Mary invests £12000 into a savings account. The account pays 1.5% compound interest per year.
Work out the value of her investment after two years.

Answer:

The number of pennies owned is 7 pennies

Step-by-step explanation:

The given parameters are;

The number of pennies left over when we break the pennies into groups of 2s = 1 penny

The number of pennies left over when we break the pennies into groups of 3s = 1 penny

Let the number of pennies owned = c

What we are given are as follows;

2 × a = c - 1

3 × b = c - 1

2 × a = 3 × b

a/b = 3/2

Therefore, if we multiply 2 by 3, and 3 by 2 we get 6

2 × 3 = 6, similarly 3 × 2 = 6

If we put 6 = c - 1, we get;

c = 6 + 1 = 7

c = 7

The number of pennies owned = 7 pennies.

Answer:

Solving for x

3(3x+y)=477

3x+y=477/3

3x+y=159

3x=159 -y

x=159-y/3

Now solving for y

3(3x+y)=477

3x+y=477/3

3x+y=159

y= 159-3x

Answer:

Option 3

Step-by-step explanation:

If you multiply the numbers inside the root of option 3, you get the equation

2 * 2 * 3 * 3 * 5

Which equals 180

Replacing the root sign will show that you have the right answer.

Based on simultaneous equations, Kaun has deposited in each account the following:

When two or more algebraic equations are solved concurrently, we call them simultaneous equations.

We can solve simultaneous equations by graphing, elimination, or substitution methods.

The total deposit in the two accounts = R 5,400

The annual interest in Account A = 3% or 0.03

The annual interest in Account B = 2% or 0.02

The total interest earned from both accounts for the year = R 140

Let Account A be designated as a and Account B be designated as b.

a + b = 5,400 ... Equation 1

0.03a + 0.02b = 140 ... Equation 2

Eliminate a by multiplying Equation 1 by 0.03:

0.03a + 0.03b = 162 ... Equation 3

Subtract Equation 2 from Equation 3:

0.03a + 0.03b = 162

-

0.03a + 0.02b = 140

= 0.01b = 22

b = 2,200

From Equation 1, substitute b:

a + 2,200 = 5,400

a = 3,200 (5,400 - 2,200)

Check:

In equation 2:

0.03a + 0.02b = 140

0.03(3,200) + 0.02(2,200) = 140

96 + 44 = 140

140 = 140

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Answer:

When we have an empty circle in a point, this means that the value of the point is not included.

This would be used for something like:

x > a

The value a is not a solution, because x needs to be larger than a, then we should use the empty circle.

A filled circle is used when the value is included in the solutions.

This is used for inequalities like:

x ≥ a

Where x = a is a possible solution.

Then if we have te set:

Z ≥ 3

We should have a filled circle at the value 3.

Answer:

\((x) = 1 + \frac{1}{2x} \\ f {}^{ - 1} (x) = \frac{1}{2(x - 1)} \)

Answer:

the three vertices are (1, 1), (2, 0), (-1, -3).

The vertices of the triangles are the coordinates of the point of

intersection of the graph of the equation of the three lines.

Correct response:

The coordinates of the three vertices of the triangles are;

E. \(\underline{(2, 0), \ (1, -1), \ and \ (-1, -3)}\)

The equation of the given lines are;

y = -x + 2, y = 2·x - 1, y = x - 2

The point of the intersection of the two lines, gives the vertices, and are

the solution of the two linear equations of the lines.

At the points where the lines intersect, we have;

-x + 2 = 2·x - 1

Which gives;

3·x = 3

x = 1

y = -1 + 2 = -1

A vertex is at the point (1, -1)

The coordinate of the second vertex is given as follows;

2·x - 1 = x - 2

2·x - x = -2 + 1 = -1

x = -1

y = -1 - 2 = -3

The second vertex is; (-1, -3)

The coordinates of the third vertex is given as follows;

-x + 2 = x - 2

2·x = 4

x = 2

y = 2 - 2 = 0

Which gives the point; (2, 0)

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Answer:

40*8.5=340

6*90=540

total=880/2.5=352bags

Step-by-step explanation:

Use Pythagarus theorem

17^2=15^2 +x^2

289= 225 + x^2

64=x^2

x = 8 m

The maximum profit if the profits per acre are $75 for corn and $40 for soybeans is $371,255.83. Therefore, the correct option is c.

To find the maximum profit from planting corn and soybeans, we can use linear programming. Let's first define the variables and write the constraints.

Let x be the number of acres of corn and y be the number of acres of soybeans.

1. Total acre constraint: x + y ≤ 6,000

2. Fertilizer/herbicide constraint: 9x + 3y ≤ 40,501

3. Labor constraint: 0.75x + y ≤ 5,250

The objective function to maximize is the profit function: P(x,y) = 75x + 40y

Now, we will use the Solver to find the maximum profit:

Step 1: Set up a spreadsheet with the constraints and the objective function.

Step 2: Go to the Data tab and click on Solver. If Solver is not available, you may need to add it in Excel Options.

Step 3: Set the objective function by selecting the cell with the profit function.

Step 4: Choose "Max" for the objective.

Step 5: Add the constraints by selecting the corresponding cells.

Step 6: Click on "Solve" and the Solver will find the optimal values for x and y.

After using Solver, we find that the optimal values are x = 4,363.89 (corn) and y = 1,636.11 (soybeans), which yields a maximum profit of $371,255.83. Therefore, the correct answer is c: $371,255.83

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Step-by-step explanation:

a) (i) length = 2(pi)r = 2(3.14)(.5 m) = 3.14 m

(ii)3.14 m × ($4.70/m) = $14.76

b) A = (pi)r^2 = (3.14)(18 m)^2 = 1017.9 m^2

The child passes through 18π radians in the course of the carousel ride.

To determine the number of radians the child passes during the 6-minute ride on the carousel, we need to know the distance traveled in terms of radians.

Since there are 20 horses spaced evenly around the carousel, each horse is separated by an angle of 360/20 = 18 degrees or π/10 radians.

Therefore, during one rotation of the carousel, the child passes through 20π/10 = 2π radians. And since the carousel completes one rotation every 40 seconds, the angular velocity is 2π/40 = π/20 radians per second.

To find the total distance traveled in radians during a 6-minute ride, we need to multiply the angular velocity by the time elapsed.

6 minutes is equal to 360 seconds,

so the child passes through π/20 x 360 = 18π radians during the ride.

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Answer: 96 servings.

Step-by-step explanation:
There are 16 cups in 1 gallon, so 3 gallons of punch would be equal to:

3 gallons x 16 cups/gallon = 48 cups

If each serving size is 1/2 cup, then the number of servings in 3 gallons of punch would be:

48 cups / (1/2 cup/serving) = 96 servings

Therefore, 3 gallons of punch would provide 96 servings, assuming each serving size is 1/2 cup.

Answer:

60 DEG

Step-by-step explanation:

Angle on a straight line = 180 DEG

Equation:

4x + 2x + 90 DEG = 180 DEG

6x = 90 DEG

x = 15 DEG

Therefore,

angle LMN = 15 * 4 = 60 DEG

The predicted weight of a girl who is 11 years old, if B0 equals 3, and B1 equals 7, is 80. The correct option is 80.

To find the predicted weight of an 11-year-old girl using the given model, follow these steps:

1. Plug in the given values for B0, B1, and Age into the equation: Weight = B0 + B1*Age + E
2. In this case, B0 = 3, B1 = 7, and Age = 11: Weight = 3 + 7*11 + E
3. Calculate the product of B1 and Age: 7 * 11 = 77
4. Add the result to B0: 3 + 77 = 80
5. Since E represents the error term and is not provided, we will assume it to be zero for this prediction. Thus, the predicted weight is 80.

So, the predicted weight of an 11-year-old girl is 80 (choice A).

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Answer:

3 17/18 rounds up to 3.94

Using the fundamental theorem of calculus, we can evaluate the definite integral ∫[1 to 0] (y^2 + y^6) dy exactly.

To evaluate the definite integral ∫[1 to 0] (y^2 + y^6) dy, we can apply the fundamental theorem of calculus. The fundamental theorem states that if F(x) is an antiderivative of a function f(x) on an interval [a, b], then the definite integral of f(x) from a to b is equal to F(b) - F(a).

Let's find the antiderivative of the integrand (y^2 + y^6). The antiderivative of y^2 with respect to y is (1/3)y^3, and the antiderivative of y^6 is (1/7)y^7. Thus, the antiderivative of the integrand is (1/3)y^3 + (1/7)y^7.

Applying the fundamental theorem of calculus, the definite integral becomes [(1/3)(0^3) + (1/7)(0^7)] - [(1/3)(1^3) + (1/7)(1^7)]. Simplifying, we get (0 + 0) - (1/3 + 1/7) = -10/21.

Therefore, the exact value of the definite integral ∫[1 to 0] (y^2 + y^6) dy is -10/21.

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The probability of being dealt 4​, ​5, 6​, 7​, and 8​, not necessarily in the same​ suit is  0.00039.

The cards 4,5,6,7, and 8 are given to us. We must figure out the probability of obtaining these cards in a deal. As we already know, probability equals the number of possible card selection methods divided by the total number of possible card selection methods. The amount of card selection options will therefore be determined initially.

We know that there are four cards of each number, 4, 5, 6, 7 and 8, in a deck of 52 cards. This means that there will be an equal number of possibilities to choose one card from the decks of 4, 5, 6, 7 and 8 when raised to the power of five.

Possible ways= 4^5= 1024

Total selection= C(52,5)= 2598960

Probability of being dealt with  4​, ​5, 6​, 7​, and 8​ is 1024/2598960 which is equal to 0.00039.

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2000/10=200

The answer is 200 times

Line c is also perpendicular to line a.

Suppose that c and b are perpendicular. This implies that:

option 1) b and a are the same line or,

option 2) b is parallel to a

Since we know that a and b are different lines, hence, the option 2 is the correct.

To prove that n^3 + 3n^4 is θ (2n^3), we need to show that there exist positive constants c1, c2, and n0 such that

c1 * 2n^3 ≤ n^3 + 3n^4 ≤ c2 * 2n^3 for all n ≥ n0.

First, we will show that n^3 + 3n^4 ≤ c2 * 2n^3 for all n ≥ 1, where c2 = 4. For n ≥ 1, we have

n^3 + 3n^4 ≤ 4n^4 = 2(2n^3) ≤ 2n^3 * c2

Therefore, n^3 + 3n^4 is O(n^3), and hence it is also O(2n^3).

Next, we will show that n^3 + 3n^4 ≥ c1 * 2n^3 for all n ≥ 1, where c1 = 1/4. For n ≥ 1, we have

n^3 + 3n^4 ≥ (1/4) * 3n^4 = (3/4) * 4n^4/4 = (3/4) * 2n^3

Therefore, n^3 + 3n^4 is Ω(n^3), and hence it is also Ω(2n^3).

Since n^3 + 3n^4 is both O(2n^3) and Ω(2n^3), we conclude that n^3 + 3n^4 is θ(2n^3).

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The strawberries that are way more than 2 ounces will be 24 strawberries.

It should be noted that the information stated that 30 of the 54 strawberries she picked the way less than 2 ounces.

Therefore, the strawberries that are way more than 2 ounces will be the difference between the total number picked and 30.

This will be:

= 54 - 30

= 24

Therefore, the strawberries that are way more than 2 ounces will be 24 strawberries.

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The possible values are -

(a²,b²) = p

(a²,b) = p if p|-r and (a²,b) = p² if p|r

(a²,b³) = p² if p|-r and (a²,b³) = p³ if p|r

What is gcd?

The greatest common factor (GCF) that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor is another name for it (HCF).

Since (a, b) = p it can be written a = pr and b = ps where r and s are integers such that (r, s) = 1.

Then a² = p²r².

Then by Theorem 1.7, (a²,b) = (p²r²,ps) = p(pr²,s).

By Theorem 1.8, (r²,s) = 1 .

Thus, there are two cases to consider: if p|s then, (a²,b) = p², and if p|-s then (pr²,s) = 1 (Again by Theorem 1.8)  so that (a²,b) = p in that case.

Thus, there are two cases for (a²,b): namely p or p².

The same analysis shows that (a³,b) must be either p, p² or p³ depending on the power of p that divides b.

Analyze (a²,b³) as follows.

Using the notation already introduced, and

Theorem 1.7, it is obtained that (a²,b³) = (p²r²,p³s³) = p²(r²,ps³).

Since, (r, s) = 1, Theorem 1.8 shows that (r²,s³) = 1.

Therefore, there are two possibilities for (a²,b³) -

(a²,b³) = p² if p|-r and (a²,b³) = p³ if p|r.

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Answer:

Katelynn has $285 already saved. The bike she likes starts at 475. It starts at, it's not exactly. However, we are looking for the least amount she needs to save. Therefore, we need to subtract what she has saved from the least amount she is trying to save or reach. least amount needed $475 minus-saved $285 this equals $190.

Step-by-step explanation:

Answer:

53 will be the correct answer

Step-by-step explanation:

odbsisocbx

Answer:

Pls rate Brainliest and See Explanation

Step-by-step explanation:

Ans is 53

First you replace z with u in the equation

Then you mutiply 8 and 7 making 56

Last you subtract 3

Answer:

1 row = 205plants

9*205=1845plants

Therfore 1845 plants are there in 9 rows of tomato.

Step-by-step explanation:

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