Which best describes the tasks kathy, sean, and joan perform? kathy and joan perform tasks common to the engineering and technology pathway and sean performs tasks common to the science and math pathway. kathy performs tasks common to the engineering and technology pathway and sean and joan perform tasks common to the science and math pathway. sean performs tasks common to the engineering and technology pathway and kathy and joan perform tasks common to the science and math pathway. sean and joan perform tasks common to the engineering and technology pathway and kathy performs tasks common to the science and math pathway.

the number that divided by 6 leaves a remainder of 5, divided by 5 leaves a remainder of 4, divided by 4 leaves a remainder of 3, is 60.

To solve this problem, we can use the Chinese Remainder Theorem.

Let's denote the number we're looking for as x.

According to the given conditions:

- When x is divided by 6, it leaves a remainder of 5.

- When x is divided by 5, it leaves a remainder of 4.

- When x is divided by 4, it leaves a remainder of 3.

We can set up the following system of congruences:

x ≡ 5 (mod 6)

x ≡ 4 (mod 5)

x ≡ 3 (mod 4)

To find the solution using the Chinese Remainder Theorem, we need to find the least common multiple (LCM) of the moduli (6, 5, 4), which is 60.

Next, we can rewrite the system of congruences as follows:

x ≡ 5 (mod 6)  -->  x ≡ 5 (mod 60)

x ≡ 4 (mod 5)  -->  x ≡ 4 (mod 60)

x ≡ 3 (mod 4)  -->  x ≡ 3 (mod 60)

Now, we can combine these congruences into a single congruence:

x ≡ (5 * 60 * 7 + 4 * 60 * 12 + 3 * 60 * 15) (mod 60)

x ≡ 540 + 2880 + 2700 (mod 60)

x ≡ 6120 (mod 60)

x ≡ 0 (mod 60)

Therefore, the number we're looking for, x, is a multiple of 60. The smallest positive solution is x = 60.

In conclusion, the number that divided by 6 leaves a remainder of 5, divided by 5 leaves a remainder of 4, divided by 4 leaves a remainder of 3, is 60.

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A) The value of p(x=5) is 0.2017

B) The value of p(x=8) is 0.1167

C) The expected value (mean) of x7.89.

A) We are required to find P(x = 5).P(x = 5) is the probability that 5 out of the 10 students selected chose the stated option.

Using the binomial distribution formula, we have

P(x = 5) = nCx px q(n - x)

where n = 10, x = 5, p = 45/57 = 0.789, and q = 1 - p = 1 - 0.789 = 0.211

Thus, P(x = 5) = (10C5) (0.789)5 (0.211)5= 0.2017 (rounded to four decimal places)

B) We are required to find P(x = 8).P(x = 8) is the probability that 8 out of the 10 students selected chose the stated option.

Using the binomial distribution formula, we have

P(x = 8) = nCx px q(n - x)

where n = 10, x = 8, p = 45/57 = 0.789, and q = 1 - p = 1 - 0.789 = 0.211

Thus, P(x = 8) = (10C8) (0.789)8 (0.211)2= 0.1167 (rounded to four decimal places)

C) We are required to find the expected value (mean) of x.

Using the binomial distribution formula, we have

E(x) = np

where n = 10, and p = 45/57 = 0.789

Thus, E(x) = 10 × 0.789= 7.89 (rounded to two decimal places)

Therefore, the expected value (mean) of x is 7.89.

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Answer:

\(x=25\)

Step-by-step explanation:

\(x-16=9\\x=9+16\\x=25\)

Hope it helps

The distance in kilometers, d, expressed as a function of time in hours, t is  d = 3t km

From the question,

A pedestrian is walking at a speed of 3 km/h.

To express the distance in kilometers, d, as a function of time in hours, t

We will use the formula connecting speed, distance and time.

The formula connecting speed, distance and time is

\(Speed =\frac{Distance}{Time}\)

Let speed = s

distance = d

and time = t

∴ We can write that

\(s = \frac{d}{t}\)

Since the given speed, s = 3km/h

Then, we can write that

\(3 =\frac{d}{t}\)

Then, the distance, d expressed as a function of time, t will be

d = 3t km

Hence, the distance in kilometers, d, expressed as a function of time in hours, t is  d = 3t km

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Answer:

3t

Step-by-step explanation:

Answer:

5 weeks

Step-by-step explanation:

$18 / week

goal is $90

18x = 90

90/18 = 5

18(5) =90

It will take him 5 weeks to save enough money to buy the skateboard

Answer:

$63

Step-by-step explanation:

First find the cost of bananas per kilogram. To find that, divide $147 by 21

147/21=7

One kilogram of bananas costs $7

Now that you know the cost per kilogram, multiply $7 by the number of kilograms asked in the question, which in this case is 9

7*9=$63

9 kilograms of bananas costs $63

Answer: 63

Step-by-step explanation:

You can set up a proportion cost/weight=cost/weight

\(\frac{147}{21} = \frac{x}{9}\)        Costs go on the top so x is cost for 9 kg

\(x=\frac{147*9}{21}\)

x=63

Boi stop cheatin and draw ur own tape diagram

Answer: Let's assume the cost of 1 kilogram of bananas is represented by 'x'.

According to the given information, 4.5 kg of bananas and 3.5 kg of apples together cost £6.75. We also know that the cost of 1 kg of apples is £5.40.

Using this information, we can set up the following equation:

4.5x + 3.5(£5.40) = £6.75

Now let's solve for 'x':

4.5x + 3.5(£5.40) = £6.75

4.5x + £18.90 = £6.75

4.5x = £6.75 - £18.90

4.5x = -£12.15

x = (-£12.15) / 4.5

x ≈ -£2.70

The cost of 1 kilogram of bananas, based on this calculation, is approximately -£2.70. However, it's important to note that a negative cost doesn't make sense in this context. It's possible there may be an error in the given information or the setup of the equation.

Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

Answer:

d: 729/64

Step-by-step explanation:

Plug-in the variables

Answer:

B.

Step-by-step explanation:

The midpoint of a line segment is found by taking the average of the x-coordinates and the y-coordinates of the endpoints of the segment.

The midpoint of segment AB can be found as follows:

Midpoint of AB = ((-7/2 + -7)/2, (3/2 + 3)/2) = (-7, 3)

Since the midpoint of AB is the same as point B, we can conclude that the midpoint of segment AB is (-7, 3).

Note that the sum of the angles in a triangle is always 180 degrees.

So it follows that :

The triangle has a right angle at G, and a right angle measures 90 degrees.

angle F = 4x + 15

and

angle H = 3x + 12

Substitute the angle values to the formula and solve the value of x :

Now we have the value of x, substitute this value to the angles.

Therefore, the angles are :

F = 51 degrees

G = 90 degrees

H = 39 degrees

Answer:

-14

Step-by-step explanation:

If u put x+5y into -2(-x+5y)

Add all that up

-2(x+5y) =(-2) (7) = -14

Answer:

dude where is the question???

Step-by-step explanation:

Answer:

What are the questions? I can try

Step-by-step explanation:

Your answer is option b)

The time at which a star rises shifts approximately 4 minutes earlier each day, due to Earth's orbit around the Sun. Since there are roughly 30 days in a month, we can calculate the change in the rise time of Aldebaran over the course of a month.

Step 1: Calculate the time change over one month
30 days * 4 minutes per day = 120 minutes

Step 2: Convert minutes to hours
120 minutes ÷ 60 minutes per hour = 2 hours

Step 3: Subtract the time change from the current rise time
2:00 am - 2 hours = 12:00 am (midnight)

Therefore, you can expect Aldebaran to rise next month at midnight. The correct answer is b) midnight.

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Answer:

The diameter is 6.76

Please read the exaplanation... it always helps!

Step-by-step explanation:

Area of circle = r^2 pi

if the area is 36 then...

36 = r^2 pi           to solve for r divide both sides by pi

36/pi = r^2

11.45 = r^2             take the square root of both sides

√11.45 = r                 RADIUS = 3.38

then multiply by two since the diameter is 2 (radius) and you get...

diameter = 6.76

i hope this helpssssss!!!!!!!

Answer:

\(area = \pi {r}^{2} \)

\(36 = 3.14 \times {r}^{2} \)

\( \frac{36}{3.14} = {r}^{2} \)

\( {r}^{2} = 11.46\)

\(r = \sqrt{11.46} \)

\(r = 3.39\)

\(diameter = 2 \times radius\)

\(diameter = 3.39 \times 2\)

\( = 6.78\)

you should invest approximately $500,000 today at 9% simple interest to reach your retirement goal of $1,175,000 in 15 years.

To determine how much you should invest today at 9% simple interest to reach your retirement goal of $1,175,000 in 15 years, we can use the formula for simple interest:

A = P(1 + rt)

Where A is the future value, P is the principal (the amount you should invest today), r is the interest rate, and t is the time in years.

We can rearrange the formula to solve for P:

P = A / (1 + rt)

Plugging in the values, we have:

P = 1,175,000 / (1 + 0.09 * 15)

P = 1,175,000 / (1 + 1.35)

P = 1,175,000 / 2.35

P ≈ $500,000

Therefore, you should invest approximately $500,000 today at 9% simple interest to reach your retirement goal of $1,175,000 in 15 years.

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Total number of songs downloaded: 48

Songs by his favourite band: 12

A. Divide the number of songs by his favorite band by the total number of songs:

12/48 = 0.25

B. is decimal terminating

Answer:

Additive Identity is 0

Multiplicative identity is 1

Step-by-step explanation:

Adding 0 to anything results to that number. This is additive Identity.

Multiplying 1 to anything results to that number. This is multiplicative identity.

The inequality that models this situation is 20,000 - 50b > 6,000.

Here are inequality signs and what they mean:

The inequality sign that would be used is the greater than sign, >.

The form of the inequality is:

Total number of cards he has - (number of card per bundle x number of bundles) > least number of trading card he wants to keep

20,000 - (50 x b) > 6,000

20,000 - 50b > 6,000

Where, b is the number of bundles Mr. Williams sells

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The homogeneous system of linear equations has a solution space with a basis of {(1, 2, -1)}. The dimension of the solution space is 1.

To find a basis for the solution space of the given homogeneous system of linear equations, we need to solve the system and express the solutions in terms of a linear combination of vectors.

The system of equations is as follows:

Equation 1: -x + y - z = 0

Equation 2: 2x - y = 0

Equation 3: 2x - 3y - 4z = 0

We can start by using the equations to eliminate variables. From Equation 2, we can express y in terms of x as y = 2x. Substituting this into Equation 1 gives us -x + 2x - z = 0, which simplifies to x - z = 0. Rearranging this equation, we have x = z.

Now, we can express the variables in terms of a single parameter. Let's choose z as the parameter. Thus, x = z and y = 2x = 2z.

Now, we can express the solutions in vector form as (x, y, z) = (z, 2z, z) = z(1, 2, 1). This means that the solution space is spanned by the vector (1, 2, 1).

To find the basis for the solution space, we need to check if the vector (1, 2, 1) is linearly independent. Since it is the only vector spanning the solution space, it is linearly independent. Therefore, the basis for the solution space is {(1, 2, 1)}.

The dimension of the solution space is equal to the number of vectors in the basis, which in this case is 1. Therefore, the dimension of the solution space is 1.

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Answer:

1 solution

Step-by-step explanation:

-5(x-1)=25

-5x+5=25

-5x=20

x=-4

The general solution of the equation \(\(x = p(t) x g(t)\)\) can be represented as the sum of a particular solution \(\(x_p\)\) and the general solution \(\(x_c\)\) of the corresponding homogeneous equation. This implies that any solution of the original equation can be expressed as the sum of these two components, and the sum satisfies the equation.

In order to demonstrate this, we establish two key points. Firstly, we show that any solution of the original equation can be written as the sum of a particular solution \(\(x_p\)\)  and a solution of the homogeneous equation. By subtracting \(\(x_p\)\) from the original equation, we define a new variable\(\(y\)\) that satisfies the homogeneous equation. Therefore, any solution \(\(x\)\) can be expressed as \(\(x = x_p + y\)\), with \(\(x_p\)\) as a particular solution and \(\(y\)\) as a solution of the homogeneous equation.

Secondly, we establish that the sum of a particular solution \(\(x_p\)\) and a solution of the homogeneous equation \(\(x_c\)\) satisfies the original equation. By substituting \(\(x = x_p + x_c\)\) into the equation \(\(x = p(t) x g(t)\),\) we distribute \(\(p(t) g(t)\)\) and observe that \(\(x_p\)\) satisfies the equation. Furthermore, we can rewrite the equation as \(\(x_c = p(t) x_c g(t)\)\). Ultimately, after substituting these expressions back into the equation, we find that \(\(x_p + x_c\)\) is equivalent to \(\(x_p + x_c\)\).

Consequently, we have successfully shown that the general solution of \(\(x = p(t) x g(t)\)\) is the sum of a particular solution \(\(x_p\)\)and the general solution \(\(x_c\)\)of the corresponding homogeneous equation.

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The coordinates of A' and C' will not be the same. The perimeter and area of ΔA'B'C' will be the same. The measure of ∠B' and the slope of A'C' will be the same.

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

As per the given translation,

2 units down and 3 units right

The coordinate will change as,(x,y) → (x+3,y-2) so it will change.

The transformation consists only of linear transformation no rotation exists thus area and perimeter will remain the same.

The slope and angle are unchanged irrespective of any transformation.

Hence "A' and C' will not have the same coordinates. The boundaries and surface area of ΔA'B'C' will be identical. The slope of A'C' and the measure of ∠B will be equal.".

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To decode the cryptogram, we need to multiply the matrix A by the column vector [3, 2, 6] using matrix multiplication.

Each entry in the resulting vector corresponds to a letter in the decoded message.

Let's perform the matrix multiplication:

A =

[1 1 3]

[1 1 4]

Column vector: [3, 2, 6]

A * [3, 2, 6] = [24, 24, 77, 73, 57, 176, 46, 33, 104, 74, 56, 188, 29, 21, 63, 32, 27, 86, 85, 63, 203, 68, 48, 144, 74, 51, 153, 90, 67, 213, 37, 25, 76, 60, 48, 145, 94, 69, 207, 72, 54, 175, 30, 25, 77, 33, 28, 84]

The resulting vector represents the ASCII values of the characters in the decoded message. Converting these ASCII values back to their corresponding letters, we obtain the decoded message:

"SEMPTEMBER THE ELEVENTH WILL ALWAYS REMEMBER"

Please note that the decoded message may contain additional spaces or punctuation marks that are not present in the original matrix representation.

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Answer:

Step-by-step explanation:

the answermis ooo

Write the equation of the line parallel to y=2x-5 and passes through the point (2,4). Please help ... We must have slope m=2, and we need to find b the y-intercept. ... b is the y intercept when x=0. Let's plug in the point (2,4) to find b. ... ˆ ˜ ° − ± ÷ ⁄ × ƒ ∫ ∑ ∞ √ ∼ ≅ ≈ ≠ ≡ ∈ ∉ ∋ ∏ ∧ ∨ ¬ ∩ ∪ ∂ ∀ ∃

Answer:

5 x - 6 y - 8 = 0.

Step-by-step explanation:

Answer:

answer is the butt world

The distance from the center of dilation, Q, to the image of vertex A will be 4 units.

According to the given rule of dilation, D subscript Q, two-thirds, the triangle ABC will be dilated with a scale factor of two-thirds centered at point Q.

Since point Q is the center of dilation and the distance from triangle ABC to point Q is 6 units, the image of vertex A will be 2/3 times the distance from A to Q. Therefore, the distance from A' (image of A) to Q will be (2/3) x 6 = 4 units.

By applying the scale factor to the distances, we can determine that the length of A'B' is (2/3) x  3 = 2 units, the length of B'C' is (2/3) x 7 = 14/3 units, and the length of A'C' is (2/3) x 8 = 16/3 units.

Thus, the distance from the center of dilation, Q, to the image of vertex A is 4 units.

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