If Alice wants to have R12 000 saved in 4 years' time at 12% simple interest,
how much will she need to invest now?

Answer:

47.37 Inches

Step-by-step explanation:

We start by assuming that we're at zero years when the tree is at 13.63 inches. We then ignore that height, and look at the rate of growth, which is 2.41 in / year.

The question asks how tall the tree is when it's 14 years old, so we multiply 2.41 inches / year by 14 years to get 33.74 inches.

The final step is to add that 33.74 onto the original 13.63 to get a new total of 47.37 inches when the sapling is 14 years old.

Place value of 432 is 400 +30+02 .

What is place value?

In math, each digit in a very variety features a place value. Place value is outlined because the price pictured by a digit in a very variety on the premise of its position within the variety.

Main body:

The place value of a digit will increase by 10 times as we move  left on the place worth chart and reduces by ten times as we tend to move right.

The place of digit 4 will be hundreds.

The place of digit 3 will be tens.

The place of digit 2 will be ones.

Hence place value of 432 is  400 +30+02 .

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there are 128 fluid ounces in 1 gallon, that means that 25 gallons is 25 * 128 = 3200 ounces.

so if we know that for 20 ounces is 3.54, how much will it be for 3200 ounces?

\(\begin{array}{ccll} \$ & oz\\ \cline{1-2} 3.54 & 20\\ x& 3200 \end{array} \implies \cfrac{3.54}{x}=\cfrac{20}{3200}\implies \cfrac{3.54}{x}=\cfrac{1}{160}\implies 566.4=x\)

Answer:

-8 feet

Step-by-step explanation:

5 + 3 = 8

Answer:

its 8 feet down...

Step-by-step explanation:

just add 5 plus 3 ? well maybe your doing the math different if it's wrong I'll edit it to make it right.

Answer:

8 Goldfishes

Step-by-step explanation:

This Question tests on the concept of Ratio Conversion.

Ratios are proportional numbers that has a specific value assigned to their corresponding number of units.

Example: Max 3 : 4 Tyler

Max has 45 cards, 1 unit = 45 ÷ 3 = 15 cards, which means Tyler has 4 units = 15 × 4 = 60 cards.

In this question , we know that the ratio:

Guppies 1 : 2 Goldfish

We know that there are 4 guppies.

Which means:

1 Unit = 4

Therefore , number of Goldfish = 2 units = 2 × 4 = 8

Answer:

inconsistent

Step-by-step explanation:

inconsistent

Answer:

32%

Step-by-step explanation:

To compute the length of the segment tangent from the origin to the circle that passes through the points $(3,4),$ $(6,8),$ and $(5,13),$ we can follow these steps:

Step 1: Find the equation of the circle.
Since the circle passes through three points, we can use the formula for the equation of a circle passing through three non-collinear points. Let's call the center of the circle $(h, k)$ and the radius $r$. The equation of the circle is then:
$(x-h)^2 + (y-k)^2 = r^2$

Step 2: Substitute one of the given points into the equation.
Let's substitute the point $(3,4)$ into the equation. We get:
$(3-h)^2 + (4-k)^2 = r^2$

Step 3: Substitute the other two points into the equation.
Substituting the other two points $(6,8)$ and $(5,13)$ into the equation, we get two more equations:
$(6-h)^2 + (8-k)^2 = r^2$
$(5-h)^2 + (13-k)^2 = r^2$

Step 4: Solve the system of equations.
We now have a system of three equations with three unknowns $(h, k, r)$. We can solve this system to find the values of $h$, $k$, and $r$.

Step 5: Find the distance from the origin to the center of the circle.
Once we have the center of the circle $(h, k)$, we can use the distance formula to find the distance from the origin to the center:
$D = \sqrt{h^2 + k^2}$

Step 6: Find the length of the segment tangent from the origin to the circle.
Finally, we can subtract the radius of the circle from the distance from the origin to the center to find the length of the segment tangent from the origin to the circle:
$length = D - r$

By following these steps, you will be able to compute the length of the segment tangent from the origin to the circle that passes through the given points.

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For given average temperatures and °C=5/9°F-32 C represents temperature unit in celsius.

What is average?

In Maths, an average of a list of data is the expression of the central value of a set of data. Mathematically, it is defined as the ratio of summation of all the data to the number of units present in the list. In terms of statistics, the average of a given set of numerical data is also called mean. For example, the average of 2, 3 and 4 is (2+3+4)/3 = 9/3 =3. So here 3 is the central value of 2,3 and 4.  Thus, the meaning of average is to find the mean value of a group of numbers.

Average = Sum of Values/Number of Values

Also

Suppose, we have given with n number of values such as x1, x2, x3 ,….., xn. The average or the mean of the given data will be equal to:

Average = (x1+x2+x3+…+xn)/n

Now,

Given formula

°C=5/9°F-32, C represents  where °c is temperature unit in Celsius and

°F represents unit of temperature in Fahrenheit.

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Answer:

49.7142857143

Step-by-step explanation:

17.40/35%

9514 1404 393

Answer:

  6<x<12

Step-by-step explanation:

No side of a triangle can be more than the sum of the other two sides, or less than their difference.

  9-3 < x < 9+3

  6 < x < 12

Answer:

2.45%

Step-by-step explanation:

(2.86 - 2.79) / 2.86 = 0.0245

0.0245 x 100 = 2.45%

The statement is not true in general. The correct formula relating the second differential equations of y with respect to x and t is:

(d²y)/(dx²) = [(d²y)/(dt²)] / [(d²x)/(dt²)]

This formula is known as the Chain Rule for Second Derivatives, and it relates the rate of change of the slope of a curve with respect to x to the rate of change of the slope of the curve with respect to t. However, it is important to note that this formula only holds under certain conditions, such as when x is a function of t that is invertible and has a continuous derivative.

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The distance between the centers of the spheres defined by the equations x²-2x+y²+46y+z²=-529 and 2x²-4x+2y²+2z²+8z=-5 can be found by comparing the coefficients of the corresponding quadratic terms.

To find the distance between the centers of the spheres, we need to examine the coefficients of the quadratic terms in each equation.

For the first equation, x²-2x+y²+46y+z²=-529, the center of the sphere can be found by completing the square for the x, y, and z terms. By rearranging the equation, we have (x²-2x) + (y²+46y) + z² = -529. Completing the square for each variable, we get (x-1)² - 1 + (y+23)² - 529 + z² = -529. Simplifying further, we have (x-1)² + (y+23)² + z² = 0. This indicates that the center of this sphere is located at the point (1, -23, 0).

Similarly, for the second equation, 2x²-4x+2y²+2z²+8z=-5, completing the square yields (x-1)² - 1 + (y-0)² - 0 + (z+1)² - 1 = -5. Simplifying, we get (x-1)² + (y-0)² + (z+1)² = 3, indicating that the center of this sphere is located at the point (1, 0, -1).

To find the distance between the centers, we can use the distance formula. The distance between the points (1, -23, 0) and (1, 0, -1) is given by sqrt((1-1)² + (-23-0)² + (0-(-1))²), which simplifies to sqrt(0 + 529 + 1) = sqrt(530).

Therefore, the distance between the centers of the two spheres is sqrt(530).

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The triangle is a scalene triangle.

The measures of the three angles of a triangle are x, x+10, and 2x-6. What type of triangle must it be? The sum of the measures of the three angles in a triangle is 180 degrees, which means that:

   x + x + 10 + 2x - 6 = 180

This simplifies to,

   4x + 4 = 180,

   or 4x = 176, or x = 44

Once we have found x, we can now find the measures of the three angles of the triangle: the first angle is x, which is 44°, the second angle is x+10, which is 54°; and the third angle is 2x-6; which is 82°. A scalene triangle is a triangle with all sides and angles of unequal lengths. Since none of the angles has the same measure, the triangle is scalene. The correct answer is option C. Scalene Triangle.

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Step-by-step explanation:

Refer to attachment.

Hope it helps.

The total surface area of a hemisphere is 27π.

The radius of the given hemisphere is 3 cm.

The total surface area of a hemisphere = 3πr² square units

Where π is a constant whose value is equal to 3.14 approximately. “r” is the radius of the hemisphere.

Here, surface area of a hemisphere = 3π×3²

= 27π

Therefore, the total surface area of a hemisphere is 27π.

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Answer:

The ones selected are correct

Answer:

The slope of a line perpendicular to the given line will be –5/2

Step-by-step explanation:

Perpendicular lines will have a slope which is the opposite (switch from positive to negative or vice-versa) and the reciprocal (invert the fraction)

422₅ - 143₅ = 224₅

We convert each number to base 10.

So 422₅ = 4 × 5² + 2 × 5¹ + 2 × 5⁰

= 4 × 25 + 2 × 5 + 2 × 1

= 100 + 10 + 2

= 112₁₀

143₅ = 1 × 5² + 4 × 5¹ + 3 × 5⁰

= 1 × 25 + 4 × 5 + 3 × 1

= 25 + 20 + 3

= 48₁₀

So 422₅ - 143₅ = 112₁₀ - 48₁₀ = 64₁₀

We now convert 64₁₀ to base 5

64 ÷ 5 = 12 r 4,

12 ÷ 5 = 2 r 2

2 ÷ 5 = 0 r 2

Counting upwards,

So, 65₁₀ = 224₅

So, 422₅ - 143₅ = 224₅

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The four criteria that can be used to prove triangles are congruent and can be used to prove the triangles are congruent.

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and all three of their corresponding angles have the same measurements. These triangles can be moved around, rotated, flipped, and turned to have a same appearance. They match up with one another when moved.

The four criteria that can be used to prove triangles are congruent are SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and SSS (Side-Side-Side). Additionally, CPCTC (Corresponding Parts of Congruent Triangles are Congruent) can be used to prove the triangles are congruent.

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Smallest integer a = -1.

We need to find the smallest integer a such that the intermediate value theorem guarantees that f(x) has a zero on the interval (−2,a).

f(x) = -x² - 2x - 1

We need to find the value of 'a'.

To find that we need to apply the intermediate value theorem .To apply intermediate value theorem, we need to check if the function changes sign in the given interval, i.e., if f(-2) and f(a) are of opposite signs. If they are of opposite signs, the function changes sign and there exists at least one root in the interval. We have:

f(x) = -x² - 2x - 1f(-2) = -(-2)² - 2(-2) - 1 = -3f(a) = -a² - 2a - 1

Now we need to find the value of 'a' such that f(-2) and f(a) are of opposite signs.

Substituting a = -1 in f(a), we have:

f(-1) = -(-1)² - 2(-1) - 1 = -2

This means f(-2) and f(-1) are of opposite signs. Hence, there exists a value of 'a' in (-2, -1) such that f(x) has a zero. Therefore, the smallest integer a such that the intermediate value theorem guarantees that f(x) has a zero on the interval (−2,a) is -1.

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Answer:

Step-by-step explanation:

\(y = \frac{1}{3} x +4\) , \(slope, m_1 = \frac{1}{3}\)

Let the slope of the new line be \(m_2\)

Since the lines are parallel , \(m_1 = m_2\)

                                               \(m_2 = \frac{1}{3}\)

\((x_1, y_1) = (-3, 1) \ , \ m_2 = \frac{1}{3}\\\\Equation \ of \ the \ new \ line : (y - y_1) = m(x - x_1)\)

                                        \(y - 1 = \frac{1}{3}(x -(-3)) \\\\y - 1 = \frac{1}{3}(x +3)\\\\y - 1 =\frac{1} {3}x + 1 \\\\y = \frac{1}{3}x + 2\)

Answer:

x=-45/11

Step-by-step explanation:

2x/3-3/2=5x/2+6

2x/3=5x/2+7.5

11x/6=7.5

11x=45

x=-45/11

The required equation of the parabola in the vertex form is \(x = - \frac{1}{6} (y+5)^2+\frac{9}{2}\)

A plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line is called a parabola.

Given that, a parabola has the directrix x=6 and the focus (3,-5), we need to find the equation of the parabola,

The standard form of a left-right parabola is given as:

4p(x-h) = (y-k)²

Focus = (p+h, k)

Therefore,

h+p = 3....(i)

Directrix =

x = h-p

h-p = 6...(ii)

Solving the equations we get,

h = 9/2

p = -3/2

Substitute into the standard form:

4p(x-h) = (y-k)²

4(-3/2)(x-9/2) = (y+5)²

-6(x-9/2) = (y+5)²

\(x = - \frac{1}{6} (y+5)^2+\frac{9}{2}\)

Hence, the required equation of the parabola in the vertex form is \(x = - \frac{1}{6} (y+5)^2+\frac{9}{2}\)

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The question is incomplete so, i solved for the attached question

In the given Markov chain, State 1 is absorbing, State 4 is periodic, State 1 is recurrent, and States 3, 4, and 5 are recurrent.

A Markov chain is a stochastic model that represents a sequence of states where the probability of transitioning from one state to another depends only on the current state. Let's analyze the given Markov chain to determine the properties of each state.

State 1: This state has a probability of 1 in the first row, indicating that it is an absorbing state. An absorbing state is one from which there is no possibility of leaving once it is reached. Therefore, statement a) is correct, and State 1 is absorbing.

State 2: There are no transitions from State 2 to any other state, which means it is an absorbing state as well. However, since it is not explicitly mentioned in the question, we cannot determine its status based on the given information.

State 3: This state has non-zero probabilities to transition to other states, indicating that it is not absorbing. Furthermore, it has a loop back to itself with a probability of 1/6, making it recurrent. Hence, statements c) and e) are incorrect, while statement f) is correct. State 3 is recurrent.

State 4: State 4 has a transition probability of 1/3 to State 3, which means there is a possibility of leaving this state. However, there are no outgoing transitions from State 4, making it an absorbing state. Moreover, since there is a loop back to itself with a probability of 2/3, it is also recurrent. Therefore, statement b) is correct, and State 4 is periodic and recurrent.

State 5: Similar to State 4, State 5 has a transition probability of 2/3 to State 3 and no outgoing transitions. Hence, State 5 is also an absorbing and recurrent state. Consequently, statement e) is correct.

To summarize, State 1 is absorbing and recurrent, State 4 is periodic and recurrent, and States 3 and 5 are recurrent.

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9514 1404 393

Answer:

  4.17 hours

Step-by-step explanation:

The speed of light is about 670,616,629.4 miles per hour, so the travel time to Neptune is ...

  (2,798,842,000 mi)/(670,616,629.4 mi/h) ≈ 4.17 h

It takes about 4.17 hours for light to travel from the sun to Neptune.

Answer:

The federal government's "enumerated powers" are listed in Article I, Section 8 of the Constitution. Among other things, they include: the power to levy taxes, regulate commerce, create federal courts (underneath the Supreme Court), set up and maintain a military, and declare war. It is their job to carry out constitutional responsibilities for society.

Step-by-step explanation: