how do you re right an integer slope as a fraction?

Answer:

10 adult tickets cost £75 , 20 child tickets cost £60

Step-by-step explanation:

let a be the cost of an adult ticket and c the cost of a child ticket , then

4a + c = 33 → (1)

2a + 7c = 36 → (2)

multiplying (2) by - 2 and adding to (1) will eliminate a

- 4a - 14c = - 72 → (3)

add (1) and (3) term by term to eliminate a

0 - 13c = - 39

- 13c = - 39 ( divide both sides by - 13 )

c = 3

substitute c = 3 into either of the 2 equations and solve for a

substituting into (1)

4a + 3 = 33 ( subtract 3 from both sides )

4a = 30 ( divide both sides by 4 )

a = 7.5

the cost of an adult ticket is £7.50

then 10 adult tickets cost 10 × £7.50 = £75

the cost of a child ticket is £3

the cost of 20 child tickets is 20 × £3 = £60

\(5 + n = 12 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \)

Symbolically, they correspond to the relationships between the coefficients of the equations.

A system of 2 linear equations in 2 variables can have one of the following three possible solutions:

One unique solution: In this case, the two lines intersect at exactly one point, and this point is the solution to the system. Visually, the two lines are not parallel, but they are not the same either. Symbolically, the system is represented as:

a1x + b1y = c1

a2x + b2y = c2

where a1, b1, c1, a2, b2, and c2 are constants, and x and y are variables.

Infinitely many solutions: In this case, the two lines coincide and are on top of each other, meaning they have the same slope and the same y-intercept. Visually, the two lines are identical. Symbolically, the system is represented as:

a1x + b1y = c1

ka1x + kb1y = kc1

where a1, b1, and c1 are constants, x and y are variables, and k is any non-zero constant.

No solution: In this case, the two lines are parallel and never intersect. Visually, the two lines are distinct and never meet. Symbolically, the system is represented as:

a1x + b1y = c1

a2x + b2y = c2

where a1, b1, c1, a2, b2, and c2 are constants, and x and y are variables, and the slope of one line is not equal to the slope of the other.

Geometrically, these cases correspond to the three possible positions of two lines in the coordinate plane. Symbolically, they correspond to the relationships between the coefficients of the equations.

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The result of the integral ∫e^(24(3 + 5t - 2)) dt is (1/5) * (1/24) * e^(24(5t + 1)) + C

Reference to Power rule for integrals. To evaluate the integral ∫e^(24(3 + 5t - 2)) dt, we can simplify the expression inside the exponential function first:

3 + 5t - 2 = 5t + 1

Now we can rewrite the integral as:

∫e^(24(5t + 1)) dt

To evaluate this integral, we can use a substitution. Let u = 5t + 1. Then, du = 5dt, and dt = du/5.

Substituting these values into the integral, we have:

∫e^(24u) * (1/5) du

Now the integral becomes:

(1/5) ∫e^(24u) du

To integrate e^(24u), we can use the power rule for integrals. The integral of e^x is e^x, so the integral of e^(24u) will be (1/24)e^(24u). Applying this to the integral, we get:

(1/5) * (1/24) * e^(24u) + C

where C is the constant of integration.

Substituting back u = 5t + 1, we have:

(1/5) * (1/24) * e^(24(5t + 1)) + C

This is the result of the integral ∫e^(24(3 + 5t - 2)) dt.

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The probabilities are given as follows:

The mass probability formula, giving the probability of x successes, is of:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

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

The parameters are given by:

The parameter values for this problem are given as follows:

Hence the probability of one senior having the birthday on the same day as the graduation is of:

P(X = 1) = 68 x 1/365 x (364/365)^67 = 0.1550.

The probability of more than one is given as follows:

P(X > 1) = 1 - P(X <= 1).

In which:

P(X <= 1) = P(X = 0) + P(X = 1)

Hence:

Finally:

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Answer:

A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.

Answer:

sin (Q) = 15/17

sin (R) = 8/17

cos (Q) = 8/17

cos (R) = 15/17

tan (Q) = 15/8

tan (R) = 8/15

Step-by-step explanation:

Step 1:  Find the length of side QR (i.e., the hypotenuse):

a^2 + b^2 = c^2, where

Thus, we can plug in 16 and 30 for a and b to find x, the hypotenuse (aka the length of side QR):

16^2 + 30^2 = c^2

256 + 900 = c^2

1156 = c^2

√1156 = √1156

34 = c

Thus, the length of side QR (the hypotenuse) is 34 units.

Step 2:  Find sin Q and sin R:

sin Q:

The sine ratio is given by sin (θ) = opposite / hypotenuse, where

Thus, sin (Q) = 30/34.  This simplifies to sin (Q) = 15/17.

sin R:

When angle R is the reference angle, QS is the opposite side and QR is the hypotenuse.

Thus sin (R) = 16/34.  This simplifies to sin(R) = 8/17.

Step 3:  Find cos Q and cos R:

The cosine ratio is given by:

cos (θ) = adjacent / hypotenuse, where

cos Q:

Thus cos (Q) = 16/34.  This simplifies to cos (Q) = 8/17.

cos R:

Thus, cos (R) = 30/34.  This simplifies to cos (R) = 15/17.

Step 4:  Find tan Q and tan R:

The tangent ratio is given by:

tan (θ) = opposite / adjacent, where

tan (Q):

Thus tan (Q) = 30/16.  This simplifies to tan (Q) = 15/8.

tan (R):

Thus, tan (R) = 16/30.  This simplifies to tan (R) = 8/15.

If 95% confidence interval based on this sample is: 0.9 hours to 2.7 hours, the sample mean (x') is estimated to be 1.8 hours.

The sample mean (x;) is not explicitly given in the information provided. However, we can infer it from the 95% confidence interval.

A 95% confidence interval is typically constructed using the sample mean and the margin of error. The interval provided (0.9 hours to 2.7 hours) represents the range within which we are 95% confident the true population mean lies.

To find the sample mean, we take the midpoint of the confidence interval. In this case, the midpoint is (0.9 + 2.7) / 2 = 1.8 hours.

The 95% confidence interval indicates that, based on the sample data, we are 95% confident that the true mean time all high school students study for Geometry tests falls between 0.9 hours and 2.7 hours, with the estimated sample mean being 1.8 hours.

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Therefore, buying a bag of cookies at the grocery store is the best way for John to save money on this expense. Not only is it cost-effective,

To answer your question, I would recommend option D - buying a bag of chocolate chip cookies at the grocery and eating one each day. This is the best way for John to save money on this expense. However, there is a long answer to why this is the best option.

Firstly, by buying a bag of cookies at the grocery store, John can save money as the cost per cookie is likely to be lower than $1.25. Additionally, buying a bag of cookies means John can control his cookie intake and potentially save money on other food expenses throughout the day.

Option A - giving up the daily cookie - is also a viable option but may not be sustainable in the long term. John may end up craving a cookie and buying one anyway, which defeats the purpose of trying to save money.

Option B - offering to help out at the bakery - may not be feasible as John may not have the time or skills to do so. Additionally, covering the cost of cookies by working may not be worth it if John's time and effort could be better spent elsewhere.

Option C - asking for a discount for buying 5 cookies - may work, but it is unlikely that the cashier will give a significant discount. It also means John will need to spend more money upfront and may end up overeating or wasting cookies.

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It will take 23.50 years for the investment to double.

The investment has the formula y= 5000(1.03)ˣ . Therefore, let's find the time in years the investment will double in value when starting at 5000 units.

The double of 5000 units is 10000 units.

Therefore,

y = 5000(1.03)ˣ

where

Hence,

y = 5000(1.03)ˣ

10000 = 5000(1.03)ˣ

divide both sides by 5000

10000 / 5000 = (1.03)ˣ

2 = (1.03)ˣ

log both sides

x = In 2 / In 1.03

x = 23.4977

Therefore,

x = 23.50 years

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The mean of the boat lengths in the marina is 27.85. The median, which represents the middle value in the dataset, is 27. The mode, or the value(s) that appear most frequently, is 25 and 27, both occurring three times each.

a. To calculate the mean using Python, we can sum up all the boat lengths and divide it by the total number of lengths. In this case, the sum of all the lengths is 695. Dividing it by the number of lengths, which is 25, we get the mean as 27.8. Rounded to two decimal places, the mean is 27.85.

b. To find the median, we need to determine the middle value in the dataset. Since the number of lengths is odd, we can directly identify the median as the 13th value in the ordered list, which is 27. Thus, the median is 27.

c. To identify the mode, we observe that the values 25 and 27 appear most frequently, each occurring three times. These values have the highest counts of occurrences, making them the mode of the dataset.

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By organizing countless data points into comprehensible ranges or bins, the histogram, which resembles a bar graph in appearance, condenses a data series into an understandable visual. So Histograms based on data on housing, prices and salaries typically are skewed to the right.

A histogram in statistics is a graphic depiction of the data distribution. The histogram is shown as a collection of rectangles that are next to one another, where each bar represents a different type of data.

A branch of mathematics called statistics is used in many different fields. Frequency is the term for how often numbers appear in statistical data; it can be shown as a table and is known as a frequency distribution.

A histogram is a bar graph-like data visualization that groups various class levels into columns along the horizontal x-axis. The numerical count or percentage of occurrences for each column in the data are shown on the vertical y-axis.

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Answer:

i think its 45/2

decimal form= 22.5

Answer:

184

Step-by-step explanation:

Answer:

number of $8 sold= 200

Number of $10 tickets sold= $150

Number of $12 tickets sold = $50

Step-by-step explanation:

Let the quantity of $8 ticket be represented as  x

Let the quantity of $10 ticket be represented as  y

Let the quantity of $12 ticket be represented as  z

Such that total tikets sold = 400 can be represented as x+y+z= 400

Prices of$8, $10 and $12 gave a total income of $3,700  such that it can be represented as

8x +10y + 12z =$3,700

Also given that combined number of $8 and $10 priced tickets sold was 7 times the number of $12 tickets sold, we have that

x+y = 7z

Giving us the equations to solve to  be

x+y+z= 400------ equation 1

8x +10y + 12z =$3,700---- equation 2

x+y = 7z------equation 3

Step 2- solving

Putting equation 3 i n equation 1, we have that

7z+z = 400

8z= 400

z= 400/8= 50

also puting the value of z= 50 in equation 1

x+y+z= 400

x+y+50= 400

x+y = 350---- equation 4

putting z= 50 into equaton 2 and solving out

8x +10y + 12z =$3,700

8x +10y + 12x 50 =$3,700

8x +10y + 600 =$3,700

8x +10y =3,700 - 600

8x +10y=3,100---------equation 5

Multiplying equation 4 by 8  and subtracting from equation 5

8x +10y=3,100

-8x+8y= 2,800

2y=300

y= 300/2

y=150

to find x, when y= 150 using equation 4

x+y = 350

x= 350-150

x= 200

Therefore number of $8 sold= 200

Number of $10 tickets sold= $150

Number of $12 tickets sold = $50

To find the composition of relations r ◦ s, we need to determine the set of ordered pairs that satisfy the composition.

The composition r ◦ s is defined as follows:

r ◦ s = {(x, z) | there exists y such that (x, y) ∈ s and (y, z) ∈ r}

Let's calculate the composition:

For each pair (x, y) ∈ s, we check if there exists a pair (y, z) ∈ r that satisfies the condition. If so, we include (x, z) in the composition.

For (a, c) ∈ s:

There is no pair (y, z) ∈ r where (c, y) and (y, z) hold simultaneously. Therefore, (a, c) does not contribute to the composition.

For (b, d) ∈ s:

There is no pair (y, z) ∈ r where (d, y) and (y, z) hold simultaneously. Therefore, (b, d) does not contribute to the composition.

For (d, a) ∈ s:

There exists a pair (y, z) = (a, b) in r, where (a, y) and (y, z) hold simultaneously. Therefore, (d, b) contributes to the composition: (d, b).

Hence, the composition r ◦ s is {(d, b)}.

Therefore, the composition of relations r ◦ s is {(d, b)}.

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Answer:

y=1/2x+2

Step-by-step explanation:

hope this helped

Answer: 3x+12

Step-by-step explanation:

Using the distributive property we can distribute the 3 to each of the terms in the parenthesis.

Therefore, 3(x+4) -= 3x+ 3*4 = 3x +12

Answer:

Step-by-step explanation

3x + 12=0

3x= -12

x = -12/3

x= -4:

Answer:

d divided by 1/15 is o.75

Step-by-step explanation:

We get the value of x as 6 in part 1 and x as 3 in part 2.

We are given that E is the mid point of DF.

so, we get that it will divide DF into two equal parts that is both the parts will have the equal length.

DE = EF

For part 1, we get

5 x + 3 = 33

5 x = 33 - 3

5 x = 30

x = 30 / 5

x = 6

For part 2, we get that

3 x = x + 6

3 x - x = 6

2 x = 6

x = 6 / 2

x = 3

Therefore, we get the value of x as 6 in part 1 and x as 3 in part 2.

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7, 14, 28, 56, 112.

The 5th term is 112

Answer:

-1

Step-by-step explanation:

countdown till you reach 5 or use a\(a_{n} = d (n - 1) + c\)

Answer:

Two lines in the same plane that do not intersect are called parallel lines. When a line intersects two parallel lines, several pairs of angles that are formed have equal measures.

Step-by-step explanation:

Tell me if you need more explanation.

Answer: Angle 1 and angle 5 are corresponding angles

The calculation (3.4876)/(4.11+1.2) should be reported with three significant figures: 0.657.

To determine the number of significant figures in the answer to the calculation (3.4876)/(4.11+1.2), we need to consider the number of significant figures in the given values and apply the rules for significant figures in mathematical operations.

First, let's analyze the number of significant figures in the given values:

- 3.4876 has five significant figures.

- 4.11 has three significant figures.

- 1.2 has two significant figures.

To perform the calculation, we divide 3.4876 by the sum of 4.11 and 1.2. Let's evaluate the sum:

4.11 + 1.2 = 5.31

Now, we divide 3.4876 by 5.31:

3.4876 / 5.31 = 0.6567037...

Now, let's determine the number of significant figures in the result.

Since division and multiplication retain the least number of significant figures from the original values, the result should be reported with the same number of significant figures as the value with the fewest significant figures involved in the calculation.

In this case, the value with the fewest significant figures is 5.31, which has three significant figures.

Therefore, the answer to the calculation (3.4876)/(4.11+1.2) should be reported with three significant figures: 0.657.

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The value of y is 1 when the coefficient of x^3 in P3(x) is 6, based on the given data points and Lagrange interpolation.

The interpolating polynomial P3(x) is a third-degree polynomial that passes through the given data points (0, 0), (0.5, y), (1, 3), and (2, 2). Since the coefficient of x^3 in P3(x) is 6, we can set up the Lagrange interpolation formula to find the value of y.

We have four data points, which means we need four terms in our polynomial. The general form of P3(x) is P3(x) = a0 + a1x + a2x^2 + a3x^3. To determine the coefficients a0, a1, a2, and a3, we can use the Lagrange basis polynomials.

Using the Lagrange basis polynomials, we can set up the following equations:

P3(0) = a0 + a1(0) + a2(0)^2 + a3(0)^3 = 0
P3(0.5) = a0 + a1(0.5) + a2(0.5)^2 + a3(0.5)^3 = y
P3(1) = a0 + a1(1) + a2(1)^2 + a3(1)^3 = 3
P3(2) = a0 + a1(2) + a2(2)^2 + a3(2)^3 = 2

Solving these equations will give us the values of a0, a1, a2, and a3. By substituting the coefficient of x^3 as 6 into the equation, we can find the specific value of y, which turns out to be 1.

Therefore, the value of y is 1 when the coefficient of x^3 in P3(x) is 6.

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Answer:

$0.31

Step-by-step explanation:

$2.48/8 = $ 0.31

Answer: between $1.00 and $1.99

Step-by-step explanation:

The intersection of the planes in part (a) is a single point, while the planes in part (b) do not intersect and are parallel.

Part (a):

To find the intersection of the planes in part (a), we need to solve the system of equations. Rewriting the equations in matrix form, we have:

| 1 2 3 | | x | | -1 |

| 1 4 8 | | y | = | 9 |

| 1 1 2 | | z | | -2 |

Applying row operations to the augmented matrix, we can reduce it to row-echelon form:

| 1 2 3 | | x | | -1 |

| 0 2 5 | | y | = | 10 |

| 0 -1 -1 | | z | | 1 |

From the row-echelon form, we can solve for the variables. By back substitution, we find x = -4, y = 5, and z = -1. Therefore, the planes intersect at the point (-4, 5, -1).

Part (b):

For the planes in part (b), we can rewrite the equations in matrix form:

| 1 2 0 | | x | | -5 |

| 3 -1 14 | | y | = | 6 |

| 1 2 0 | | z | | 5 |

Applying row operations to the augmented matrix, we can reduce it to row-echelon form:

| 1 2 0 | | x | | -5 |

| 0 -5 14 | | y | = | 21 |

| 0 0 0 | | z | | 0 |

From the row-echelon form, we can see that the third row of the matrix corresponds to the equation 0z = 0, which is always true. This indicates that the system is underdetermined and the planes are parallel. Therefore, the planes in part (b) do not intersect.

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The total number of t-shirts sold by Tom equals to 17 t-shirt.

Basically, a profit refers to the difference between the revenue that an entity has received from its outputs and the opportunity costs of its inputs.

We need to note that he made a total profit of $125. From here, we will proceed to use that data to solve other sections.

From the total profit of $125, he also made a profit of $40 from selling hats. That means that the T-shirt sales alone gives him a profit of $85 ($125 - $40).

Total quantity of t-shirt sold is computed as follows:

= Total profit from t-shirt / Profit per shirt

= $85 / $5

= 17 t-shirt

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