A corner store sells two kinds of baked goods: cakes and pies. A cake costs $4 and a pie costs $11. In one day they sold 11 baked goods for a total of $100. How many cakes did they sell?

Students who test positive face serious consequences, including letters to their parents,

Answer:

1. 1/5  1/3  4/6

2. 3/5  3/4  7/8

3. 87 nickels

4. 150 minutes

5. 2

6.  3/4

Step-by-step explanation:

1.  least to greatest:  1/5  1/3  4/6

2.  least to greatest:  3/5  3/4  7/8

3. 1 nickel = 5 cents

So 485 ÷ 5 = 87 nickels

4. Total number of minutes = 50 x 2 = 150 minutes

5. A composite number is a whole number that can be made by multiplying other whole numbers.

3 x 3 = 9  ⇒  composite number

3 x 5 = 15  ⇒  composite number

3 x 7 = 21  ⇒  composite number

Therefore 2 is NOT a composite number (it is a prime number)

6. 6/8 = 3/4

Answer:

x=-2

y=5

Step-by-step explanation:

x+2y=8   equation-1  

-x+3y=17 equation-2

5y=25

Both side divided 5,

y=5

Equation-1, y=5

x+2(5)=8

x+10=8

Both side -10

x+10-10=8-10

x=-2

Equation-2, y=5

-x+3(5)=17

-x+15=17

Both side -15

-x+15-15=17-15

-x=2

x=-2

Answer:

Step-by-step explanation:

Working hours:

Earning in a month = $5350

Hourly earning rate:

Answer:

1^8, 2^4, 5^2, 3^3 is the answer.

The numbers ordered from the smallest to the largest is \(1^{8} , 2^{4} , 5^{2} , 3^{3}\).

In order to determine the order of the numbers, we have to solve for the numbers. The power of a number can be solved by multiplying a number by its number of power.

\(5^{2}\) = 5 x 5 = 25

\(1^{8}\) = 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 = 1

3³ = 3 x 3 x 3 = 27

\(2^{4}\) = 2 x 2 x 2 x 2 = 16

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Answer:

9.3 ft

Step-by-step explanation:

According to Financial experts you should save between 10% to 15% of your annual income for retirement. For a salary of $79,000/year, the minimum saved should be between $790,000 to $948,000.

Financial experts generally recommend that you should aim to save between 10% to 15% of your income each year for retirement. For a salary of $79,000 per year, this means saving between $7,900 to $11,850 annually.

Assuming you have been saving for retirement throughout your working years and are ready to retire, financial experts suggest that you should have saved at least 10 to 12 times your current annual income to maintain your pre-retirement standard of living. Therefore, the minimum you should have saved in retirement accounts is

$79,000 x 10 = $790,000 (using the conservative end of the range)

or

$79,000 x 12 = $948,000 (using the more aggressive end of the range)

Therefore, the minimum you should have saved in retirement accounts if you are currently making $79,000/year is between $790,000 to $948,000, depending on the end of the range you choose to follow.

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The velocity of the stream is approximately 2.13 feet per second.

To calculate the velocity of the stream, we can use the formula:

Velocity = Distance / Time

Given that the drop of food coloring travels 32 feet in 15 seconds, we can plug in these values into the formula:

Velocity = 32 feet / 15 seconds

To find the velocity, we divide 32 by 15:

Velocity ≈ 2.13 feet per second

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Step-by-step explanation:

x = length

y = width

x×y = 48 ft²

y = x - 2

using the second in the first equation we get

x × (x - 2) = 48

x² - 2x - 48 = 0

we can solve this quickly by finding the factors of -48 that are only 2 apart in their absolute value, and the negative factor must be 2 larger in its absolute value than the positive one.

simply because

(a + b)(a - c) = a² - ac + ab - bc

-bc = -48

-ac + ab = -2x

a = x

-c + b = -2

and so we see, 48 = 6×8 (2 difference between the factors).

the larger number must be negative, so, -8×6

and we get

(x + 6)(x - 8)

therefore, the solutions are

x = -6 and x = 8

a negative length does not makes sense here, so x = 8 is or solution.

the length of the garden is 8 ft.

the width is 8 - 2 = 6 ft.

Answer:

16

Step-by-step explanation:

create a t chart on one side put 3 and on the other put 2.

times 3 by 8 (you'll get 24) and then times 2 by 8 (you'll get 16.

Simplifying

X + 20x + 10x = 20 + 9x

Combine like terms: 20x + 10x = 30x

X + 30x = 20 + 9x

Solving

X + 30x = 20 + 9x

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Add '-30x' to each side of the equation.

X + 30x + -30x = 20 + 9x + -30x

Combine like terms: 30x + -30x = 0

X + 0 = 20 + 9x + -30x

X = 20 + 9x + -30x

Combine like terms: 9x + -30x = -21x

X = 20 + -21x

Simplifying

X = 20 + -21x

The correct answer is E) Both A and C are true. In summary, the line integral jĚ.dr of a smooth, positive function f of two variables, where F = Vf, is positive for all smooth paths C and positive for all closed smooth paths C.

Explanation:

The line integral jĚ.dr represents the work done by the vector field F on a particle that moves along the path C. In this case, since F = Vf, we have jĚ.dr = VfĚ.dr. By the fundamental theorem of calculus for line integrals, we have:

jĚ.dr = VfĚ.dr = f(P) - f(Q)

where P and Q are the endpoints of the path C. Since f is positive everywhere, we have f(P) > f(Q), which implies that jĚ.dr is positive for all smooth paths C.

Moreover, since f is positive everywhere, we have f(P) > f(Q) for any two points P and Q on a closed path C. Therefore, jĚ.dr is positive for any closed smooth path C. This means that the vector field F is "circulation-preserving", meaning that the work done by F on a particle that moves around a closed loop is always positive.

In conclusion, both A and C are true, as jĚ.dr is positive for all smooth paths C and positive for all closed smooth paths C.

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Farmer Ed has 3,000 meters of fencing and wants to enclose a rectangular plot that borders on a river.The largest area that can be enclosed is 750,000 square meters.

To get the largest area that can be enclosed, we have to find the dimensions of the rectangular plot. Let's assume that the width of the rectangle is x meters.The length of the rectangle can be found by subtracting the width from the total length of fencing available:L = 3000 - x. The area of the rectangle can be found by multiplying the length and width:Area = L × W = (3000 - x) × x = 3000x - x²To find the maximum value of the area, we can differentiate the area equation with respect to x and set it equal to zero.

Then we can solve for x: dA/dx = 3000 - 2x = 0x = 1500. This means that the width of the rectangle is 1500 meters and the length is 3000 - 1500 = 1500 meters.The area of the rectangle is therefore: Area = L × W = (3000 - 1500) × 1500 = 750,000 square meters. So the largest area that can be enclosed is 750,000 square meters.

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Answer:

Look down

Step-by-step explanation:

multiply each side by 7

0.3*7=2.1

Answer:

A

Step-by-step explanation:

2/3x + 4 = 2/3 (x + 4/(2/3)) = 2/3 (x + 6)

Topic: Algebraic equations + factorisation

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Answer:

14

Step-by-step explanation:

Answer:

answer: 14

Step-by-step explanation:

got it right

The shooting method is a numerical technique used to solve differential equations with specified boundary conditions. In this case, we will apply the shooting method to solve the second-order differential equation \(7d^2y/dx^2 - 2dy/dx - yx = 0\) with the boundary conditions y(0) = 5 and y(20) = 8.

To solve the given differential equation using the shooting method, we will convert the second-order equation into a system of first-order equations. Let's introduce a new variable, u, such that u = dy/dx. Now we have two first-order equations:

dy/dx = u

du/dx = (2u + yx)/7

We will solve these equations numerically using an initial value solver. We start by assuming a value for u(0) and integrate the equations from x = 0 to x = 20. To satisfy the boundary condition y(0) = 5, we need to choose an appropriate initial condition for u(0).

We can use a root-finding method, such as the bisection method or Newton's method, to adjust the initial condition for u(0) until we obtain y(20) = 8. By iteratively refining the initial guess for u(0), we can find the correct value that satisfies the second boundary condition.

Once the correct value for u(0) is found, we can integrate the equations from x = 0 to x = 20 again to obtain the solution y(x) that satisfies both boundary conditions y(0) = 5 and y(20) = 8.

The shooting method involves converting the given second-order differential equation into a system of first-order equations, assuming an initial condition for the derivative, and iteratively adjusting it until the desired boundary condition is satisfied.

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Answer: x+5x+4x=40

Step-by-step explanation:

The Probability that 4 games will be played in total and determine the likelihood that b will win the game are 2[(p³(1-p) + p(1-p)³] and p² / [p² + (1-p)²]

Given that,

A and B engage in a number of games. A and B each win a game with a probability of p and 1-p, respectively. They come to an end when one player has two more victories overall than the other player. The contest is decided by whoever player has accrued the most victories overall.

To find : The Probability that 4 games will be played in total and determine the likelihood that b will win the game.

Determine first which exact order of wins causes games.

The first game is won by A: B triumphs in game two ( if A wins again, Awon and the game is over)A or B might win the following two games to give themselves a two-game lead equivalently in the scenario if B triumphs in game one.

The ordering can be ABAA, ABBB, BAAA, or BABB.

P(4 games  precisely) = P(ABAA) + P(ABBB) + P(BAAA)+ P(BABB)

P(4 games  precisely)  = 2[(p³(1-p) + p(1-p)³]

The likelihood that b will win the game is therefore 2[(p3(1-p) + p(1-p)3] and the probability that 4 games will be played overall. as well as p2 / [p2 + (1-p)2]

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It will take approximately 8.84 years for the car's value to be $5000.

We can use the formula for exponential decay to find the time it takes for the car's value to reach $5000:

V = V0 * \(e^{(-rt)\)

where V is the current value, V0 is the initial value, r is the decay rate, and t is the time in years. We can rearrange this formula to solve for t:

t = -ln(V/V0) / r

Plugging in the given values, we get:

t = -ln(5000/17000) / (-0.17) = 8.84 years (rounded to two decimal places)

Therefore, it will take approximately 8.84 years for the car's value to be $5000.

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The width of a cuboid is 7 cm

In geometry, a cuboid is a solid shape or a three-dimensional shape. A convex polyhedron that is bounded by six rectangular faces with eight vertices and twelve edges is called a cuboid. A cuboid is also called a rectangular prism. A cuboid with six square faces is called a cube. An example of a cuboid in real life is a rectangular box.

volume = l * b * h = 490

7 * b *10 = 490

b = 7 cm

In Maths, we can observe other shapes which are exactly the same as cuboid, they are rectangular cuboid, rectangular box, right rectangular prism, right cuboid, rectangular parallelepiped, and rectangular hexahedron

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Answer:

above sea level

Step-by-step explanation:

1) Considering that the sum of the interior angles of a triangle is 180º, i.e., what the triangle angle-sum theorem means

2) Let' solve for y

y+27°+4y+113=180 Combine like terms

5y +140 = 180 Subtract 140º from both sides.

5y = 40 Divide both sides by 5

y=8

2) Hence y = 8

By graphing the system of equations, we can see that the solution is (4, -2)

Here we want to solve the system of equations:

y = (-3/2)*x + 4

y = (1/2)*x - 4

To solve this graphically, we just need to graph both equations on the same coordinate axis and find the point where the lines intersect.

The graph can be seen on the image at the end.

We can see that the solution is (4, -2)

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Answer:

x = 4

Step-by-step explanation:

-6x = -24

/-6      /-6

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

x = 4

The technique being described is random sampling without replacement, which is option a.

This technique is called "sampling without replacement."

However, you've also mentioned convenience sampling, which is a different method.

Let me briefly explain both concepts.

Sampling without replacement is a method in which each item, score, event, or participant is chosen from the population and is not returned to the pool for further selections.

This ensures that each element can only be selected once, eliminating the chance of duplication in the sample.

This method is often used in surveys, experiments, and research to maintain the independence of observations and provide a more accurate representation of the population.
Select an item, score, event, or participant from the population.
Record the selected item and remove it from the population.

Repeat steps 1-2 until the desired sample size is obtained.
Convenience sampling, on the other hand, is a non-probability sampling method where researchers select participants based on their accessibility and ease of recruitment.

This approach may introduce bias and limit the generalizability of the study results, as it does not ensure that the sample is representative of the population.
Identify the target population.
Recruit participants who are easily accessible and willing to participate.
Collect data from the selected participants.
In summary, sampling without replacement is a technique that prevents the same item from being selected more than once, while convenience sampling is an approach that focuses on selecting participants based on their accessibility. Both methods serve different purposes in research and should be chosen based on the study's objectives and available resources.

Option a is correct.

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