Ruggiero Brothers Oil has an R85 000 liability it must pay four years from today. The company is opening a savings account, so that the entire amount will be available when this debt needs to be paid. The plan is to make an initial deposit today, and then deposit an additional R16 000 each year for the next four years, starting one year from today. The account pays a 6% rate of return. How much does the firm need to deposit today?

Answer: I think its C

Answer:

Step-by-step explanation:

C is false. [tex]\angle BEC = \angle AED=126[/tex]   (vertically opposite).

The rest are correct.

Answer:

     6.75 inches.

Step-by-step explanation:

[tex]183.69 = 2*3.14*3^2 + 2*3.14*3*h[/tex]

[tex]= 56.52 + 18.84h[/tex]

[tex]183.69 - 56.52 = 18.84h[/tex]

[tex]127.17 = 18.84h[/tex]

[tex]=\frac{127.17}{18.84}[/tex]

[tex]=6.75[/tex]

The side lengths of such a triangle with a leg length of 5 and angles of 45, 45, and 90 are not listed in any of the options.

The right angle is established when 2 straight lines cross at a 90° angle or when they are perpendicular at the intersection. The symbol is used to indicate a right angle.

For the given question:

Triangle with degree angles - 45-45-90

It means two legs are of same length 5 units.

Then, hypotenuse H will be:

H² = 5² + 5²

H² = 25 + 25

H² = 50

H = 5√2

Thus, the correct third side of the triangle will be 5√2.

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It switches between negative and positive every 40 seconds.  it switches between positive and negative every 80 seconds. So correct statements are B and E.

Mathematics' branch of algebra deals with symbols and the formulas used to manipulate them. It is an effective tool for dealing with issues involving mathematical expressions and equations. In algebra, variables—which are typically represented by letters—are used to represent unknowable or variable quantities.

Equations represent mathematical relationships between variables in algebra. An equation is made up of two expressions, one on either side of an equal sign, separated by an equation. Algebraic expressions can involve constants, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

As we can see from the first roller coaster's graph, Michael's height changes from positive to negative after 40 seconds, whereas it was positive for the first 40. It remains negative between 40 and 80 seconds. It continues to be positive from 80 to 120, and so forth.

As a result, every 40 seconds it alternates between negative and positive.

B is accurate.

We can see from the second roller coaster's table that it stays positive from 0 to 80. It continues to be negative from 80 to 160, and so forth.

As a result, every 80 seconds it alternates between positive and negative.

E is accurate.

The complete question is:

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To convert miles to feet, we need to multiply the number of miles by the number of feet in one mile. There are 5,280 feet in one mile. So, to find out how many feet Rachel ran, we can multiply 3 miles by 5,280 feet/mile:

3 miles x 5,280 feet/mile = 15,840 feet

Therefore, Rachel ran 15,840 feet. Answer: 15,840 feet.

Answer:

Step-by-step explanation:

adjacent:   [tex]\angle BOC, \angle EOD[/tex]   (both are adjacent)

complementary:  [tex]\angle BOC[/tex]

supplementary:   [tex]\angle EOD[/tex]

vertical angles:   [tex]\angle AOE[/tex]

Answer: The building is approximately 16.6 feet tall.

Step-by-step explanation:

Use Pythagorean theorem (a²+b²=c²) to solve this.

We know that the ladder is 26 feet long so that would be our hypotenuse (c²). and the distance between the ladder and the building is 20 feet. So, this is the base. The remaining side is x.

Your equation would be: 20²+x²=26²

subtract 20² from 26² --> 276=x²

then take the square root --> 16.6=x

Using trigonometric functions, we can find that the value of the angle N is 3°.

The six fundamental trigonometric operations make up trigonometry. Trigonometric ratios are useful for describing these methods. The sine, cosine, secant, co-secant, tangent, and co-tangent functions are the six fundamental trigonometric functions. On the ratio of a right-angled triangle's sides, trigonometric identities and functions are founded. Trigonometric formulas are used to determine the sine, cosine, tangent, secant, and cotangent values for the perpendicular side, hypotenuse, and base of a right triangle.

Here, using the cosine theorem:

CosM = n² + l² - m²/2nl

⇒ Cos 149° = 27² + 70² - m²/2 × 27 × 70

⇒ -0.981 = 729 + 4900 - m²/3780

⇒ 5629 - m² = -3708

⇒ m² = 9337.

Now Cos N = m² + l² - n²/2ml

= (9337 + 4900 - 729) / (2 × √9337 × 70)

= 0.9985

Cos N = 0.9985

Putting [tex]Cos^{-1}[/tex] on both sides:

[tex]Cos^{-1}[/tex] Cos N = [tex]Cos^{-1}[/tex] 0.9985

⇒ N ≈ 3°

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The complete question is:

In ΔLMN, n = 27 inches, l = 70 inches and ∠M=149°. Find ∠N, to the nearest degree.

Answer:

2n + 14 = 30

Step-by-step explanation:

Since you know that 2n + 14 = 30, we can determine the values by first subtracting 14 from 30. Our equation would then be 2n = 16. Divide 2 from both sides and n = 8.

This model represents the total on the top and the 2 parts on the bottom.

Answer:

$6235 1

' 1 . ' 8

Answer:

Step-by-step explanation:

The tοtal price οf the game including tax is $29.96.

Physical assets such as prοperty and transactiοns such as the sale οf stοck οr a hοme are subject tο taxatiοn. Taxes include incοme, cοrpοrate, capital gains, prοperty, inheritance, and sales taxes.

Because the tax rate is 7%, the tax amοunt is 7% οf the purchase price. Tο calculate the tax, multiply the purchase price by the tax rate expressed as a decimal:

0.07 x $28 = $1.96 in taxes

As a result, the purchase tax is $1.96.

Tο calculate the tοtal price, add the purchase price and the tax:

Purchase price + Tax = Tοtal Price

Tοtal cοst: $28 + $1.96 = $29.96

As a result, the tοtal cοst οf the game, including tax, is $29.96.

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Answer:

I got 28

Step-by-step explanation:

use the formula k=y/x. 6/8=0.75

21/0.75=

The correct answer is B. Symmetric property.

The symmetric property states that if a = b, then b = a. In the context of geometry, this property can be used to show that if one side of a figure is congruent to another side, then the second side is also congruent to the first. In the case of the given proof, it is possible that the symmetry of the figure is used to show that opposite sides of the rhombus are congruent.

The reflective property (A) is not typically used to prove that a figure is a rhombus, as it relates to the reflection of a figure across a line. The transitive property (C) and the addition property (D) are also unlikely to be used in this context, as they relate to the properties of equality and addition, respectively, rather than geometric properties of figures.

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Answer:

Since only 66 states approve the amendment, it falls short of the required 7/9 majority. Therefore, the constitution will not be amended.

Step-by-step explanation:

To determine whether the constitution will be amended, we need to compare the number of states that have approved the amendment to the required number of states needed for approval.

The requirement is that 7/9 of the 84 states must approve the amendment. So, we need to calculate 7/9 of 84 to find out how many states need to approve the amendment:

(7/9) x 84 = 66.67

Rounding up, we see that 66.67 is equivalent to 67 states. This means that in order for the amendment to be approved, at least 67 states must approve it.

Since only 66 states approve the amendment, it falls short of the required 7/9 majority. Therefore, the constitution will not be amended.

Answer:

44 students

Step-by-step explanation:

1200 for the first year

a third of that is 400

400 for the second year

a third of that is 133.4

133.4 for the third year

a third of that is 44

Combining the like terms of the expressions (x² - 4x+9)-(3x² - 6x-9) gives -2x² + 2x + 36

Algebraic expressions are simply described as those mathematical expressions that are known to consist of certain variables, coefficients, terms, factors and constants.

Algebraic expressions are also identified with arithmetic operations. These arithmetic operations are;

From the information given, we have;

(x² - 4x+9)-(3x² - 6x-9)

First, expand the bracket

x² - 4x + 9 - 3x² + 6x + 27

Now, collect the like terms

x²- 3x² - 4x + 6x + 9 + 27

Add or subtract

-2x² + 2x + 36

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Answer:

The notation Σ-2 (3η + 5) is incorrect for representing the arithmetic series 8 + 11+ ... + 29.

The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:

Σ_{i=1}^{11} (6i + 2)

The series has 11 terms, and each term can be found by adding 3 to the previous term, starting with the first term 8. Therefore, the general form of the series is 6i + 2, where i represents the index of the term in the series.

In contrast, the notation Σ-2 (3η + 5) appears to have multiple errors. The use of a negative index (-2) is not valid, as the index should start from 1 or 0. Also, the use of the Greek letter eta (η) instead of i as the index variable is unconventional and likely to cause confusion. Finally, the expression inside the parentheses does not appear to correspond to the terms of the arithmetic series.

The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:

Σ_{i=1}^{11} (6i + 2)

To explain the error in the given notation Σ-2 (3η + 5), we can break it down as follows:

The use of a negative index (-2) is incorrect. The index of summation should always be a non-negative integer.

The use of the Greek letter eta (η) instead of i as the index variable is unconventional and may cause confusion or errors.

The expression inside the parentheses, 3η + 5, does not represent the terms of the arithmetic series. In particular, it does not involve the index variable i or the common difference 3.

Therefore, the correct notation for the given arithmetic series is Σ_{i=1}^{11} (6i + 2).

Answer:

-2cotxcscx

Step-by-step explanation:

Step 1: Find a common denominator

Step 2: Simplify

Answer:

Find the Exact Value tan(49). tan(49) tan ( 49 ). Step 1. The result can be shown in multiple forms. Exact Form: tan(49) tan ( 49 ). Decimal Form:

Step-by-step explanation:

The wrestler's weight before he went on his diet was 78.0 kilograms.

What is y-intercept?

In the context of a graph of a function, the y-intercept is the point where the graph intersects the y-axis. It is the value of the dependent variable (y) when the independent variable (x) is zero. Geometrically, the y-intercept is the value of the function at the point where it crosses the y-axis.

To determine the wrestler's weight before he went on his diet, we need to find the y-intercept of the linear function that represents his weight gain over time. This is because the y-intercept corresponds to the initial weight of the wrestler, i.e., his weight before he started his diet.

We can use the two data points where the time is 0 (i.e., at the start of the diet) to find the slope of the linear function:

(1.5, 85.8) and (3.0, 93.6)

The change in weight over the time interval of 1.5 to 3.0 months is:

93.6 - 85.8 = 7.8

The change in time over that interval is:

3.0 - 1.5 = 1.5

So the slope of the linear function is:

7.8 / 1.5 = 5.2

Now we can use the point-slope form of a linear function to write an equation for the wrestler's weight gain over time:

y - 85.8 = 5.2(x - 1.5)

where y represents the wrestler's weight and x represents the time in months.

To find the wrestler's weight before he went on his diet, we need to evaluate this equation at x = 0:

y - 85.8 = 5.2(0 - 1.5)

y - 85.8 = -7.8

y = 78.0

Therefore, the wrestler's weight before he went on his diet was 78.0 kilograms.

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The term “inverse” in mathematics generally refers to an operation that undoes or reverses another operation. However, the phrase "inverse of maths tools" doesn't really make sense because “maths tools” is not a specific mathematical operation.

Mathematical tools can refer to various instruments or techniques used in mathematics, such as calculators, rulers, compasses, graph paper, software, etc. Each of these tools has its own purpose and may or may not have an inverse operation or tool associated with it.

For example, the inverse of addition is subtraction, the inverse of multiplication is division, and the inverse of differentiation is integration. However, it's not clear what the inverse of a “maths tool” would be.

Therefore,  a) The inverse of “Add 25” would be “Subtract 25.”What is the  b) The inverse of “Divide -18” would be “Multiply -18.” c) The inverse of “Subtract 3” would be “Add 3.” d) The inverse of “Multiply 14” would be “Divide 14.”

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Answer:

the answer is supposably 75900000

Answer:

We are given the function S = m^2 + 6m + 8 which models the growth of book sales in m months, where S is an amount in thousands of dollars. We want to find in how many months book sales reach $80,000.

We can set up an equation as follows:

S = m^2 + 6m + 8 = 80

Subtracting 80 from both sides, we get:

m^2 + 6m - 72 = 0

We can factor this quadratic equation as:

(m + 12)(m - 6) = 0

This gives us two possible solutions:

m + 12 = 0 or m - 6 = 0

Solving for m in each case, we get:

m = -12 or m = 6

Since we are looking for a number of months, we can discard the negative solution.

Therefore, book sales reach $80,000 in 6 months.

So, the answer is: 6 months.

Answer:

To determine which statements are true, we can use the standard form of the equation of a circle:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center of the circle and r is the radius.

Using this form, we can rewrite the given equation as:

(x - 1)^2 + y^2 = 3^2 + 1^2 = 10

Comparing this to the standard form, we can see that the center of the circle is (1, 0), so the statement "The center of the circle lies on the x-axis" is true. However, the statement "The center of the circle lies on the y-axis" is false.

To find the radius, we can rearrange the equation as follows:

x^2 - 2x + y^2 = 8

Completing the square for x, we get:

(x - 1)^2 + y^2 = 9

This shows that the radius of the circle is 3, so the statement "The radius of the circle is 3 units" is true, as well as the statement "The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9."

Therefore, the three true statements are:

1.The radius of the circle is 3 units.

2.The center of the circle lies on the x-axis.

3.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Step-by-step explanation:

hope its help <:

The two statements that are both true are as follows: line

AC is perpendicular to line HB and line AC is parallel to FG. That is option A.

A perpendicular line is defined as the line that forms angle 90° where it meets with another line in a plane.

A line is said to be parallel to each other when they do not intercept as they are both on the same plane.

From the given diagram, line AC is perpendicular to line HB because they form angle 90° at the point of intersection.

Also, line AC is parallel to FG, because they can never intersect till infinity.

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(a) The 95% confidence interval for the difference in proportions of people who may find these medications effective is 0.029 to 0.231, which suggests that medication A is more effective than medication B in relieving joint pain.

(b) No, the interval does not contain zero, which means that the difference in proportions is statistically significant and supports the hypothesis that medication A is more effective than medication B.

Answer:

D. 50 square centimeters

Answer:

44.064x

Step-by-step explanation:

Answer: when you time 88.128 by 0.5, it gives you an answer of 44.064

Hope this helps :)

Answer:

-2

Step-by-step explanation: