You invested $28,000 in two accounts paying 3% and 6% annual interest, respectively. If the total interest earned for
the year was $1590, how much was invested at each rate?
The amount invested at 3% is $
The mount invested at 6% is $

Answer:

true

Step-by-step explanation:

the answer of both the smaller squares added is the same as the andwer of the bigger square

The first mistake on the finding on the continuity of the function happened on Step 3, hence option B is correct.

A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is, if these three conditions are respected:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

To verify the continuity on this problem, the limit was first found at x = 4. Following the standard procedure, replacing each instance of x by 4, an undetermined value of 0/0 is reached. Thus the correct procedure was undertaken, factoring each polynomial in the numerator and in the denominator, then simplifying the common terms and calculating the limit.

However, to calculate the numeric value of the function at x = 4, the simplification cannot be applied, each instance of 4 needs to be replaced.

Replacing each instance of x by 4, the denominator will be of 0, meaning that the function is not defined at x = 4, hence the first mistake was in Step 3 and option B is correct.

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Given:

The formula is

Required:

Make h the subject of the formula.

Explanation:

We will put formula in terms of h as:

Answer:

Hence, above is the answer.

Minimum number of gallons pumped after 30 days = 24,192,000 gallons

The minimum amount of water pumped in 1 minute = 1120 gallons

The minimum number of hours used for pumping per day = 12 hours

Number of minutes in 1 hour = 60 minutes

Number of minutes in 12 hours = 12 x 60 = 720 minutes

The minimum amount of water pumped per day = 1120 x 720

The minimum amount of water pumped per day = 806400 gallons

Let the number of days used for pumping be x

Let the total number of gallons pumped x days after pumping begins = y

Since 806400 gallons is pumped per day:

y = 806400x

Minimum number of gallons pumped after 30 days, that is, x = 30

y = 806400 (30)

y = 24,192,000 gallons

Minimum number of gallons pumped after 30 days = 24,192,000 gallons

The number of stocks that went up yesterday given the stocks that went down yesterday is 618.

Ratio is used compare two or values together. It shows the number of times that one value is contained in another value or values. According to the information provided in the question,  the ratio of stocks that go up and the stock that goes down is 6 : 7.

The number of stocks that went up yesterday = (ratio of stocks that went up x number of stocks that went down yesterday) / ratio of stocks that went down yesterday

The number of stocks that went up yesterday =(6 x 721) / 7 = 618

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Answer:

15th customer

Step-by-step explanation:

to find the answer to this, you have to find the least common multiple(I think that’s what it is called). In this case, in order to find it, you can just multiply 5*3 to get 15 for the answer

The area of the shaded portion of the diagram is 9.12 mm²

The triangle is inside the semi circle.

The shaded region of the semi circle is outside the triangle.

Therefore,

area of the shaded region = area of the semi circle - area of triangle

Therefore,

area of the semi circle = 1 / 2 πr²

where

Hence,

r = 4 mm

area of the semi circle = 1 / 2 × 3.14 × 4²

area of the semi circle = 50.24 / 2

area of the semi circle = 25.12 mm²

area of the triangle = 1 / 2 bh

where

Hence,

b = 8mm

h = 4mm

area of the triangle = 1 / 2 × 8 × 4

area of the triangle = 32 / 2

area of the triangle = 16 mm²

Therefore,

area of the shaded region = 25.12 - 16

area of the shaded region = 9.12 mm²

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Answer:800

Step-by-step explanation:

x + 4x = 1000

   5x     = 1000

    x     = 1000/5 = 200 dollars.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Which postulate establishes the congruence of triangles SSS AAS SAS ASA?

According to the Angle-Side-Angle Postulate (ASA), two triangles are congruent if two angles and the included side of one triangle are congruent with two angles and the included side of another triangle.

Congruence exists between one comparable pair of sides.

Detailed explanation:

If two triangles have three matching angles that are congruent,

The following postulates will be required to demonstrate the congruence of the triangles:

1) AAS ( Angle-Angle-Side ) ( Angle-Angle-Side )

2) ASA ( Angle - Side - Angle) ( Angle - Side - Angle)

Since we require at least one pair of congruent sides in both postulates.

Given that two triangles have three congruent corresponding angles, the extra information that will be utilized to prove their congruence is that "they have one pair of congruent corresponding angles."

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Answer: 270

Step-by-step explanation: A tip for multiplying a number with any power of 10 is to just "add" a 0 to the end of the number depending on how many 0's there are in the power of 10.

For example, there is one 0 in 10. So I would just add a 0 to the end of 27 to get 270. If I were to multiply 27 by 100, there are two 0's in 100 so it would be 2700. 27 x 1000 would be 27000.

Hope this helped

Answer:

can i see a ss of the question?

Step-by-step explanation:

Answer:

168

Step-by-step explanation:

Hello I need to find the answer on how to find (-8)(-7)(3):

This is asking to find: -8 × -7 × 3 = ?

Because a negative times a negative = positive we have:

56 × 3 = 168

Answer:

Step-by-step explanation:

A) 5x+3x

5x+3x

= 8x

B) 9s-3s+4s

9s-3s+4s

6s+4s

=10s

From the given quadratic equation, we have that:

A quadratic equation is modeled by the following rule:

y = ax^2 + bx + c

The vertex has these following coordinates.

[tex](x_v, y_v)[/tex]

In which:

Considering the coefficient a, we have that the vertex can represent either a maximum or a minimum point, as follows::

For this problem, the function is:

h(t) = -16t² + 160t + 200.

Then the coefficients are:

a = -16, b = 160, c = 200.

And the maximum height, in feet, will be of:

[tex]y_v = -\frac{160^2 - 4(-16)(200)}{4(-16)} = 600[/tex]

The ball hits the ground for the positive root when h(t) = 0, hence after 8.9 seconds.

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Answer:

14.2 feet

Step-by-step explanation:

Use the Pythagorean Theorem to solve both parts.

Part 1.

35 is the hypotenuse and 21 is a leg.

[tex]a^{2} +b^{2} =c^{2} \\a^{2} +21^{2} =35^2\\a^2 + 441 = 1225\\a^2 +441-441=1225-441\\a^2 =784\\\sqrt{a^2} =\sqrt{784} \\a = 28 feet[/tex]

28 feet represents how far the base of the ladder is from the house.

Part 2.

Now move the ladder 4 feet farther from the house. 28 + 4 = 32 ft.

Now you have a leg that is 32 feet and the hypotenuse is still 35 feet. Solve for the other leg.

[tex]a^{2} +b^{2} =c^{2} \\a^{2} +32^{2} =35^2\\a^2 + 1024 = 1225\\a^2 +1024-1024=1225-1024\\a^2 =201\\\sqrt{a^2} =\sqrt{201} \\a = 14.177 feet[/tex]

Round to the nearest tenth and you have 14.2 feet

Answer:

A

Step-by-step explanation:

[tex]\sqrt{3x+3}=x+1 \\ \\ 3x+3=x^2+2x+1 \\ \\ x^2-x-2=0 \\ \\ (x-2)(x+1)=0 \\ \\ x=-1, 2[/tex]

Upon substituting both of the values back into the original equation, we see they both work.

[tex]11.9375\%[/tex] is the cost of equity using the capital asset pricing model if the risk free rate is 4.5%, the beta is 1.75 and the equity risk premium is 4.25%.

In the given question we have to find the cost of equity using the capital asset pricing model if the risk free rate is 4.5%, the beta is 1.75 and the equity risk premium is 4.25%.

Firstly we learn about terms used in this question,

The return needed by either a business or an individual to justify an investment in equity is known as the cost of equity.

The relationship between systemic risk, or the general dangers of investing, and expected return for assets, particularly equities, is described by the Capital Asset Pricing Model.

Since we have to find the cost of equity using the capital asset pricing model. So the formula is

Cost of equity = Risk free rate + Beta * Equity Risk Premium

Risk free rate = 4.5%

Beta = 1.75

Equity Risk Premium = 4.25%

Now putting the value in the formula

Cost of equity [tex]=4.5\%+1.75\times4.25\%[/tex]

Simplifying

Cost of equity [tex]=4.5\%+7.4375\%[/tex]

Cost of equity [tex]=11.9375\%[/tex]

Hence, [tex]11.9375\%[/tex] is the cost of equity using the capital asset pricing model if the risk free rate is 4.5%, the beta is 1.75 and the equity risk premium is 4.25%.

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The multiplication of  [tex](9n- \frac{4}{7} z)^{2}[/tex]   [tex]=81n^{2} -\frac{72}{7} nz +\frac{16}{49} z^{2}[/tex]

How is the expression  [tex](9n- \frac{4}{7} z)^{2}[/tex]  solved?

[tex](9n- \frac{4}{7} z)^{2} \\\\=(9n- \frac{4}{7} z) (9n- \frac{4}{7} z)\\\\=81n^{2} -\frac{36}{7} nz -\frac{36}{7} nz +\frac{16}{49} z^{2} \\\\=81n^{2} -\frac{72}{7} nz +\frac{16}{49} z^{2}[/tex]

What is the binomial squares pattern?

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The equation that represents the total points on the test, including the 2-point and 4-point problems is 2x + 4y = 100

From the information, the test in math class has problems with 2 points (x) and problems worth 4 points (y) and the test has 100 points. The equation to illustrate this will be:

2x + 4y = 100

When one answers 30 2-point questions and 8 4-point questions correctly, the score will be:

= 2x + 4y

= 2(30) + 4(8)

= 60 + 32

= 92

The score is 92 points.

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Before change

Dimensions: r= 2 ; h=7

Lateral Surface area=  2πrh= 28π sqyd

Total Surface area= 2πr(h+r)=4π(9)= 36π sqyd

After change(trippling radius)

Dimensions: r= 6 (3*2); h=7

Lateral Surface area=  2πrh= 84π sqyd

Total Surface area= 2πr(h+r)=12π(13)= 156π sqyd

What is surface area of a cylinder?

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Answer:

Crow=

50×2

100 leg.

cat=

49×4

196 leg.

Answer:

1. 12 days

2. more than 200 miles

3. 11 lawns

4. at least 9 hours (about 9.92 hours)

Step-by-step explanation:

1. 20x < 254, so x < 12.7. We need an integer here, so x = 12 days.

2.

[tex]70 + .15x < 50 + .25x[/tex]

[tex]20 < .10x[/tex]

[tex]200 < x[/tex]

[tex]x > 200[/tex]

3. 65x > 699, so x > 10.8. Since fractions of lawns are not accepted here, Mark must mow at least 11 lawns.

4. Assuming that the speed stays constant, 65x = 645, so x = 9.92 hours. The trip will take at least 9 hours, actually close to 10 hours.

First, let's see the points on the coordinate plane:

Now, let's remember that a function has every element of it's domain related with only one element from it's image.

Therefore, x = 2 would create a set of ordered pairs that is not a function. Let's see it in the plane:

As we can see, x = 2 has two values on the image: f(2) = 6 and f(2) = 7, and this never can happen in a function.

The equation that represents the possible tables that may be used to seat 200 people at the wedding is 8x + 10y = 200.

The combination will be 10 round tables and 12 rectangular tables; 15 round tables and 8 rectangular tables.

Based on the information, there can be round tables that sit 8 people and rectangular tables that sit 10 people and the total number will be 200.

Therefore, the equation that represents the possible tables is 8x + 10y = 200

where x = number of round table

y = number of rectangular tables

The possible combinations of table types that your sister can use at her wedding reception will be 10 round tables and 12 rectangular tables. This will be:

8x + 10y = 8(10) + 10(12) = 200

Another combination will be 15 round tables and 8 rectangular tables

8x + 10y = 8(15) + 10(8) = 200

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1. Solution of the rational equation [tex]\frac{x}{3} -6=\frac{9}{3}[/tex]   is x = 27

How is the equation solved?

[tex]\frac{x}{3} -6=\frac{9}{3}\\\\\frac{x- 18}{3} =\frac{9}{3}\\\\x= 18+9\\\\x= 27[/tex]

2.The two numbers = 2, 6

How to find the two numbers?

Let the two whole numbers = x, y

Given:

x+ y =8 --- (1)

1/x+1/y = 2/3 ---(2)

Considering (2),

[tex]\frac{1}{x} +\frac{1}{y} =\frac{2}{3}\\\\\frac{x+ y}{x y} =\frac{2}{3}\\\\\text{Applying } (1),\\\\\frac{8}{x(8-x)} =\frac{2}{3}\\\\(8x-x^{2} )2 =24\\\\(8x-x^{2} ) =12\\\\x^{2} -8x+12 =0\\\\(x-6) (x-2)= 0\\\\x= 2, 6[/tex]

Substituting  x in (1)

We have,

When x = 2 ; y= 6

When x = 6 ; y = 2

So, the two numbers = 2, 6

3. The two numbers = 3, 9

How to find the two numbers?

Let the two whole numbers = x, y

Given:

x- y =6 --- (1)

1/y -1/x = 2/9 ---(2)

Considering (2),

[tex]\frac{x-y}{xy} =\frac{2}{9} \\\\\text{Applying } (1)\\\\\frac{6}{x y} =\frac{2}{9} \\\\x y = 27\\\\(6+y)y = 27\\\\y^{2} +6y-27=0\\\\(y+9) (y-3) = 0\\\\y= 3, -9[/tex]

Since x and y are whole numbers we will have y = 3

When y = 3 ; x=9 (substituting in (1))

So, the two numbers = 9,3

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Answer:

simply divide 12.50 by 5. Therefore each bracelet costs $2.05 : 2$ and 5 cents.

Step-by-step explanation:

The cost of each bracelet will be $2.5.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The cost of 5 bracelets = $12.50

Now,

Since, The cost of 5 bracelets = $12.50

So, The cost of 1 bracelets = $12.50 ÷ 5

                                         = $2.5

Thus, The cost of each bracelet will be $2.5.

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A polynomial of degree 4 in factored form with zeros 1, -4, 0, and 6 is

f(x) = x(x - 1)(x + 4)(x - 6).

Given:

x₁ = 1

x₂ = -4

x₃ = 0

x₄ = 6

Utilize the fact that x - b is a factor of the polynomial if b is a root.

Simply take each zero, modify its sign, and add an x in front of it to obtain the four factors.

The polynomial is,

f(x) = (x - x₁)(x - x₂)(x - x₃)(x - x₄)

f(x) =  (x - 1)(x - (-4))(x - 0)(x - 6)

     = (x - 1)(x + 4(x)(x - 6)

Therefore,a 4 degree polynomial in factored form with zeros 1, -4, 0,and 6 is x(x - 1)(x + 4)(x - 6).

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a) The total central angle of a circle is 360 degrees.

Therefore, the angle of the shaded area is,

Therefore, the angle of the shaded area is 240 degrees.

b) The percent of the circle shaded is,

Therefore, the percent of the circle shaded is 66.67%.

c) The fraction of the circle shaded is,

Therefore, the fraction of the circle shaded is 2/3.