If you start with a number divide it by 4 then multiply it by two you end up with 8 squared

The measure of an exterior angle of a regular 11-sided polygon is 32.73°.

The measure of an exterior angle of a regular 11-sided polygon can be calculated using the formula:

60° divided by the number of sides.

In this case, for an 11-sided polygon, each exterior angle would measure 360° / 11 = 32.73°.

Final answer:

To solve this problem, set up a system of equations and solve for the variables. Isaiah is 28 years old and Jacob is 35 years old.

Explanation:

To solve this problem, we can set up a system of equations.

Let's say Isaiah's age is represented by x. Jacob's age is then represented by x + 7, since he is 7 years older than Isaiah.

We know that the sum of their ages is 63, so we can set up the equation: x + (x + 7) = 63.

Simplifying the equation gives us: 2x + 7 = 63.

Subtracting 7 from both sides of the equation gives us: 2x = 56.

Dividing both sides of the equation by 2 gives us: x = 28.

So, Isaiah is 28 years old, and Jacob is 28 + 7 = 35 years old.

Answer:

$4236.

Step-by-step explanation:

We have been given that Jamie has invested $1500 in a savings account. Each month the account pays an interest of 3.8%. We are asked to find the total amount Jamie will have in her account after 4 years.

We will use simple interest formula to solve our given problem.

[tex]A=P(1+rt)[/tex], where,

A = Final amount after t years,

P = Principal amount,

r = Interest rate in decimal form,

t = Number of years.

Let us convert our given rate in decimal form.

[tex]3.8\%=\frac{3.8}{100}=0.038[/tex]

Since the we have been given monthly interest rate, so we will convert the given rate to annual interest rate by multiplying 0.038 by 12.

Upon substituting our given values in above formula we will get,

[tex]A=\$1500(1+0.038*12*4)[/tex]  

[tex]A=\$1500(1+1.824)[/tex]

[tex]A=\$1500(2.824)[/tex]  

[tex]A=\$4236[/tex]  

Therefore, Jamie will have $4236 in her account after 4 years.

Answer:

[tex]\sin\theta=-\dfrac{\sqrt{5}}{3}[/tex]

Step-by-step explanation:

If θ is in Quadrant III

[tex]\cos\theta=-\dfrac{2}{3}[/tex]

As we know in III quadrant cosine and sine both are negative.

using trigonometry identity

[tex]\sin\theta=-\sqrt{1-\cos^2\theta}[/tex]

[tex]\sin\theta=-\sqrt{1-(\frac{2}{3})^2}[/tex]

[tex]\sin\theta=-\sqrt{1-\frac{4}{9}}[/tex]

[tex]\sin\theta=-\dfrac{\sqrt{5}}{3}[/tex]

Hence, The value of [tex]\sin\theta=-\dfrac{\sqrt{5}}{3}[/tex]

Answer:

13, 10, 8, 5

Step-by-step explanation:

2+7=9 9=9 the requirment is it has to be greater than the third length not equal to

Getting two 6's in four rolls can happen in 6 ways. 4C2 = 6

The probability of getting two 6's is 1/36. Therefore,

6 times 1/36 = 1/6 or 0.16666666...

 Converting to a percent to the nearest tenth is 16.7%

Answer:

3750

Step-by-step explanation:

3750

A +B = 181

A=181-B

4.70A+5.90B= 967.10

4.70(181-B) +5.90B =967.10

850.70-4.70B+5.90B=967.10

850.70+1.2B =967.10

1.2B=116.40

B =116.40/1.2 = 97

A=181-97 = 84 pounds of type A coffee

Answer:

the volume of the sphere will be 4 times the volume of the cone;

Step-by-step explanation:

The question is on volume comparison

Volume of a sphere=4/3 ×r³

Volume of a cone= /3×r²h

where r is the radius and h is the height

Apply the condition

If r=h=1 unit

Then volume of sphere will be= 4/3 × ×1³ = 4/3

And volume of the cone will be= /3 ×1²×1 =/3

We can see the volume of the sphere will be 4 times the volume of the cone;

4/3 = 4×/3

divide the discount by the percentage off

 so:

99.90/0.27 = 370

 the original price was 370 dollars

To tell if there is a horizontal asymptote, for rational functions, compare the degrees of the numerator and denominator; if they are equal, the asymptote is the ratio of their leading coefficients. If the numerator's degree is less, the asymptote is at y=0; if greater, there is no horizontal asymptote. Polynomials do not have horizontal asymptotes.

To determine if a function has a horizontal asymptote, we look at the behavior of the function as x approaches infinity (x →∞). For rational functions, the degrees of the numerator and denominator play a crucial role. If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is the ratio of the leading coefficients of the numerator and denominator. For instance, as x approaches infinity, the term with the highest power dominates and the constant terms become less significant, leading to the horizontal asymptote at y = 1.

In a scenario where the degree of the numerator is less than the degree of the denominator, the function will have a horizontal asymptote at y = 0, since the function approaches zero as x increases without bound. Conversely, if the degree of the numerator is greater than the degree of the denominator, no horizontal asymptote exists because the function grows without limit.

Remember, polynomials do not have horizontal asymptotes, as their values continue to increase or decrease indefinitely with x.

Answer: (A) sin x° = 3/z

Step-by-step explanation: i couldnt find it anywhere else but i figured it out and dont worry i got it right on the quiz

Answer:

The correct option is B.

Step-by-step explanation:

The equation of linear parent function is

[tex]y=x[/tex]

Key property of the linear parent function are:

1. It is in quadratic l and lII.

2. It has a slope of 1.

3. It is a straight line.

4. It passes through the origin.

The graph of parent function is shown below.

In the given options only the statement " It has a slope of 1" is true.

Therefore the correct option is B.

The expression (2x² + 4x – 7)(x – 3) is equivalent to the expression (2x² + 4x – 7)(x) + (2x² + 4x – 7)(–3) option (D) is correct.

It is defined as the combination of constants and variables with mathematical operators.

We have an expression:

= (2x² + 4x – 7)(x – 3)

After using the distributive property:

= (2x² + 4x – 7)(x) + (2x² + 4x – 7)(–3)

Distributed the whole term (2x² + 4x – 7) with (x - 3)

Thus, the expression (2x² + 4x – 7)(x – 3) is equivalent to the expression (2x² + 4x – 7)(x) + (2x² + 4x – 7)(–3) option (D) is correct.

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Answer:

The answer is pi/4

Step-by-step explanation:

You substitute each x for "pi/4", you will see that the equation is incorrect, the two values are no longer equal.

The equation is not an identity. Value of x = nπ, where n∈I , I → set of integers, for which both sides are defined but not equal.

Equations using trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.

We have the equation,

cos x - (cos x) (sin x) = cos³x

Simplifying,

cos x [ 1 - (sin x) ]  = cos²x (cos x)

1  - sinx = cos²x

1  - sinx = 1 - sin²x

1  - sinx = 1² - sin²x

1  - sinx = (1  - sinx)(1 +sinx)

1 = 1  + sinx

sinx = 0

x = nπ, where n∈I , I → set of integers.

It is not an identity equation.

cos x - (cos x) (sin x) ≠ cos³x

Therefore,  both sides are defined but not equal.

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Answer: -3

Step-by-step explanation:

The points (1,1) (2,-2) plugged into slope formula m = y2 - y2/x2 - x1

-2 is y2

1 is y1

2 is x2

1 is x1

Subtract and simplify

To factor 2x^3y + 18xy - 10x^2y - 90y, find the GCF of the terms, rewrite the expression, factor out the GCF from the terms inside the parentheses, and simplify the expression.

To factor the expression 2x^3y + 18xy - 10x^2y - 90y, we can begin by finding the greatest common factor (GCF) of the terms. The GCF of the coefficients is 2, and the GCF of the variables is y.

So, we can rewrite the expression as 2y(x^3 + 9x - 5x^2 - 45).

Next, we can factor out the GCF from the terms inside the parentheses. The GCF of x^3, 9x, -5x^2, and -45 is x. Factoring out x, we get x(x^2 + 9 - 5x - 45).

Finally, we simplify the expression inside the parentheses. Rearranging the terms, we have x(x^2 - 5x + 9 - 45). Combining like terms, we get x(x^2 - 5x - 36).

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x = correct answer

y = incorrect answer

0.50x-0.30(100-x)=22.00
0.50x-30.00+0.30x=22.00
0.80x=22.00+30.00
0.80x=52.00
x=52.00/0.80

x= 65

y=100-65 = 35

0.5x65 = 32.50

35*0.30=10.5

32.5-10.5 = 22

 there were 65 correct answers

Answer:

65 problems were solved correctly, 35 incorrecly.

Step-by-step explanation:

1. Data:

Total answers= 100

50 cent = $0.50 for each correct answer

-30 cent = -$0.30 for each incorrect answer

Net reward= $22.00

2. Define Variables:

x= Correct answers

y= Incorrect answers

3. Formulate the Equations

Total number of answers (Eq 1)

[tex]x+y=100\\y=100-x[/tex]

Net reward (Eq 2)

[tex]0.50*x-0.30*y=22.00[/tex]

4. Solve by replaccing the Eq 1 in Eq 2 as follows:

[tex]0.50*x-0.30*y=22.00\\0.50*x-0.30*(100-x)=22.00[/tex]

5. Apply distrivutive property and operate:

[tex]0.50x-(0.30*100)+(0.30*x)=22.00\\0.50x-30.00+0.30x=22.00[/tex]

6. Separate numbers and variables on each side of the equation and solve

[tex]0.50x+0.30x=22.00+30.00\\0.80x=52.00[/tex]

7. Solve x

[tex]x=\frac{52.00}{0.8} \\x=65[/tex]

Now you know that correct answers are equal to 65

8. Find Incorrect Answers with Eq 1.

[tex]y=100-x\\y=100-65\\y=35[/tex]

Now you know that incorrect answers are equal to 35

9. Answer

65 problems were solved correctly, 35 incorrecly.

Based on the actual production, the rate of 2 mousetraps per minute is not accurate.

Rate of a quantity is the amount of that quantity with respect to some amount of another quantity.

If the quantity with respect to which the rate is measured is taken as single unit or one unit, then the rate is called unit rate.

Production of mousetraps by the worker in 6 hours = 198

Production of mousetraps by the worker in 1 hour = 198/6 = 33

That is, production of mousetraps by the worker in 60 minutes = 33

Production of mousetraps by the worker in 1 minute = 33/60 = 0.55

The worker produced mousetraps at a rate of 0.55 mousetraps per minute.

But the report states that this worker produced at a rate of 2 mousetraps per minute, which is not correct.

Hence the statement of report that the worker produced at a rate of 2 mousetraps per minute is not accurate, because he is only producing 0.55 mousetraps per minute.

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AE x BE = DE x CE

6x5 = 30

6 x DE = 30

DE = 30/6 =5

DC = DE +CE = 5+6 =11

Answer is C) 11

To find the equation of a parabola with a vertex at (0,0) and a directrix of y=-6, we determine the focus is at (0,6), leading to the standard form equation of the parabola as y = 1/4x^2.

The question asks for the equation of a parabola in standard form given its vertex at (0,0) and directrix as y=-6. In parabolic equations, the standard form is usually y = ax^2 + bx + c for horizontal parabolas, or x = ay^2 + by + c for vertical parabolas. Given the vertex is at the origin (0,0) and the directrix is y = -6, this means the focus is at (0,6) because the distance from the vertex to the focus is equal to the distance from the vertex to the directrix but in the opposite direction.

For a parabola that opens upwards or downwards, the standard form is y = ax^2 (since the vertex is at the origin, b and c are 0). Given that the distance from the vertex to the focus (which is also the distance from the vertex to the directrix) is 6, the parabola opens upwards, and its focal distance (p) is 6. Hence, the value of 4p = 24, which leads us to conclude that a = 1/4. Therefore, the equation of the parabola is y = 1/4x^2.