What is the value of c?
a)4 units
b)5 units
c)6 units
d)7 units

The APR of the credit card that has a monthly rate of 3.5% is 42%. The correct option is therefore;

B. 42%

The APR (Annual Percentage Rate) can be calculated from the monthly interest rate using the formula;

Monthly interest rate = APR/12

Therefore; APR = 12 × The monthly interest rate

The monthly interest rate charged by the credit card = 3.5%

The number of months in a year = 12

Annual percentage rate = The monthly interest rate × Number of months

Therefore, the annual percentage rate of the credit card = 3.5% × 12 = 42%

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The product of (2x + 3) and [tex](4x^2 - 5x + 6) = 8x^3 + 2x^2 - 3x + 18.[/tex]

To find the product of (2x + 3) and (4x^2 - 5x + 6), we need to use the distributive property. We multiply each term in the first binomial by each term in the second binomial and then combine like terms.

Let's go through the steps:

1. Distribute the second binomial to each term in the first binomial:

  (2x + 3)(4x^2 - 5x + 6) = 2x(4x^2 - 5x + 6) + 3(4x^2 - 5x + 6)

2. Multiply each term in the first binomial by each term in the second binomial:

  = [tex](2x * 4x^2) + (2x * -5x) + (2x * 6) + (3 * 4x^2) + (3 * -5x) + (3 * 6)[/tex]

3. Simplify each term:

  = 8x^3 - 10x^2 + 12x + 12x^2 - 15x + 18

4. Combine like terms:

  =[tex]8x^3 + (12x^2 - 10x^2) + (12x - 15x) + 18[/tex]

  = 8x^3 + 2x^2 - 3x + 18

Therefore, the product of (2x + 3) and (4x^2 - 5x + 6) is 8x^3 + 2x^2 - 3x + 18.

In general, to find the product of two binomials, you need to distribute each term from the first binomial to each term in the second binomial and then combine like terms. It's important to pay attention to the signs and simplify the resulting expression.

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The measure of the indicated internal angle in the circle is 113 degrees.

The inscribed angle theorem states that an angle x inscribed in a circle is half of the central angle 2x that subtends the same arc on the circle.

It is expressed as:

Internal angle = 1/2 × ( x + y )

From the image:

Intercepted arc TU = x = 125 degrees

Intercepted arc SP = y = 101 degrees

Internal angle = ?

Plug the given values into the above formula and solve for the internal angle:

Internal angle = 1/2 × ( x + y )

Internal angle = 1/2 × ( 125 + 101 )

Internal angle = 1/2 × 226

Internal angle = 113°

Therefore, the internal angle is 113 degrees.

Option B) 113° is the correct answer.

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The equivalent expression to [tex]3\sqrt{6}[/tex] is given as follows:

[tex]\sqrt{54}[/tex]

Two expressions are defined as equivalent expressions when they have the same result.

The expression for this problem is given as follows:

[tex]3\sqrt{6}[/tex]

For the equivalent expression, we can move the outer term 3 inside the root, with it being squared, as follows:

[tex]3\sqrt{6} = \sqrt{3^2 \times 9} = \sqrt{54}[/tex]

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To solve for x, we need to isolate x on one side of the equation. We can do this by adding 9 to both sides of the equation:

3x - 1 + 9 = 2x - 9 + 9

3x + 8 = 2x

Now we can subtract 2x from both sides of the equation:

3x - 2x + 8 = 2x - 2x

x + 8 = 0

Finally, we can subtract 8 from both sides of the equation:

x + 8 - 8 = 0 - 8

x = -8

Therefore, x equals -8.

The surface areas are given as;

a.  2700 cm²

b. 280. 6 cm²

c. 815. 3 cm²

The formula for calculating the surface area of a cuboid is expressed as;

Surface area (SA) = 2lw+2lh+2hw

Such that l is the length, w is the width and h is the height

Substitute the values, we have;

a. Surface area = 2(25×25) + 2(4 ×25) + 2(25 ×25)

expand the bracket, we have;

Surface area = 1250 + 200 + 1250

Surface area = 2700 cm²

b. Surface area of the pyramid = √3/ 2a²

Substitute the value

Surface area = √3 /2 × 18²

Find the square, we have;

Surface area = 280. 6 cm²

c. The total surface area to be painted ;

= 675 + √3/4a²

= 675 + 140.3

= 815. 3 cm²

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]The particle is moving from left to right for t > 2 or 0 < t < 1.5.

The path of a particle defined by s(t) = t⁴/4 − t³ + t², t ≤ 0. The particle is moving from left to right when its velocity is positive.

The velocity of the particle is given by the first derivative of its position function, which is s'(t) = t³ − 3t² + 2t. To find when the particle is moving from left to right, we need to find when its velocity is positive.
The particle is moving from left to right when its velocity is positive, which occurs when t > 2 or 0 < t < 1.5. Therefore, the particle is moving from left to right for t > 2 or 0 < t < 1.5.

The velocity function, s'(t) = t³ − 3t² + 2t, can be factored as s'(t) = t(t − 1)(t − 2).

This means that the velocity of the particle is 0 when t = 0, t = 1, and t = 2.

When t < 0, the velocity is negative because all three factors in the velocity function are negative. When 0 < t < 1, only one factor is negative (t − 2), so the velocity is positive.

When 1 < t < 2, two factors are negative (t − 1) and (t − 2), so the velocity is negative. When t > 2, all three factors are positive, so the velocity is particle .

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The values of x from the graph for which y = 0 are -3 and 4

From the question give above, we obtained the following:

The value of x from the graph can be obtained as follow:

y = x² - x - 12

but

y = 0

Thus, we have

x² - x - 12 = 0 (a quadratic function)

Thus, the vales of x will be the solutions of the equation x² - x - 12 = 0.

From the graph, the values of x when y = 0 will be the point when the line cuts across the x-axis.

From the graph, the line cuts across the x-axis at -3 and 4.

Thus, we can conclude that the value of x from the graph is -3 and 4.

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Using this property on the given expression, we get:

[tex]{(x^3/4)^2/3} = x^(3/4*2/3)[/tex] {multiplying the exponents}= [tex]x^(1/2)[/tex]

Now, we can rewrite the expression in radical form as √x which is the required answer.

The given expression to rewrite with rational exponents as a radical expression by extending the properties of integer exponents is:

[tex]{(x^3/4)^2/3}[/tex]

To rewrite this expression with rational exponents as a radical expression by extending the properties of integer exponents, the general formula of the power rule of exponents can be used, which states that [tex](a^m)^n = a^(mn)[/tex].

Now applying this power rule of exponents on the given expression:

[tex]{(x^3/4)^2/3}={x^(3/4*2/3)}={x^(1/2)}[/tex]= √x

Hence, the required expression, when rewritten with rational exponents as a radical expression by extending the properties of integer exponents, is √x.
To understand the solution, let's understand the concepts and formulas used in it.

The given expression is {(x^3/4)^2/3}. Now, to rewrite this expression with rational exponents as a radical expression by extending the properties of integer exponents, we need to use the power rule of exponents.

The power rule of exponents is an important property of the exponents that states that when we raise a power to another power, we need to multiply the exponents.

That is (a^m)^n = a^(mn).

Using this property on the given expression, we get:

[tex]{(x^3/4)^2/3} = x^(3/4*2/3)[/tex] {multiplying the exponents}= [tex]x^(1/2)[/tex]

Now, we can rewrite the expression in radical form as √x which is the required answer. Hence, the given expression rewritten with rational exponents as a radical expression by extending the properties of integer exponents is √x.

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Matching of the polygon coordinates with their perimeters are:

38 units → U(4, -1), V(12, -1), W(20,-7), X(8, -7), Y(4,-4)

25.4 units → P(7,2), Q (12,2), R(12,6), S(7,10), T(4,6)

50 units → A( 1, 1), B(6,13), C(8,13), D(16,-2) E(1, -2 )

19.24 units → K(4,2), L(8,2), M(12,5), N(6,5), O(4,4)

The formula to find the distance between two coordinates is:

Distance = √(y₂ - y₁)² + (x₂ - x₁)²

1) The coordinates are given as:

A( 1, 1), B(6,13), C(8,13), D(16,-2) E(1, -2 )

Using the earlier formula we have:

Perimeter = AB + BC + CD + DE + EA

Perimeter = 13 + 2 + 17 + 15 + 3

Perimeter = 50 units

2) The coordinates are given as:

K(4,2), L(8,2), M(12,5), N(6,5), O(4,4)

Perimeter = KL + LM + MN + NO + OK

Perimeter = 4 + 5 + 6 + √5 + 2

Perimeter = 17 + 2.24

Perimeter = 19.24 units

3) The coordinates are given as:

F(14,-10), G(16, -10), H(19,-6), I (14,-2), J(11,-6)

Perimeter = FG + GH + HI + IJ + JF

Perimeter = 2 + 5 + √41 + 5 + 5

Perimeter = 19 + 6.40

Perimeter = 25.40

4) The coordinates are given as:

P(7,2), Q (12,2), R(12,6), S(7,10), T(4,6)

Perimeter = PQ + QR + RS + ST + TP

Perimeter = 5 + 4 + √41 + 5 + 5

Perimeter = 19 + 6.40

Perimeter = 25.40 units

5) The coordinates are given as:

U(4, -1), V(12, -1), W(20,-7), X(8, -7), Y(4,-4)

Perimeter = UV + VW + WX + XY + YU

Perimeter = 8 + 10 + 12 + 5 + 3

Perimeter = 38 units

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Answer:5 drops

Step-by-step explanation:

Every 100 nanograms is 0.1 microgram so 500 nanograms + 0.5 micrograms so 5 drops because everydrop is 100 nanograms

Answer:

Vivek has Rs. 150

Step-by-step explanation:

Amount of Money Vivek has = x

Irfan = 7x

Irfan = 900 + x

Set Irfan's equations equal to one another:

7x = 900 + x

=> 6x + x = 900 + x (Now you can subtract x from both sides)

=> 6x = 900

=> x = 900/6 (Divide both sides by 6 to isolate x)

=> x = 150

Irfan has Rs. 1050 (7 x 150 = 1050)

Since Vivek's money is x, Vivek has Rs. 150

The arranged expressions from least to greatest are: 1, 203.69

To arrange the expressions from least to greatest, let's simplify them first:

Expression 1: (72 / 8) - 2 x 3 + 172 / (8 - 2) x 3 + 172 / (8 - 2) x 3 + 172 / (8 - 2) x (3 + 1)

Expression 2: 72 / 8 - 2 x (3 + 1)

Simplifying Expression 1:

(72 / 8) - 2 x 3 + 172 / (8 - 2) x 3 + 172 / (8 - 2) x 3 + 172 / (8 - 2) x (3 + 1)

= 9 - 6 + 172 / 6 x 3 + 172 / 6 x 3 + 172 / 6 x 4

= 9 - 6 + 28.67 x 3 + 28.67 x 3 + 28.67 x 4

= 9 - 6 + 86.01 + 86.01 + 114.68

= 9 - 6 + 200.69

= 3 + 200.69

= 203.69

Simplifying Expression 2:

72 / 8 - 2 x (3 + 1)

= 9 - 2 x 4

= 9 - 8

= 1

Now, let's arrange the expressions from least to greatest:

1 < 203.69

Therefore, the arranged expressions from least to greatest are:

1, 203.69

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The installment price of the TV is $1,195.56.

To find the installment price of the TV, we need to calculate the total amount paid over the installment period.

The down payment is $60, and there are 12 monthly payments of $104.63 each.

Total amount paid over 12 months = Monthly payment x Number of payments

= $104.63 x 12

= $1,255.56

Now, we can calculate the installment price by subtracting the down payment from the total amount paid:

Installment price = Total amount paid - Down payment

= $1,255.56 - $60

= $1,195.56

Therefore, the installment price of the TV is $1,195.56.

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Hello!

2x² - 11x - 6

= (2x² + x) + (-12x - 6)

= x(2x + 1) - 6(2x + 1)

= (x - 6)(2x + 1)

Answer:

the answer is 150 degrees because it is the biggest

Answer:

V = 1/3 π r^2 h

Step-by-step explanation:

V = 1/3 area base*height

1. work out the area

2. base*height

3. area*answer

4. you get full answer

The  12 feet of carpet is needed.

To round 11.5 feet to the nearest foot, we look at the decimal part, which is 0.5. According to the Rounding Rules, if the number being looked at is 5 or above, we round up by giving it a shove! Since 0.5 is exactly 5, we round up to the next whole number, which is 12 feet.

So, after rounding 11.5 feet to the nearest foot, we get 12 feet.

To determine how much carpet is needed, we use the rounded measurement, which is 12 feet.

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If α is an ordinal and β ∈ α, then β satisfies all three properties of an ordinal. Therefore, β is also an ordinal.

To prove the statement "If α is an ordinal and β ∈ α, then β is an ordinal," we need to demonstrate that if α is an ordinal and β is an element of α, then β satisfies the three properties of an ordinal:

Well-Ordering: Every element of β is strictly well-ordered by the membership relation ∈. This property holds because α is an ordinal and satisfies the well-ordering property, and β being an element of α inherits this property.

Transitivity: For any two elements γ and δ in β, if γ ∈ δ and δ ∈ β, then γ ∈ β. Since β is an element of α and α is transitive, the transitivity property carries over to β.

Trichotomy: For any two elements γ and δ in β, either γ ∈ δ, δ ∈ γ, or γ = δ. Again, this property is inherited from α, as β is an element of α.

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Solution for the given system of equations is : a = -2, b = -13 by substitution method.

To solve the system of equations:

a - 4b = 50    ...(1)

b + 5 = 4a    ...(2)

We can use the method of substitution or elimination. Let's solve it using the substitution method.

From equation (2), we can express b in terms of a:

b = 4a - 5

Now we substitute this value of b in equation (1):

a - 4(4a - 5) = 50

a - 16a + 20 = 50

-15a = 50 - 20

-15a = 30

a = 30 / -15

a = -2

Substitute this value of a back into equation (2) to solve for b:

b + 5 = 4(-2)

b + 5 = -8

b = -8 - 5

b = -13

Therefore, the solution to the system of equations is a = -2 and b = -13.

To verify the solution, substitute these values back into the original equations:

For equation (1): -2 - 4(-13) = 50

-2 + 52 = 50 (True)

For equation (2): -13 + 5 = 4(-2)

-8 = -8 (True)

Thus, the solution is confirmed to be correct. The values a = -2 and b = -13 satisfy both equations in the system.

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Answer:

A.

Step-by-step explanation:

New x-coordinate = (-4) * (4/5) = -16/5 = -3.2

New y-coordinate = 6 * (4/5) = 24/5 = 4.8

that's the only option with a -3.2 for A

The simplified equation 1,0008 = 10w can be represented as 1024 = 10w, and we can determine that w is equivalent to 24 by comparing the exponents. This implies that the value of w required to make the equation true is 24.

To simplify the equation[tex]1,000^{8}[/tex]= [tex]10^{w}[/tex], we need to recognize that 1,000 is equal to [tex]10^{3}[/tex]. Therefore, we can rewrite the equation as [tex](10^{3})^{8}[/tex] = [tex]10^{w}[/tex]

Using the property of exponents, when raising a power to another power, we multiply the exponents. Applying this property, we get [tex]10^{3*8}[/tex] = [tex]10^{w}[/tex].

Simplifying further, we have [tex]10^{24}[/tex] = [tex]10^{w}[/tex].

In order for two exponential expressions to be equal, their bases must be the same. In this case, both bases are 10. Therefore, we can conclude that the exponents must also be equal.

Hence, w = 24.

The simplified equation 1,000^8 =[tex]10^{w}[/tex]can be expressed as [tex]10^{24}[/tex] = [tex]10^{w}[/tex], and by comparing the exponents, we find that w is equal to 24. This means that the value of w that makes the equation true is 24.

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The value of (F - G)(-5) when F(x) = x² - 1 and G(x) = 3 - x is -13.

To find (F - G)(-5), we need to substitute -5 for x in both F(x) and G(x) and then subtract G(-5) from F(-5).
So, F(-5) = (-5)² - 1 = 24 and G(-5) = 3 - (-5) = 8.
Therefore, (F - G)(-5) = F(-5) - G(-5) = 24 - 8 = -13.
In order to find (F - G)(-5), we first need to determine what F(x) and G(x) are.

F(x) is given as x² - 1, so we can write F(x) as:

F(x) = x² - 1  

Similarly, G(x) is given as 3 - x, so we can write G(x) as:

G(x) = 3 - x

We now need to find (F - G)(-5), which means we need to evaluate F(-5) and G(-5) and then subtract G(-5) from F(-5).

Let's start by finding F(-5). To do this, we simply substitute -5 for x in F(x):F(-5) = (-5)² - 1F(-5) = 25 - 1F(-5) = 24

Now we need to find G(-5). To do this, we substitute -5 for x in G(x):G(-5) = 3 - (-5)G(-5) = 3 + 5G(-5) = 8

We now have F(-5) and G(-5), so we can find (F - G)(-5) by subtracting G(-5) from F(-5):

(F - G)(-5) = F(-5) - G(-5)(F - G)(-5) = 24 - 8(F - G)(-5) = -13

Therefore, (F - G)(-5) = -13.

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The missing angle measurements are:

Angle G = 66.67 degrees

Angle H = 113.32 degrees

Angle Z = 66.68 degrees

Angle I = 66.68 degrees

Let's analyze the given information and solve for the missing angle measurements:

From the diagram, we can see that angle H and angle G are adjacent angles, and the line segment HG acts as a transversal. We are given that the measure of angle G is 2x, and we need to find the missing angle measurements, which are the measures of angle H, angle Z, and angle I.

Since angle G and angle H are adjacent angles, their measures add up to 180 degrees. So we can set up the equation:

2x + (4x - 20) = 180

Simplifying the equation:

6x - 20 = 180

Next, we solve for x:

6x = 200

x = 200/6

x = 33.33

Now that we have found the value of x, we can substitute it back into the original equation to find the measures of the missing angles:

Angle G = 2x = 2(33.33) = 66.67 degrees

Angle H = 4x - 20 = 4(33.33) - 20 = 133.32 - 20 = 113.32 degrees

Angle Z = 180 - Angle H = 180 - 113.32 = 66.68 degrees

Angle I = Angle Z = 66.68 degrees

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Looking at the distribution sets 1-8 the one that seems to be closest to the mean is distribution 1 because all the data of distribution 1 lie on 5.

The distribution closest to the mean is determined by comparing the mean of the dataset, to the given mean.

The mean of the various distributions is determined as;

Distibution 1; mean = (9 x 5) = 45/9 = 5

Distibution 2; mean = (2x3  + 3 +  4x2  +  8 + 9 + 11) /9 = 5

Distibution 3; mean = (2x3  +  4x2  +  5 + 7 + 9 + 10) /9 = 5

Distibution 4; mean = (2x3  +  4x2  +  5 + 7 + 9 + 10) /9 = 5

The mean of the remaining distributions, from 5 to 8 is also 5, as already given in the statement.

If we look at all the distributions, we would see that, all the data of distribution 1 lie on 5, making it the most closest the mean of the distribution.

Thus, looking at the distribution sets 1-8 the one that seems to be closest to the mean is distribution 1 because all the data of distribution 1 lie on 5.

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The value of x is $6,666.67.Assume that x equals the amount Seema invested at 3% interest. Also, let us designate the interest from Seema's $4,000 investment at 5% by I1 and the interest from Seema's x dollars investment at 3% by I2.

Simple interest is calculated as Simple Interest = (Principal * Rate * Time)/100.

Because we want to compute the return at the end of the year, we know the time for both investments is one year.

We may write two equations using this formula: I₁ = (4000 * 5 * 1) / 100 = 200I₂ = (x * 3 * 1) / 100 = 0.03x

We also know that Seema's return on investment is the same for both investments. As a result, we may write: I1 = I2 200 = 0.03x

We may now solve for x: x = 200/0.03x = 6666.67.

Therefore, the value of x is $6,666.67.

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Step-by-step explanation:

To calculate the number of different license plates that can be made if the first character is a letter followed by 3 numbers, followed by 2 letters, we can use the multiplication principle.

There are 26 letters in the alphabet and 10 digits (0-9). Therefore, there are 26 choices for the first letter, 10 choices for each of the next three digits, and 26 choices for each of the last two letters.

Using the multiplication principle, we can multiply these numbers together to get the total number of possible license plates:

26 × 10 × 10 × 10 × 26 × 26 = **45,697,600**.

Therefore, there are **45,697,600** different license plates that can be made if the first character is a letter followed by 3 numbers, followed by 2 letters.