I need help. I have no idea on this question

For

The balance in the continually compounded account after four years is roughly $ \(2,517.45.\)

To properly comprehend the precise interest rate being offered on any loan or investment, it is crucial to carefully analyse the terms and circumstances.

The formula for continuously compounded interest is:

\(A = P * e^(rt)\)

where A is the final amount, P is the principal, r is the annual interest rate, t is the time in years, and e is the mathematical constant approximately equal to 2.71828.

Substituting the given values, we have:

\(A = 2000 * e^(0.054 * 4)\)

Using a calculator, we get:

\(A ≈ $2,517.46\)

Rounding this to the nearest cent, we get:

\(A ≈ $2,517.45\)

Therefore, the balance after 4 years in the continuously compounded account is approximately $  \(2,517.45.\)

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Answer: If 1 and 2 are adjacent right angles, they are both 90º.

1 and 3 are vertical, which means they must be congruent, so 3 is also 90º

So: 90 + 90 - 90 = 90

Step-by-step explanation:

Answer:

...

Step-by-step explanation:

the central angle is the same as the arc

mDE= 104°

mFE= 76°

mDEF= 180°

mCFD= 180°

mDFE= 256°

Answer:

B. The product of 5 and a number.

Product means multiplication is taking place. In this case, 5 is being multiplied with n.

Hope this helps!

The polynomials completely factorized have the following expressions;

50). x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)

51). x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)

52). x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)

53). x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)

For the polynomial x³ - 3x² - 26x - 12 divisible by x - 6;

(x³ - 3x² - 26x - 12)/(x - 6) = x² + 3x + 2

x² + 3x + 2 = (x + 1)(x + 2)

so;

x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)

For the polynomial x³ - 12x² + 12x + 80 divisible by x - 10;

(x³ - 12x² + 12x + 80)/(x - 10) = x² - 2x - 8

x² - 2x - 8 = (x + 2)(x - 4)

so;

x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)

For the polynomial x³ - 18x² + 95x + 126 divisible by x - 9;

(x³ - 12x² + 12x + 80)/(x - 9) = x² - 9x + 14

x² - 9x + 14 = (x - 2)(x - 7)

so;

x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)

For the polynomial x³ - x² + 21x + 45 divisible by x + 5;

(x³ - x² + 21x + 45)/(x + 5) = x² - 6x + 9

x² - 6x + 9 = (x - 3)(x - 3)

so;

x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)

Therefore, by complete factorization the expressions (x - 6)(x + 1)(x + 2), (x - 10)(x + 2)(x - 4), (x - 9)(x - 2)(x - 7), and (x + 5)(x - 3)(x - 3) are the factors of their respective polynomial.

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Answer:

y = (1/2)x + (5/2)

Step-by-step explanation:

(7, 6), (-1, 2)

(x₁, y₁)  (x₂, y₂)

        y₂ - y₁          2 - 6          -4          1

m = ------------- = ------------ = ------- = -------

        x₂ - x₁           -1 - 7          -8         2

y - y₁ = m(x - x₁)

y - 2 = (1/2)(x - (-1)

y - 2 = (1/2)(x + 1)

y - 2 = (1/2)x + (1/2)

  +2                +2

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

y = (1/2)x + (5/2)

I hope this helps!

The required coefficients are:4, -1, -11, and 7.

Coefficients refer to the numerical values that are assigned to variables in mathematical equations, models, or formulas. They indicate the relative importance or contribution of each variable in the equation. Coefficients are used to determine the relationship between variables and are often estimated through statistical analysis or optimization techniques.

In algebraic equations, coefficients are the numbers multiplied by variables. For example, in the equation 2x + 3y = 5, the coefficients are 2 and 3.

In statistical models, such as linear regression, coefficients represent the slopes or weights assigned to the predictor variables. These coefficients indicate how much the response variable is expected to change for a unit change in the corresponding predictor variable, assuming all other variables are held constant.

We need to consider the polynomial:

(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)

To combine the like terms and find the coefficients of each term, we can write the polynomial in the following form:

4mn^2n - 2mn + 6 + 6mn^2 - 1 - mn^2 + 2 - 9mn

Taking the coefficients of the terms with "mn^2"4mn^2n - mn^2

Taking the coefficients of the terms with "mn"-2mn - 9mn = -11mn

Taking the coefficients of the constant terms6 + 2 - 1 = 7

Therefore, the required coefficients are:4, -1, -11, and 7.

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The 1995 processor when compared to the processor in today's phones is 12 .5 times larger .

To find how much larger the 1995 processor is , you first need to find the area of the processors.

Area of 1995 processor:

= 3. 8 x 2 . 9

= 11. 02 cm ²

Area of 2005 processor :

= 1. 1 x 0. 8

= 0. 88 cm ²

In comparison to the 2009 processor, the 1995 processor is :

= 11. 02 / 0.88

= 12 .5 times larger

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Answer:

The Area of the trapezium is \(60cm^2\)

Step-by-step explanation:

Given,

Height (h)= 8cm

Sum of the parallel sides (a+b)= 15cm

Area of trapezium = \(1/2*h*(a+b)\)

                              =\(1/2*8*15\)

                              =\(4*15\)

Area of trapezium=60cm^2

Answer: Area = 60 cm²

Step-by-step explanation:

To find the area of a trapezium we use the formula

Area of trapezium = 1/2 (sum of parallel sides) × height

∴ Area = 1/2 ×15 cm × 8 cm

           = 60 cm²

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Answer:

c < 10 = The bag contains fewer than 10 carrots.

c > 10 = Catherine biked farther than 10 miles.

c < 20 = The chair is shorter than 20 inches

c > 20 = Carlos scored over 20 points

Answer:

See below

Step-by-step explanation:

1. Reflection by a factor of (-3) and vertical shift down -12 units

2. Vertical shift up by 4 units and reflection by a factor of (-3)

By AAS congruency the two triangles are congruent

Step-by-step explanation:

Given - In selecting a sulfur concrete for roadway construction in regions that experience heavy frost, it is important that the chosen concrete has a low value of thermal conductivity in order to minimize subsequent damage due to changing temperatures. Suppose two types of concrete, a graded aggregate and a no-fines aggregate, are being considered for a certain road. The table below summarizes data on thermal conductivity from an experiment carried out to compare the two types of concrete.

Type            ni                xi                  si

Graded       42           0.486            0.187

No-fines      42           0.359           0.158

To find - a. Formulate the above in terms of a hypothesis testing problem.

b. Give the test statistic and its reference distribution (under the null hypothesis).

c. Report the p-value of the test statistic and use it to assess the evidence that this sample provides on the scientific question of difference in mean conductivity of the two materials at the 5% level of significance.

Proof -

a.)

Hypothesis testing problem :

H0 : There is significant difference between mean conductivity for the graded concrete and mean conductivity for the no fines concrete.

H1 : There is no significant difference between mean conductivity for the graded concrete and mean conductivity for the no fines concrete.

b)

Test statistic :

\(Z = \frac{x_{1} - x_{2} }{\sqrt{\frac{s_{1} ^{2} }{n_{1}} + \frac{s_{2}^{2} }{n_{2}} } }\)

\(Z = \frac{0.486 - 0.359 }{\sqrt{\frac{0.03496 }{42} + \frac{0.02496 }{42} } }\)

\(Z = \frac{0.127 }{\sqrt{0.001468}}\)

\(Z = \frac{0.127 }{0.0377}\)

⇒Z(cal) = 3.3687

Z(tab) = 1.96

As Z (cal) > Z(tab)

So, we reject H0 at 5% Level of significance

p-value = 0.99962

Hence

There is significant difference in mean conductivity at the two materials.

Answer:

Step-by-step explanation:

148 people

Answer:

y=1/3x-4

Step-by-step explanation:

the slope-intercept format of the line is y=mx+b, where m is the slope and b is the y intercept.

we are given the slope (1/3) and the y intercpet (-4).

substitute the numbers into the equation

y=1/3x-4

the answer is y=1/3x-4

hope this helps!

Let’s solve the equation x^2 - 4x = 5 by factoring:

First, we’ll move all the terms to one side of the equation:

x^2 - 4x - 5 = 0

Now, we’ll factor the left side of the equation. We’re looking for two numbers that multiply to -5 and add to -4. Those numbers are -5 and 1. So we can write:

(x - 5) (x + 1) = 0

Now we’ll use the zero-product property to solve for x. This property states that if the product of two numbers is zero, then at least one of the numbers must be zero. So we have:

x - 5 = 0 or x + 1 = 0

Solving each equation separately, we find that x = 5 or x = -1.

So, the solutions to the equation x^2 - 4x = 5 are x = 5 and x = -1.

answer is 9

Step-by-step explanation:

12/4=3

1/4=3

3/4=9

Answer:

58 members of the House of Representatives, and 28 members of the senate.

Step-by-step explanation:

We can find the answer to this by simply subtracting:

86 - 58 = 28

So, there are 58 members of the House of Representatives, and 28 members of the senate.

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Given:

The first term

The common difference, d=6

To find

Using the nth term formula,

Hence, the answer is,

The next three values of  the trigonometry of cos 2a are √3/2, -1/2 + √3/2, and √3/2.

We can use the identity sin 3a = 3 sin a - 4 sin³ a and rewrite sin 3a = 2 sin a as follows:

2 sin a = 3 sin a - 4 sin³ a

4 sin³ a - sin a = 0

sin a (4 sin² a - 1) = 0

So, sin a = 0 or sin a = ±1/2√2.

If sin a = 0, then a = nπ, where n is an integer. In this case, cos 2a = cos 2nπ = 1.

If sin a = 1/2√2, then a = π/12 + 2nπ or a = 5π/12 + 2nπ, where n is an integer. Similarly, if sin a = -1/2√2, then a = -π/12 + 2nπ or a = -5π/12 + 2nπ, where n is an integer. In all of these cases, we can use the double angle formula for cosine:

cos 2a = 2 cos² a - 1

If sin a = 1/2√2, then:

cos 2a = 2 cos² (π/12) - 1 = 2 (2 + √3)/4 - 1 = √3/

cos 2a = 2 cos² (5π/12) - 1 = 2 (2 - √3)/4 - 1 = -1/2 + √3/2

If sin a = -1/2√2, then:

cos 2a = 2 cos² (-π/12) - 1 = 2 (2 - √3)/4 - 1 = -1/2 + √3/2

cos 2a = 2 cos² (-5π/12) - 1 = 2 (2 + √3)/4 - 1 = √3/2

Therefore, the next three values of cos 2a are √3/2, -1/2 + √3/2, and √3/2.

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He doesn't need a truck. He can buy an aeroplane.

Answer:

Jorgen would still have enough money for the truck.

Step-by-step explanation:

Seeing as - (or negative) 0000000000000... isn't a real number and you put a comma after the 123456789, Jorgen would actually have enough for the truck. If you actually wanted the truck to be worth 123456789000000000... Jorgen would need to save up more than 9 octovigintillion to reach his goal of getting the truck, and that is one expensive truck.

The graph of the function with asymptotes at x = -2, and x = 3, and x-intercept of (3, 0), indicates that the possible equation graphed is of the form;

\(f(x) = \frac{-6\cdot (x -2)}{(x + 2)\cdot (x -3)}\)

An asymptote is the line which the graph of the function approaches when the input value of the function approaches infinity or minus infinity.

The asymptotes of the graph of the function are; x = -2, and x = 3

The possible denominators of the function are therefore; (x + 2) and (x - 3)

The value of the function when x = 0 is -2, therefore;

Numerator ÷ ((0 + 2)×(0 - 3)) = -2

When x = 0, the numerator = ((0 + 2)×(0 - 3)) × -2 = 12

The expressions in the denominator of the function, (x + 2), and (x - 3), and the shape of the graph with a x-intercept of 2, indicates that we get;

The possible numerator is; 6·(x - 2)

The equation for the function graphed is; f(x) = (6·(x - 2))/((x + 2)·(x - 3))

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According to the information, the vertex at the top left of the parallelogram is (4, 8.25). Thus, the other two vertices of the parallelogram are (2, 5), (9, 5), (7, 8), and (4, 8.25).

To find the vertex of the parallelogram we can use the point-slope form of a line: y - y1 = m(x - x1), where,

For the side sloping up from left to right, we can use the point (2, 5), since it is on the bottom side of the parallelogram. Plugging in the values, we get:

Simplifying, we get:

To find the point where this line intersects the top side of the parallelogram, we can use the fact that the length of the sloping side is 5 units. We know that the endpoint of the bottom side at (2, 5) is 5 units away from the intersection point in the x-direction, so we can add 5 to the x-coordinate to find the intersection point. Plugging in x = 7 into the equation above, we get:

Therefore, the vertex at the top right of the parallelogram is (7, 8).

For the side sloping down from left to right, we can use the point (9, 5), since it is on the bottom side of the parallelogram. Plugging in the values, we get:

Simplifying, we get:

To find the point where this line intersects the top side of the parallelogram, we can again use the fact that the length of the sloping side is 5 units. We know that the endpoint of the bottom side at (9, 5) is 5 units away from the intersection point in the x-direction, so we can subtract 5 from the x-coordinate to find the intersection point. Plugging in x = 4 into the equation above, we get:

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