An amount of $3000 is deposited for one year at an interest rate of 5.5% per annum. How much interest will be earned?

The standard form of 8 hundred + 2 hundred will be 1000.

A number can be expressed in a fashion that adheres to specific standards by using its standard form. Standard form refers to any number that may be expressed as a decimal number between 1.0 and 10.0 when multiplied by a power of 10.

Given that the number is 8 hundred + 2 hundred the standard form of the number will be:-

Standard form = 8 hundreds + 2 hundreds

Standard form = 800 + 200

Standard form = 1000

Therefore, the standard form of 8 hundred + 2 hundred will be 1000.

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The value of given function f(7) is -1.8.

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.

According to the given problem,

f(x) = [tex]\frac{3}{x + 5}- \sqrt{x - 3}[/tex]

At x = 7,

⇒ f(7) = [tex]\frac{3}{7 + 5} - \sqrt{7-3}[/tex]

⇒ f(7) = [tex]\frac{1}{4} - 2[/tex]

⇒ f(7) = [tex]-\frac{7}{4}[/tex]

⇒ f(7) = - 1.75

          ≈ -1.8

Hence, we can conclude, the value of function f(7) is -1.8.

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From the computation, a half of two dozen shirts will be greater.

A dozen = 12

It should be noted that a half dozen pair of shirts will be:

= 1/2 × 12

= 6 shirts

A half of two dozen shirts will be:

= 1/2 × (2 × 12)

= 12 shirts

Therefore, a half of two dozen shirts will be greater.

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Jane will walk 733.34 yards around the edge of the rectangular park after converting the width from feet to yards and calculating the perimeter.

Jane is going to walk once around the edge of a rectangular park. The park is 300 yards long and 200 feet wide. To determine how far Jane will walk, we need to calculate the perimeter of the rectangle. First, let's convert all measurements to the same unit. Since the length is given in yards and the width in feet, we can convert the width to yards (1 yard = 3 feet).

Width in yards: 200 feet \/ 3 feet per yard = 66.67 yards.

Now that both measurements are in yards, we can calculate the perimeter:

Perimeter = 2 ×(length + width) = 2 × (300 yards + 66.67 yards) = 2 ×366.67 yards = 733.34 yards.

Therefore, Jane will walk 733.34 yards around the edge of the park.

The series is convergent, but the number of terms needed to find the sum to a specific accuracy cannot be determined.

To determine the convergence of the series sum_(n=1)^(infinity) (-1)^(n+1)/( n^7), we can use the Alternating Series Test. The Alternating Series Test states that if the terms of a series alternate in sign and decrease in absolute value, then the series is convergent. In this case, the terms of the series alternate in sign and decrease as n increases, so the series is convergent.

To find the number of terms needed to achieve a sum with an error less than 0.00005, we need to use the Remainder Estimation Theorem. However, this theorem requires that the terms of the series decrease in absolute value, which is not the case in this series. Therefore, we cannot determine the number of terms needed to reach the desired accuracy.

Overall, the series is convergent, but we cannot determine the number of terms needed to reach a specific accuracy.

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After factored out a common factor in each term. Factor the simplified trinomial. Option c) is correct.

Step after the the third step when factoring the trinomial ax^2+bx+c to be determine.

Factors is are the sub multiples of the value.

Here,
After factored out a common factor in each term. The next step come is to factor the simplified term which implies taking common and kept in parenthesis.

Thus, after factored out a common factor in each term. Factor the simplified trinomial.

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p=2w+2(6w-4) can be simplified to:

p=2w+12w-8

p=14w-8

if w=4

p=14(4)-8

p=56-8 = 48 yards

check:

 w = 4

length = 6w-4= 6(4)-4 = 24-4=20

perimeter = 4*2 + 20*2 = 8+40 = 48

 it checks out, perimeter = 48 yards

The question is about calculating the new price of an item after a discount. The original price of the item was $51.00, and it was reduced by 15%, making the new price $43.35.

The subject of this question is Mathematics and it is looking for a solution to a percentage price reduction problem. The item had an original price of $51.00 and its price has been reduced by 15%. To find the new price after the discount, we have to calculate the amount of the reduction and subtract it from the original price.

First, let's calculate the amount of the discount: 15/100 * 51 = $7.65.}

Now, we subtract this amount from the original price: 51 - 7.65 = $43.35.

Therefore, the new price of the item after a 15% discount is $43.35.

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area = PI x r^2

 r = 20/2 = 10

3.14 x 10^2 = 314 square units

The method that can be used to find the volume of the house is:

 Add the volume of a rectangular prism to the volume of the triangular prism.

In order to find the volume of the house we need to find the volume of the bottom part of the house which in the shape of a rectangular prism or cuboid  and volume of the top of the house which is in the shape of a triangular prism.

        Hence, the total volume of the house is:

  Volume of rectangular prism+Volume of triangular prism.

we have

[tex](x + 2)^{2}-9=-5[/tex]

Adds [tex]9[/tex] both sides

[tex](x + 2)^{2}-9+9=-5+9[/tex]

[tex](x + 2)^{2}=4[/tex]

square root both sides

[tex](x+2)=(+/-)\sqrt{4}\\(x+2)=(+/-)2\\x1=2-2=0 \\x2=-2-2=-4[/tex]

therefore

the answer is

the resulting equation is [tex](x+2)=(+/-)2[/tex]

Answer:  [tex](x+2) = \pm 2[/tex]

Step-by-step explanation:

If the given expression is,

[tex](x + 2)^2 - 9 = -5[/tex]

For solving this expression, By adding 9 on both sides,

[tex](x+2)^2 = 4 [/tex]

By taking square root on both sides,

[tex]\sqrt{(x+2)^2} = \sqrt{4}[/tex]

[tex]({(x+2)^2)^{\frac{1}{2} = \pm 2[/tex]                    [tex]( \text{ Because, }\sqrt{4} = \pm 2 \text { and }\sqrt{x} = x^{\frac{1}{2}})[/tex]

[tex]{(x+2)^{2\times \frac{1}{2} = \pm2[/tex]              [tex]((a^m)^n=a^{m\times n})[/tex]

[tex](x + 2) = \pm2[/tex]

Which is the required next step.

To find and classify critical points of a two-variable function, calculate and set the first partial derivatives to zero to find critical points. Then, use the second derivatives to classify these points. The determinant of the Hessian matrix, made up of the second derivatives, contributes to this classification.

To find the critical points of the function F(x,y)=e^8x - x^2 + 8y - y^2, you first need to find the partial derivatives F_x and F_y and set them both equal to zero.

F_x = 8e^8x - 2x and F_y = 8 - 2y. By setting these equal to zero and solving for x and y, you will find the critical points.

Once the critical points are found, we classify them using the second derivative test. This involves computing the second partial derivatives F_xx, F_yy, and F_xy, and evaluating them at the critical points.

Finally, we calculate the determinant D of the Hessian matrix, composed of the second derivatives, at the critical points. The signs and values of these results and the determinants help classifying the critical points.

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The parabola and the circle have the same axis of symmetry, and can intersect at one point only.

The statement that must be true is; The maximum number of solution is one

Reason:

The given parameters are;

Location of the center of the circle = The origin (0, 0)

Location of the vertex of the parabola opening upwards = (0, 9)

Point where the circle intersects the parabola = The vertex

Required:

The statement that must be true

Solution;

The equation of the circle is x² + y² = r²

The vertex (0, 9) is a point on the circle, therefore;

0² + 9² = r²

The radius, r = 9

The highest point on the circle is the point with the maximum vertical

distance from the center, which is the point (0, 9), which is also the lowest

point on the parabola.

Therefore, the parabola and the circle can intersect at only the point (0, 9),

which gives;

The maximum number of solution is one.

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The rate of change of the base of a triangle, given an increase of the altitude at 1 cm/min and an increase in area at 2 cm2/min, when the altitude is 10 cm and the area is 100 cm2, is 4 cm/min.

The subject of this question is related to the field of calculus, specifically dealing with determining the rate of change, or the derivative, of a function. We're asked to determine the rate at which the base of the triangle is changing when the altitude is 10 cm and the area is 100 cm2, given that the altitude of the triangle is increasing at a rate of 1 cm/ min and the area of the triangle is increasing at a rate of 2 cm2 / min.

We know that the area of a triangle is given by the formula 1/2 * base * height. When it comes to rates, we can differentiate this with respect to time t to get dA/dt = 1/2 * (base * dh/dt + height * db/dt) where dA/dt is the rate of change of the area, dh/dt is the rate of change of the height, and db/dt is the rate of change of the base.

Given that dA/dt = 2 cm2/min and dh/dt = 1 cm/min, and we are finding db/dt when the height is 10 cm and the area is 100 cm2, we substitute these values to solve for db/dt. This simplifies to find that the base is increasing at a rate of 4 cm/min.

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Answer:

Thus, the expected value of points for Derek and Mia are [tex]\dfrac{-1}{9}[/tex] and [tex]\dfrac{1}{9}[/tex] respectively.

Step-by-step explanation:

Number of green marbles = 2 and Number of Yellow marbles = 1

Then, total number of marbles = 2+1 = 3

A person selects two marbles one after another after replacing them.

So, the probabilities of selecting different combinations of colors are,

[tex]1.\ P(GG)=P(G)\times P(G)\\\\P(GG)=\dfrac{2}{3}\times \dfrac{2}{3}\\\\P(GG)=\dfrac{4}{9}[/tex]

[tex]2.\ P(GY)=P(G)\times P(Y)\\\\P(GY)=\dfrac{2}{3}\times \dfrac{1}{3}\\\\P(GY)=\dfrac{2}{9}[/tex]

[tex]3.\ P(YG)=P(Y)\times P(G)\\\\P(YG)=\dfrac{1}{3}\times \dfrac{2}{3}\\\\P(YG)=\dfrac{2}{9}[/tex]

[tex]4.\ P(YY)=P(Y)\times P(Y)\\\\P(YY)=\dfrac{1}{3}\times \dfrac{1}{3}\\\\P(YY)=\dfrac{1}{9}[/tex]

Now, we have that,

If two marbles are of same color, then Mia gains 1 point and Derek loses 1 point.

If two marbles are of different color, then Derek gains 1 point and Mia loses 1 point.

Then, the expected value of points for Derek is,

[tex]E(D)= (-1)\times \dfrac{4}{9}+1\times \dfrac{2}{9}+1\times \dfrac{2}{9}+(-1)\times \dfrac{1}{9}\\\\E(D)= \dfrac{-5}{9}+\dfrac{4}{9}\\\\E(D)=\dfrac{-1}{9}[/tex]

And the expected value of points for Mia is,

[tex]E(M)= 1\times \dfrac{4}{9}+(-1)\times \dfrac{2}{9}+(-1)\times \dfrac{2}{9}+1\times \dfrac{1}{9}\\\\E(M)= \dfrac{5}{9}-\dfrac{4}{9}\\\\E(M)=\dfrac{1}{9}[/tex].

Thus, the expected value of points for Derek and Mia are [tex]\dfrac{-1}{9}[/tex] and [tex]\dfrac{1}{9}[/tex] respectively.

Answer: P(GG)= 4/9

P(GY)= 2/9

P(YG)= 2/9

P(YY)= 1/9

Derek, E(X) = -1/9

Mia, E(X) = 1/9

Step-by-step explanation: just did it on edge

5x=17

x=17/5 = 3.4

15x-11 =

15(3.4)-11 = 51-11 = 40