her goal of more than 12 tickets = 5

c) Least number of times Tom needs to play only the fishing game in order to achieve her goal of at least 15 tickets = 5

Explanation

Number of times Ring toss needs to be played is denoted as x.

Number of times Fishing game needs to be played is denoted as y.

a) For Tom

5 tickets for each ring toss = 5x

3 tickets for each fishing game = 3y

Tom needs at least 15 tickets for the prize he wants

5x + 3y ≥ 15

For Sally

3 tickets for each ring toss = 3x

4 tickets for each fishing game = 4y

Sally needs more than 12 tickets for the prize she wants

3x + 4y > 12

The system of two linear inequalities is then

5x + 3y ≥ 15

3x + 4y > 12

b) What is the least number of times Sally needs to play only the ring toss in order to have enough tickets for the prize she wants?

The inequality describing her situation is

3x + 4y > 12

We are now told that if she plays only the ring toss, (that is, no fishing game, y = 0), what would be the minimum number of times she would need to play to achieve her goal of more than 12 tickets?

3x + 4y > 12

when y = 0

3x + 4y > 12

3x + 4(0) > 12

3x + 0 > 12

3x > 12

Divide both sides by 3

(3x/3) > (12/3)

x > 4

Number of times has to be more than 4, so, minimum number of times has to be 5.

c) What is the least number of times Tom needs to play only the fishing game in order to have enough tickets for the prize he wants?

The inequality describing his situation is

5x + 3y ≥ 15

We are now told that if he plays only the fishing game, (that is, no ring toss, x = 0), what would be the minimum number of times he would need to play to achieve his goal of at least 15 tickets?

5x + 3y ≥ 15

when x = 0

5(0) + 3y ≥ 15

0 + 3y ≥ 15

3y ≥ 15

Divide both sides by 3

(3y/3) ≥ (15/3)

y ≥ 5

Number of times has to be at least 5, so, minimum number of times has to be 5.

Hope this Helps!!!

Answer:

Difference between Joyce's and her brothers age is 10 years.

Step-by-step explanation:

Let,

x be the age of Joyce

y be the age of her brother

According to given statement;

x+y=24       Eqn 1

y = 2x+3    Eqn 2

Putting value of y from Eqn 2 in Eqn 1

x+2x+3=24

3x=24-3

3x=21

Dividing both sides by 3

\(\frac{3x}{3}=\frac{21}{3}\\x=7\)

Putting x=7 in Eqn 2

y = 2(7) + 3

y = 14+3

y = 17

Difference = 17 - 7 = 10 years

Hence,

Difference between Joyce's and her brothers age is 10 years.

The surface area of the  gas tank capsule represented to 1 dp is about 9079.2 cm²

The surface area of a solid object is the area of all the faces of the object.

Part of the dimension of the gas tank obtained from a similar question on the website is; Total length of the gas tank = 85 cm

Therefore;

Radial length of the tank = (85 cm - 51 cm)/2 = 17 cm

The surface area of the tank can be found as the surface area of a composite figure. The extreme right and left part of the tank together form a sphere, while the middle portion is a cylinder. Therefore, we get;

Surface area = 4 × π × 17² + 2 × π × 17 × 51 = (1734 + 1156) × π = 2890·π

Surface area of the figure = 2890·π cm² ≈ 9079.2 cm²

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Round digits answers are 1) 132  2) 0.00451  3) 0.356

Question 1:

132.500 rounded to three significant figuresT

he first significant figure in 132.500 is 1, and the third significant figure is 2. Therefore, the digit that needs to be rounded is 5, which is followed by a 0, and we have to round up.

132.500 rounded to three significant figures is 132.

Question 2:

0.004505 rounded to three significant figures

The first significant figure in 0.004505 is 4, and the third significant figure is 5. Therefore, the fourth digit needs to be rounded, which is 5. 0.004505 rounded to three significant figures is 0.00451. We must round up because the following number is 5.

Question 3:

0.355500 rounded to three significant figures

The first significant figure in 0.355500 is 3, and the third significant figure is 5. Therefore, the digit that needs to be rounded is 5, which is followed by a 0, and we have to round up.0.355500 rounded to three significant figures is 0.356. We must round up because the following number is 5.

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Answer:

.8Km

Step-by-step explanation:

There is exactly 100,000 CM in every KM, if someone such as Ben was to measure out 80,000, to convert to KM you'd take the given value and divide by the appropriate values.

80,000cm / 100,000cm = .8 KM

The correct option e) 94.29%, for the probability that among the next 166 responses there will be at most 43 correct answers.

If we use a normal distribution to simulate any binomial distribution with p = 0.24 for n = 166 results, then:

There should be 43 correct responses, or

μ = np = 166*0.24

μ = np = 34.86

The number of accurate responses has a standard deviation of

σ = √(np(1-p))

σ = √(34.86*0.76)

σ = 5.14

43 correct responses have a z-value;

z = (x - μ)/σ

z = (43 - 34.86)/5.14

z = 1.58

The likelihood that 43 accurate responses are provided is:

N(1.58) = 0.9429

Thus, the probability that among the next 166 responses there will be at most 43 correct answers is 94.29%.

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The complete question is-

Use the normal distribution to approximate the desired probability. A certain question on a test is answered correctly by 24.0 percent of the respondents. Estimate the probability that among the next 166 responses there will be at most 43 correct answers.

a) 74.56870% b) 74.30203% c) 75.20203% d) 94.95%  e) 94.29%

Answer:

The slope is 3/2, and the y-intercept (b) is -1

Step-by-step explanation:

The slope-intercept form is y=mx+b. m is the slope and b is the y-intercept.

The fundamental frequency of the first harmonic is half of this frequency.

Fundamental frequency = 2/2 = 1. So, the correct answer is option (a) 1.

To find the fundamental frequency of the first harmonic for the Fourier series of the periodic function x(t) = cos^2(t), we need to determine the frequency at which the first harmonic occurs.

The Fourier series representation of x(t) is given by:

x(t) = a0/2 + Σ[1, ∞] (ancos(nωt) + bnsin(nωt))

Where ω is the angular frequency.

For the given function x(t) = cos^2(t), we can rewrite it using the identity cos^2(t) = (1 + cos(2t))/2:

x(t) = (1 + cos(2t))/2

Now, comparing this expression with the general form of the Fourier series, we see that the frequency of the cosine term cos(2t) is 2 times the angular frequency. Therefore, the fundamental frequency of the first harmonic is half of this frequency.

Fundamental frequency = 2/2 = 1

So, the correct answer is option (a) 1.

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prolly 4.36 just use the Pythagorean theorem

Answer:

13,160

Step-by-step explanation:

\(si \: = \frac{pnr}{100} \)

P = principle amount

n = no.of years

r = rate(%)

\( = \frac{5600 \times 45 \times 3}{100} \)

= 56 × 45× 3

= 7560

The final answer is 5600 + 7560 = 13160

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It's not entirely clear what is meant by "5 Apples in 6 rows," so I will provide a general answer that could apply to a few different interpretations of the question.

If Johnny has 5 apples and places them in 6 rows, the answer to how many apples he will have left depends on how many apples are in each row and what Johnny does with them. For example, if he eats one apple from each row, he will be left with 5 - 6 = -1 apples, which doesn't make sense. If instead he rearranges the apples into one row, he will still have 5 apples. If he gives away 2 apples, he will have 3 apples left.

In summary, the number of apples Johnny will have left depends on the details of the scenario, including how many apples are in each row and what Johnny does with them.

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The inequality representing s, the number of sets of glasses Julia should buy is 286 + 6s ≥ 316.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

Since Julia needs to order some new supplies for the restaurant where she works. The restaurant needs at least 316 glasses. There are currently 286 glasses. If each set on sale contains 6 glasses, the number of sets will be:

286 + 6s ≥ 316

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Answer:

9 pencils were sharp

Step-by-step explanation:

3*4=12 so if three fourths were sharp then 9 were

Derek's total income from selling 31 bags of popcorn at the first game is $62 and he sold 322 bags of popcorn over the whole season.

It is a branch of mathematics that deals with the occurrence of a random event.

a. Independent variable: Bags of popcorn (X)

Dependent variable: Income (I)

b. If the function is I(X) = 2X, we can find Derek's total income by plugging in the number of bags he sold at the first game, which is X = 31:

I(31) = 2(31) = 62

Therefore, Derek's total income from selling 31 bags of popcorn at the first game is $62.

c. To find out how many bags of popcorn Derek sold over the whole season, we need to rearrange the function to solve for X:

I(X) = 2X

X = I(X) / 2

We know that Derek made a total income of $644 over the whole season, so we can plug this in to find X:

X = 644 / 2 = 322

Therefore, Derek sold 322 bags of popcorn over the whole season.

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Answer:

E) the new price is going to be $3.92

   Work: 3.50 × 12 / 100 = 0.42

              3.50 + 0.42 = 3.92

F) Dont understand what this one is asking

G) You would save 1.03$ with the 10% off.

   Work: 10.3 x 10 / 100

               103 / 100

              $1.03

hope this helps