19. To the nearest year, how long would an investment need to be left in the bank at 2%, compounded annually, for the investment to double. A. 34 years C.36 years D. 37 years B. 35 years 20 Sam inhorito 150​

Answer:

10

Step-by-step explanation:

→ Calculate how many are mint ice cream's

\(\frac{1}{3}\) × \(30\) = 10

→ Calculate how many are chocolate

30 - 10 = 20

\(\frac{1}{2}\) × 20 = 10

→ Now find the vanilla

30 - ( 10 + 10 ) = 10

Answer:

\(m = \frac{5}{3}\)  

\(b = \frac{4}{3}\)

Step-by-step explanation:

The question requires you to rearrange the equation into the form:

y = mx + c

Which is the straight line equation, meaning rearrange for y:

Add 3y to both sides of the equation:

5x - 3y + 4 = 0

5x - 3y + 4 + 3y = 0 + 3y

5x + 4 = 3y

Divide both sides of the equation to isolate y:

\(\frac{5x}{3} + \frac{4}{3} = \frac{3y}{3}\)

\(y = \frac{5}{3}x + \frac{4}{3}\)

This means that  \(m = \frac{5}{3}\)  and \(b = \frac{4}{3}\).

Hope this helps!

Answer:

m = 5/3 and c = 4/3.

Step-by-step explanation:

5x - 3y + 4 = 0

-3y = -5x - 4

y = (-5/-3)x - 4/-3

y = 5/3 x + 4/3

y  = mx    +  c

So m = 5/3 and c = 4/3

Answer:

Answer is 50g/cm^3

Step-by-step explanation:

soln,

Volume of the gold cube = 9 cm^3

Mass of the gold cube = 450 g

now,

density= mass/volume

=450 / 9

=50 g/cm^3

{Therefore, the density of the gold cube is 50 g/cm^3.}

Answer:

Roy eat 4 sweets

Step-by-step explanation:

Roy =R

Mike= (R-2)

Leen= 3(R+ R-2)

R + (R-2) + 6R-6 = 24

8R-8=24

8R=32

R=4

     Mike  4-2 = 2

     Leen 3(4+2) = 18

4+2+18=24

Work Shown:

804/d = 6/4

804*4 = 6d

3216 = 6d

6d = 3216

d = 3216/6

d = 536

Answer:

Step-by-step explanation:

From ΔABD:

                   BD² + 7² = x²   ⇒  BD² = x² - 49

Form ΔBCD:

                   BD² + 3² = BC²   ⇒  BD² = BC² - 9

so:

       BC² - 9 = x² - 49   ⇒  BC² = x² - 40

From ΔABC:

                 x² + BC² = (7+3)²

                  x² + x² - 40 = 10²

                   2x² = 140

                    x² = 70

                    x = √70                    

Answer:

x = \(\sqrt{70}\)

Step-by-step explanation:

Δ ABC and Δ ADB are similar, thus ratios of corresponding sides are equal, that is

\(\frac{AB}{AD}\) = \(\frac{AC}{AB}\) ( cross- multiply )

AB² = AC × AD = 10 × 7 = 70 ( take the square root of both sides )

AB = x = \(\sqrt{70}\)

Answer:

C.

Step-by-step explanation:

Answer:

The shaded segment  = The arc area - The triangle

The arc area = pi x radius^2 x angle/360

                     = pi x 9^2 x (360-270)/360 = 63.61 (m2)

The triangle area = 9 x 9/2 = 41.5 (m2)

(because this is right triangle)

=> The shaded segment = 63.61 - 41.5 = 22.11 (m2)

Answer:

7

Step-by-step explanation:

1x2=2x3/1/2= 7

Answer:

7

Step-by-step explanation:

I did the question

The value of expression lim x→1 g(x) is 4.

In mathematics, a limit is a point at which a function becomes close to producing the desired result for the given input values. Limits are necessary for calculus and mathematical analysis and are also needed to establish integrals, derivatives, and continuity. It is used during the analysis process and continually thinks about how the function will act in a particular situation. The idea of the limit of a topological net broadens the definition of the limit of a sequence and relates it to the limit and direct limit in the theory category.

Given expression,

\(4x\leq g(x)\leq2x^{4}-2x^{2} +4\)

For x → 1

4x = 4(1)

    = 4

\(2x^{4}-2x^{2} +4\) = 2(1)-2(1)+4

                     = 4

Hence, the value of lim x→1 g(x) is 4.

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Answer:

Step-by-step explanation:

The Answer is A

The equation for a parallel street that passes through the given point is y = 4x + 12

From the question, we are to determine the equation of the street that is parallel to the first street

NOTE: Two lines are parallel if they have equal slopes.

Thus,

We will determine the slope of the first street.

From the given information,

The street passes through the points (4, 7) and (3, 3)

Using the formula,

Slope = (y₂ - y₁)/(x₂ - x₁)

x₁ = 4

y₁ = 7

x₂ = 3

y₂ = 3

∴ Slope = (3 -7)/(3 -4)

Slope = -4/-1

Slope = 4

Now,

For the equation of the parallel street

The street passes through the point (-2, 4)

Since, the street is parallel to the first street,

Slope = 4

Using the point-slope form

y - y₁ = m(x - x₁)

y - 4 = 4(x - -2)

y - 4 = 4(x + 2)

y - 4 = 4x + 8

y = 4x + 8 + 4

y = 4x + 12

Hence, the equation for a parallel street that passes through the given point is y = 4x + 12

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To analyze the test results, we need to determine the p-value associated with the test statistic value of 2.01. Since the alternative hypothesis is µ > 75, we are conducting a one-sided test.

To find the p-value, we look up the critical value corresponding to the significance level α (usually set at 0.05 or 0.01) in the appropriate distribution table (e.g., standard normal distribution table).

Alternatively, we can use statistical software or calculators to calculate the p-value directly. In this case, with a test statistic value of 2.01, we calculate the area under the curve to the right of 2.01 in the standard normal distribution.

The p-value represents the probability of observing a test statistic as extreme as 2.01 or more extreme under the null hypothesis. If the p-value is smaller than the chosen significance level (e.g., 0.05), we reject the null hypothesis. Otherwise, if the p-value is greater than the significance level, we fail to reject the null hypothesis.

Without the specific p-value or significance level, we cannot determine the conclusion of the hypothesis test based solely on the test statistic value of 2.01.

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The second derivative of the function f is expressed as f''(x) = x(x-3)^5(x-10)^2. This information provides insights into the behavior and critical points of the function.

The given expression, f''(x) = x(x-3)^5(x-10)^2, represents the second derivative of a function f with respect to the variable x. The second derivative provides valuable information about the behavior of the function, particularly regarding concavity and inflection points.

The equation indicates that the function has factors of x, (x-3)^5, and (x-10)^2. The term x indicates that the function includes a linear component, while the factors (x-3)^5 and (x-10)^2 suggest that the function may exhibit multiple inflection points and changes in concavity around x = 3 and x = 10.

The expression does not provide information about the original function f(x) or its first derivative f'(x), but it does give valuable insights into the higher-order behavior of the function and can help analyze critical points and concavity characteristics when combined with additional information about the function.

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The rectangle with dimensions 21 m by 21 m has the largest area among rectangles with a perimeter of 84 m.

To find the dimensions of a rectangle with a perimeter of 84 m that maximizes the area, we need to use the properties of rectangles.

Let's assume the length of the rectangle is l and the width is w.

The perimeter of a rectangle is given by the formula: 2l + 2w = P, where P is the perimeter.

In this case, the perimeter is given as 84 m, so we can write the equation as: 2l + 2w = 84.

To maximize the area, we need to find the dimensions that satisfy this equation and give the largest possible value for the area. The area of a rectangle is given by the formula: A = lw.

Now we can solve the perimeter equation for l: 2l = 84 - 2w, which simplifies to l = 42 - w.

Substituting this expression for l into the area equation, we get: A = (42 - w)w.

To maximize the area, we can find the critical points by taking the derivative of the area equation with respect to w and setting it equal to zero:

dA/dw = 42 - 2w = 0.

Solving this equation, we find w = 21.

Substituting this value of w back into the equation l = 42 - w, we get l = 42 - 21 = 21.

Therefore, the dimensions of the rectangle that maximize the area are l = 21 m and w = 21 m.

In summary, the dimensions of the rectangle are 21 m by 21 m, so the answer is A. 21, 21.

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1. Chicken became the key product that drove the creation of the Interstate Highway System, which led to the dominance of American trucks in the US truck market.

2. A party may want to impose a tariff to protect domestic industries from foreign competition or to generate revenue for the government.

3. A party is usually trying to protect domestic industries, but a tariff on automobiles would hurt both domestic consumers who would pay higher prices and foreign producers who would face reduced demand.

4. Competition encourages innovation by providing incentives for companies to improve their products and services to stay ahead of their rivals; American trucks stayed the same because they faced little competition due to protectionist policies.

5. Foreign companies tried to get around American-imposed tariffs on automobiles by establishing factories in the US, forming joint ventures with American companies, or exporting through third countries.

6. The methods used to get around tariffs can be efficient in the short term, but they may not be sustainable or desirable in the long term as they can lead to trade imbalances and undermine the competitiveness of domestic industries.

7. Tariffs can be used as a bargaining chip to negotiate better trade deals, but they should be imposed judiciously and only as a last resort to avoid damaging the economy and harming consumers.

1. In the podcast, chicken is cited as the reason why American trucks dominate the truck market in the United States.

This is because in the 1960s, the government imposed regulations on the trucking industry that limited the amount of weight a truck could carry.

To get around these regulations, the industry started using smaller trucks to transport goods, which were often not strong enough to handle the weight.

However, they found that if they put chicken on the back of the trucks, the weight of the cargo would distribute more evenly and the smaller trucks could handle the load.

This led to the development of the modern pickup truck, which is now a staple of the American automobile market.

2. Parties may want to impose tariffs for various reasons, such as to protect domestic industries and jobs from foreign competition, to raise revenue for the government, or to level the playing field in international trade.

Two specific reasons for imposing tariffs could be to protect national security interests or to address unfair trade practices by other countries.

3. Tariffs are usually imposed to protect domestic industries and jobs, and the parties that are being protected are typically the producers of the goods or services in question.

However, tariffs can also harm consumers who may have to pay higher prices for imported goods or may have fewer choices in the marketplace. For example, if a tariff is imposed on automobiles, domestic car manufacturers may benefit, but consumers may have to pay more for cars, and foreign automakers may lose market share.

4. Competition encourages innovation by creating incentives for companies to improve their products or services to gain a competitive advantage.

In the case of American trucks, the lack of competition may have contributed to their lack of innovation over the years. Since they dominated the market, there was little pressure to improve or innovate, and as a result, they have largely stayed the same.

However, the rise of foreign competition in recent years has led American truck manufacturers to invest more in innovation to stay competitive.

5. Foreign companies have tried to get around American-imposed tariffs on automobiles in various ways, such as by moving production to countries not subject to the tariffs, by exporting parts and assembling them in the United States, or by lobbying the government for exemptions or tariff reductions.

6. The methods used by foreign companies to get around tariffs may not be efficient for the economy as a whole because they can lead to higher costs and inefficiencies in the supply chain.

However, they may be necessary for individual companies to remain competitive in the short term.

Ultimately, a more efficient solution would be to address the root causes of the trade imbalances that lead to tariffs in the first place.

7. A tariff can be used as a bargaining chip by threatening to impose tariffs on imports from a country unless they make concessions in trade negotiations.

While this can be an effective strategy in certain situations, it can also lead to a trade war and harm both economies.

In general, tariffs should be used sparingly and as a last resort, and efforts should be made to address underlying trade issues through diplomacy and negotiation.

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In project management, a control chart is a tool used to monitor and track a project's progress over time. It provides a graphical representation of a project's performance, allowing project managers to quickly identify any deviations from the plan.

For more complex projects, statistical analysis can be applied to the control chart to identify potential causes of schedule deviation.

By analyzing the control chart data using statistical methods, project managers can determine whether the schedule deviation is due to random variation or a systematic cause. If the deviation is due to a systematic cause, the statistical analysis can help identify the root cause of the problem.

Once the root cause is identified, project managers can take corrective action to get the project back on track. The use of statistical analysis on control charts is a powerful tool for project management, enabling project managers to make data-driven decisions and minimize the risk of schedule delays and cost overruns.

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The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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Answer:

When the absolute value of the scale factor is lower than 1, it decreases the size of the shape.

When the absolute value of the scale factor is greater than 1, the shape will increase in size.

Step-by-step explanation:

can i have brainliest please

From the orthogonal basis of the given set, the values of a,b, and c can be obtained as:

a = 47/13, b = -4/13 and c = 162/13.

We use the basic principles of the Gram-Schmidt process to solve this question.

As we know, the vectors of the orthogonal basis are defined as:

v₁ = u₁ = [1, 3, 0]

v₂ = u₂ - proj(v₁, u₂)

v₃ = u₃ - proj(v₁, u₃) - proj(v₂, u₃)

We ultimately need v₃, but for that, we have to evaluate v₂.

v₂ = u₂ - proj(v₁, u₂)

= u₂ - ((u₂ · v₁) / (v₁ · v₁)) * v₁                  (Expression for Projection)

= u₂ - (([-30, 10, 40] · [1, 3, 0]) / ([1, 3, 0] · [1, 3, 0])) * [1, 3, 0]

= u₂ - ((-30 + 30 + 0) / (1 + 9 + 0)) * [1, 3, 0]

= u₂ - (0 / 10) * [1, 3, 0]

= u₂

= [-30, 10, 40].

Now, as we have v₂, we proceed with the expression for v₃, by substituting the values.

v₃ = u₃ - proj(v₁, u₃) - proj(v₂, u₃)

= u₃ - ((u₃ · v₁) / (v₁ · v₁)) * v₁ - ((u₃ · v₂) / (v₂ · v₂)) * v₂

= u₃ - (([4, -3, 2] · [1, 3, 0]) / ([1, 3, 0] · [1, 3, 0])) * [1, 3, 0] - (([4, -3, 2] · [-30, 10, 40]) / ([-30, 10, 40] · [-30, 10, 40])) * [-30, 10, 40]

= u₃ - ((4 + (-9) + 0) / (1 + 9 + 0)) * [1, 3, 0] - ((4*(-30) + (-3)10 + 240) / ((-30)² + 10² + 40²)) * [-30, 10, 40]

= u₃ - ((-5) / 10) * [1, 3, 0] - ((-120 + (-30) + 80) / (900 + 100 + 1600)) * [-30, 10, 40]

= u₃ - (-1/2) * [1, 3, 0] - (-70 / 2600) * [-30, 10, 40]

= u₃ + (1/2) * [1, 3, 0] + (7/26) * [-30, 10, 40]

= [4, -3, 2] + (1/2) * [1, 3, 0] + (7/26) * [-30, 10, 40]

= [4, -3, 2] + [1/2, 3/2, 0] + [-210/26, 70/26, 280/26]

= [4, -3, 2] + [1/2, 3/2, 0] + [-105/13, 35/13, 140/13]

= [4 + 1/2 - 105/13, -3 + 3/2 + 35/13, 2 + 0 + 140/13]

= [47/13, -4/13, 162/13].

(Note: It's better if this calculation is done in parts, and the final solution is assembled at the end)

So, the vectors v₁, v₂, and v₃ form an orthogonal basis when:

v₁ = [1, 3, 0]

v₂ = [-30, 10, 40]

v₃ = [47/13, -4/13, 162/13]

Therefore, the corresponding values of a, b, and c are:

a = 47/13

b = -4/13

c = 162/13

(The clear question has been attached for convenience)

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The required probability is 0.4408.

The operating characteristics of the loading gate problem are:

L = λ/ (μ - λ)

W = 1/ (μ - λ)

Lq = λ^2 / μ (μ - λ)

Wq = λ / μ (μ - λ)

ρ = λ / μ

P0 = 1 - λ / μ

Where, L represents the average number of cars either being loaded or waiting.

W represents the average time a car spends either being loaded or waiting.

Lq represents the average number of cars waiting.

Wq represents the average waiting time of a car.

ρ represents the utilization factor.

ρ = λ / μ represents the ratio of time the worker spends loading cars to the total time the system is busy.

P0 represents the probability that the system is empty.

The probability that there will be more than six cars either being loaded or waiting is to be determined. That is,

P (n > 6) = 1 - P (n ≤ 6)

Now, the probability of having less than or equal to six cars in the system at a given time,

P (n ≤ 6) = Σn = 0^6 [λ^n / n! * (μ - λ)^n]

Putting the values of λ and μ, we get,

P (n ≤ 6) = Σn = 0^6 [(6/ 48)^n / n! * (8/ 48)^n]

P (n ≤ 6) = [(6/ 48)^0 / 0! * (8/ 48)^0] + [(6/ 48)^1 / 1! * (8/ 48)^1] + [(6/ 48)^2 / 2! * (8/ 48)^2] + [(6/ 48)^3 / 3! * (8/ 48)^3] + [(6/ 48)^4 / 4! * (8/ 48)^4] + [(6/ 48)^5 / 5! * (8/ 48)^5] + [(6/ 48)^6 / 6! * (8/ 48)^6]P (n ≤ 6) = 0.5592

Now, P (n > 6) = 1 - P (n ≤ 6) = 1 - 0.5592 = 0.4408

Therefore, the required probability is 0.4408.

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Answer:

This process is called

Producing. underwriting.

Step-by-step explanation:

Answer:

-3/2

Step-by-step explanation:

In the image

Answer:

I think that it's +2, but seeing as I don't know what type of formula you need (several ways depending on what you are learning, solving for x, solving quadratic, etc?)

Step-by-step explanation:

The formula of the given geometric sequence is: a(n) = 1024 . (0.5)ⁿ⁻¹ and the first five terms are: 1024, 512, 256, 128, and 64.

The formula of the n-th term of a geometric sequence is:

a(n) = a₁ . r^(n-1)

Where:

a₁ is the first term

r  is the ratio = a(n)/a(n-1)

Parameters given in the problem:

a₁ =1024, r=0.5

Plug these parameters into the formula, then we get the explicit formula of the n-th term:

a(n) = 1024 . (0.5)ⁿ⁻¹

The first 5 terms:

a₁ = 1024

a(2) = 1024 . (0.5)²⁻¹

       = 1024 . (0.5)¹ = 512

a(3) = 1024 . (0.5)³⁻¹

       = 1024 . (0.5)² = 256

a(4) = 1024 . (0.5)⁴⁻¹

       = 11024 . (0.5)³ = 128

a(5) = 1024 . (0.5)⁵⁻¹

       = 1024 . (0.5)⁴ = 64

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The R9,000 loan offer can be analyzed as follows;

A loan is a financial agreement that is made between a lender and a borrower, such that the borrower accepts a certain amount of money provided by the lender, which is to be paid back after a specified period of time, with an interest.

The total amount which has to be paid as repayment for the loan can be obtained by finding the product of the monthly installment and the total number of months to repay the loan:

Total amount Theo pays = R318.92 × 48 = R15308.16

The reasons banks and other financial institutions offer loans to people that did not apply for loans includes;

Theo's investment options can be analyzed as follows;

Option 1: Investment with simple interest calculation

Interest earned = R9,000 × 8% × 4 years = R2,880

The total value of the investment after 4 years = R9,000 + R2,880 = R11,880

Option 2: Investment with compound interest calculation

The total value of the investment after 4 years = R9,000 × (1 + 7%)⁴ = R11,797.16409

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Answer:

245. 51 is the answer hope it helps

Answer:

245.51

Step-by-step explanation:

Find the number in the hundredth place 1 and look one place to the right for the rounding digit 4. Round up if this number is greater than or equal to 5 and round down if it is less than 5. Hope this helps!

Given that the basketball team has 10 players including Steve and Danny and we need to divide them into two teams of 5 for an intra-squad scrimmage. The number of ways to do this if Steve and Danny insist on playing on the same team is explained below:

Step 1: Since Steve and Danny insist on playing on the same team, they can be put on the same team in 1 way.

Step 2: Now, there are 8 players remaining and we need to divide them into 2 teams of 4 each, which can be done in the following ways. Number of ways

= 8!/(4!4!) .

= 70 Therefore, the number of ways to divide the team of 10 players into two teams of 5 if Steve and Danny insist on playing on the same team is

1 * 70 = 70.

Hence, option (A) is the correct answer.

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Answer:

c 70 chosen to sleep on the bed