Evaluate 8c2 - 7c when c = -2.

Brooklyn needs to invest $432.43, rounded to the nearest ten dollars.

To determine how much Brooklyn needs to invest in an account that pays a continuously compounded interest rate, we can use the formula:

A = \(Pe^(^r^t^)\)

where A is the future value of the account, P is the principal investment, e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years.

In this case, we want the future value of the account to be $640, the interest rate is 3.5% (or 0.035 as a decimal), and the time is 9 years. We can substitute these values into the formula and solve for P:

640 = \(Pe^(^0^.^0^3^5^*^9^)\)

640 = Pe^0.315

P =\(640/e^0^.^3^1^5\)

P = 432.43

Therefore, to have a future value of $640 in 9 years with a continuously compounded interest rate of 3.5%.

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There is no change in its slope as initial and final slope is 1.

What is slope?

In arithmetic, the slope or gradient of a line may be a variety that describes each the direction and therefore the abruptness of the line.

Main body:

formula for slope with two points form is =

y -y₁ =( y₂-y₁ /x₂-x₁ )(x - x₁)

according to question ,

points are (0,0) and (3,3)

y - 0 = (3-0/3-0)(x -0)

y = 3/3 *x

y = x

hence slope of line is 1.

Now points are (0,0) and (-3,-3).

y - 0 = (-3-0/-3-0)(x -0)

y =- 3/-3 *x

y = x

hence slope of line is 1.

So there is no change in its slope.

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The length of side AB in right angled triangle ABC  will be 48 cm.

Every triangle with one 90° angle is said to have a right angle. The triangle with a right angle is known as a right triangle because a right angle is 90 degrees.The longest side of a right angle is known as the hypotenuse, and it is opposite the right angle.

Given,

∠B= 90°, AC = 96 cm, ∠C = 30°

Now, we know, Trignometric ratio sin θ in triangle can be given by-:

sin θ = \(\frac{perpendicular}{hypotenuse}\)

From given figure,

Perpendicular= AB= ?

and Hypotenuse= AC = 96

and θ= 30°

Hence,

sin 30° =\(\frac{perpendicular}{hypotenuse}\)= \(\frac{AB}{96}\)

\(\frac{1}{2} = \frac{AB}{96}\)                                      (∵ sin 30°= 1/2)

\(AB=\frac{96}{2}\)

\(AB= 48 cm\)

Thus, AB= 48 cm

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Correct Question:ABC is a right angled triangle. if B = 90°, AC = 96 cm, C = 30°. Find AB = ?

Answer:-1/4

Step-by-step explanation:

It would be -1/4 because it's not with a variable.

Answer: 16.74

Step-by-step explanation:

Use long multiplication to evaluate.

Answer:

13

Step-by-step explanation:

\(5 + 12 - 4 = \\ 17 - 4 = 13\)

In mathematics, a sequence is an ordered list of elements, often denoted by brackets or parentheses.

The term "a sequence of length n" refers to a sequence that contains a specific number of elements, where the number of elements is denoted by "n."

When the domain of a function is the set of natural numbers (N), it is called an infinite sequence. An infinite sequence can be thought of as an ordered list that continues indefinitely.

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Answer:

\(1\frac{27}{100} \)

Step-by-step explanation:

127% = 100% + 27% = 100/100 + 27/100 = 1 + 27/100

27/100 cannot be written any simpler.

Therefore 127% = \(1\frac{27}{100} \) written as a mixed number

9514 1404 393

Answer:

  A, C, D, E

Step-by-step explanation:

Dilation does not change angles or directions. Every image point X' lies on the line containing the center of dilation and the pre-image point X. If the scale factor is other than 1, no image segment will be congruent to its pre-image segment. So, the following are true:

Answer:

The new standard deviation will be greater than $26

Step-by-step explanation:

The new bicycle has a price much larger than the price of the others. In fact it is almost double the price of the other bicycles. It causes a large increase as a result. Also, I took the quiz.

Answer:

y + 5 = 3y - 1

2y = 6, so y = 3

4x - 2 = x + 10

3x = 12, so x = 4

The advantages and disadvantages of bases other than ten are shown below.

The base-10 system is a way to give numbers a place value. As the position of the decimal point determines a number's mathematical value, it is often referred to as the place value number system or the decimal system.

In software systems, number systems with a base of 16 are frequently used. They have the fundamental benefit of being quickly convertible to binary systems.

The advantage of using number bases on 60 is that 60 may be divided by 2, 3, 4, and 6.  Its downside is that it is cumbersome.

Number systems based on 12 provide advantages comparable to those of number systems based on 60, but they give up the advantage of being divisible by 5 for the benefit of a less cumbersome system.

Therefore, base-10 number systems are not the best.

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Let's denote the amount Jolene invested at 3 percent interest as 'x' dollars. Since she put twice as much in the lower-yielding account, the amount she invested at 9 percent interest would be '2x' dollars.

To calculate the interest earned from each account, we'll use the formula: Interest = Principal × Rate × Time.

For the 3 percent interest account:

Interest_3_percent = x × 0.03

For the 9 percent interest account:

Interest_9_percent = 2x × 0.09

We know that the total annual interest is $3120, so we can set up the equation:

Interest_3_percent + Interest_9_percent = 3120

Substituting the above equations, we have:

x × 0.03 + 2x × 0.09 = 3120

Simplifying the equation:

0.03x + 0.18x = 3120

0.21x = 3120

Dividing both sides of the equation by 0.21:

x = 3120 / 0.21

x = 14857.14

Therefore, Jolene invested approximately $14,857.14 at 3 percent interest and twice that amount, $29,714.29, at 9 percent interest.

Answer:

Step-by-step explanation:

X is the amount invested at 6%

Y is the amount invested at 9%

0.06X + 0.09Y = 4998

X = 2Y

0.06(2Y) + 0.09Y  = 4998

.12Y + 0.09Y = 4998

0.21Y = 4998

21Y = 499800

Y = 499800/21 = 23800

So X = 2*23800 = 47600

$47,600 is invested at 6% and $23800 is invested at 9%

The cylinder has a volume of 150.796 in³. The cylinder has a surface area of 175.929 in².

The quantity of three-dimensional space that an object or closed surface occupies is referred to as volume in mathematics. The cubic units of volume are m³, cm³, in³, and so on.

The sum of all of an object's faces is its surface area in three dimensions. Wrapping, painting, and finally building things to achieve the best possible design are examples of real-world applications of the concept of surface areas.

Given that a volume of cylinder = h × r² × π

                         h = 12 in

                          r = 2 in

                       volume = ?

Volume of cylinder = h × r² ×π

                                 = =12 × 3.14×(2)²

                                       =37.68 × 4

                                       =150.796 in³

B). Surface area of cylinder= 2πr² + 2πrh

                                         =2× 3.14 × (2)²+2× 3.14× 2×12

                                          =175.929in²

The formula V=r²(h) can be used to determine a cylinder's volume. Simply multiplying the area of the circular base shape by the height is all that is required to determine a cylinder's volume.

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Person 3's payment exceeded person 2's payment by $20.

To find out how much more person 3 paid than person 2, we need to calculate the amounts each person paid based on the given ratio and then compare their payments.

The ratio given is 1:2:3, which means that person 1 gets 1 part, person 2 gets 2 parts, and person 3 gets 3 parts of the total amount.

Step 1: Calculate the total number of parts in the ratio.

1 + 2 + 3 = 6

Step 2: Determine the value of one part.

$120 (total amount) divided by 6 (total number of parts) = $20

Step 3: Calculate the payments for each person based on the ratio.

Person 1: 1 part * $20 = $20

Person 2: 2 parts * $20 = $40

Person 3: 3 parts * $20 = $60

Therefore, person 3 paid $60, while person 2 paid $40. To find out how much more person 3 paid than person 2, we subtract the amount person 2 paid from the amount person 3 paid:

$60 - $40 = $20

Hence, person 3 paid $20 more than person 2.

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Answer:

45 i believe

Step-by-step explanation:

Answer:

45cm2

Step-by-step explanation:

5x5 is 25, to find the triangle its base times height /2 so, 5x4 is 20 but since theres 2 of them then u just keep it.

SOLUTION

We will use the formula

Applying we have

Taking log we have

Hence the time is approximately 15 years

Given:

To find:

We need to find the type of the graph of the given polar equation.

Explanation:

The given equation is of the form

where a=3 and b=-3.

This equation is the general equation of the limacon.

Hence the given equatLimaconLimaconlimacon.

The graph of the equation:

Final answer:

The type of polar curve is Limacon.

From the graph,

f(-2) = 0

and, g(-2) = 0

(ƒ − g)(−2)= f(-2)-g(-2) = 0

OPTION B is the correct answer

Answer:

√52

Step-by-step explanation:

6^2 = 36

4^2 = 16

   a.       b

√36 + √16 = c

c = √52

Step-by-step explanation:

2

\(2 \sqrt{13 } \)

Answer:

(1,4)

Step-by-step explanation:

\(if~(x,y)~is~mid~point~of~(x_{1},y_{1})~and~ (x_{2},y_{2}~then\\x=\frac{x_{1}+x_{2}}{2} \\y=\frac{y_{1}+y_{2}}{2} \\x=\frac{5-3}{2} =\frac{2}{2}=1\\y=\frac{7+1}{2} =\frac{8}{2} =4\)

(x,y)→(1,4)

Answer:

im sorry, not sure. maybe repost and ask someone else. i dont want to give you the wrong answer

Answer:

35 degrees

Step-by-step explanation:

Since the 2 horizontal lines are parallel,

angle 4 and angle 2 are alternate interior angles, which are equal

So, angle 2 will be equal to angle 4

Angle 2 = 35 degrees

The types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.

A. To find f(x) + g(x), we add the two functions together:

f(x) + g(x) = (x + 2)/(x^2 - 9) + 11/(x^2 + 3x)

To add these fractions, we need a common denominator. The common denominator in this case is (x^2 - 9)(x^2 + 3x). So, we rewrite the fractions with the common denominator:

f(x) + g(x) = [(x + 2)(x^2 + 3x) + 11(x^2 - 9)] / [(x^2 - 9)(x^2 + 3x)]

Simplifying the numerator:

f(x) + g(x) = (x^3 + 3x^2 + 2x^2 + 6x + 11x^2 - 99) / [(x^2 - 9)(x^2 + 3x)]

Combining like terms:

f(x) + g(x) = (x^3 + 16x^2 + 6x - 99) / [(x^2 - 9)(x^2 + 3x)]

B. To find the excluded values, we look for values of x that would make the denominators zero, as division by zero is undefined. In this case, the excluded values occur when:

(x^2 - 9) = 0  --> x = -3, 3

(x^2 + 3x) = 0 --> x = 0, -3

So, the excluded values are x = -3, 0, and 3.

C. To classify each type of discontinuity, we examine the excluded values and the behavior of the function around these points.

At x = -3, we have a removable discontinuity or hole since the denominator approaches zero but the numerator doesn't. The function can be simplified and defined at this point.

At x = 0 and x = 3, we have vertical asymptotes. The function approaches positive or negative infinity as x approaches these points, indicating a vertical asymptote.

Therefore, the types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.

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From the situation described, we have that:

a) Tunnel A is a circle with center (-14, 0) and radius 12, meaning that both the width and the height are of 12.

b) Tunnel B is a parabola that has a width of 32 feet and a height of 16 feet.

c) The maximum height of Tunnel A is of 12 feet and of Tunnel B is of 16 feet, hence, since the height of the truck is of 13.5 feet, it can pass through Tunnel B without damage, as it's height is greater than 13.5 feet.

The equation of a circle of center \((x_0, y_0)\) and radius r is given by:

\((x - x_0)^2 + (y - y_0)^2 = r^2\)

For Tunnel A, the equation is given by:

x² + y² + 28x + 52 = 0

Completing the squares:

(x + 14)² + y² = -52 + 14²

(x + 14)² + y² = 144.

Hence:

Tunnel A is a circle with center (-14, 0) and radius 12, meaning that both the width and the height are of 12.

A quadratic equation is modeled by:

y = ax^2 + bx + c

The vertex is given by:

\((x_v, y_v)\)

In which:

For Tunnel B, the equation is given as follows:

x² - 36x + 16y + 68 = 0.

16y = -x² + 36x - 68.

Simplifying by 16:

y = -0.0625x² + 2.25x - 4.25.

Hence the coefficients are a = -0.0625, b = 2.25, c = -4.25, and the maximum height is:

\(y_v = -\frac{(2.25)^2 - 4(-0.0625)(-4.25)}{4(-0.0625)} = 16\)

The width is the difference between the roots, which, using a calculator, are:

2 and 34, hence the width is of 32 feet.

Then:

Tunnel B is a parabola that has a width of 32 feet and a height of 16 feet.

For item c, we have that:

The maximum height of Tunnel A is of 12 feet and of Tunnel B is of 16 feet, hence, since the height of the truck is of 13.5 feet, it can pass through Tunnel B without damage, as it's height is greater than 13.5 feet.

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Answer:

1,166 is the SA

correct me if im wrong somehow

Step-by-step explanation:

a wobble ball is a sphere

circumference=8(pi)

242=8(3.14)

so 242 divided by 25.12

this ends up with 9.633757961783439, which is the radius of the circumference

SA of a sphere= 4(pi)r²

SA=4(3.14)9.633757961783439²

SA=4(3.14)92.80929246622581

SA=1,165.684713375796

rounded to the nearest whole # = 1166

Answer:

The null hypothesis is: \(H_{0}: \mu = 100\)

The alternative hypothesis is: \(H_{a}: \mu > 100\)

Step-by-step explanation:

At the null hypothesis, we test if the mean is equal to a certain value.

At the alternate hypothesis, we test if the mean is less than, more than, or different from the value tested at the null hypothesis.

The tuft bind strength of a synthetic material used to make carpets is known to have a mean of 100 lb and standard deviation of 20 lb.

This means that the null hypothesis is: \(H_{0}: \mu = 100\)

Could it be that the average tuft strength is above 100 lb?

The world above means that the appropriate alternative hypothesis is: \(H_{a}: \mu > 100\)

Answer:

39 3/8 ft ^2

Step-by-step explanation:

To find the area of a rectangle, multiply the length times the width.

A = l*w

  = 7 1/2  * 5 1/4

Change the mixed numbers to improper fractions.

A = 15/2 * 21/4

    =315/8

Change back to a mixed number.

8 goes into 315 39 times with 3 left over.

 = 39 3/8

Answer:

(you can round to 39.4)

Step-by-step explanation:

Find the area of the rectangle shown

7 1/2 ft

5 1/4ft

7 1/2 = 7.5 ft

5 1/4 = 5.25 ft

Area = L x W

Area = 7.5 x 5.25

Area = 39.375

The measure of angle A is 63°, the measure of side b is 22.34 feet and the measure of side a is 37.57 feet.

From the given triangle ABC,

∠A+∠B+∠C=180° (Angle sum property of a triangle)

∠A+32°+85°=180°

∠A+117°=180°

∠A=180°-117°

∠A=63°

We know that, the formula for sine rule is sinA/a=sinB/b=sinC/c

Here, sin63°/a = sin32°/b = sin85°/42

sin63°/a = sin32°/b = 0.9961/42

sin32°/b = 0.9961/42 and sin63°/a = 0.9961/42

0.5299/b = 0.9961/42

0.9961b=22.2558

b=22.2558/0.9961

b=22.34 feet

sin63°/a = 0.9961/42

0.8910/a = 0.9961/42

0.9961a=37.422

a=37.422/0.9961

a=37.57 feet

Therefore, the measure of angle A is 63°, the measure of side b is 22.34 feet and the measure of side a is 37.57 feet.

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Answer:

19/20 , 1 1/4 , 1 4/5

Step-by-step explanation:

1.8 = 1 4/5 (fraction)

1.8 converts to 18/10. This can be simplified twice, firstly by making it 9/5 since both 18 and 10 are divisible by two, but can be simplified further to 1 4/5

1.25 = 1 1/4 (fraction)

1.25 converts to 125/100. This can be simplified to 5/4 or 1 1/4

0.95 = 19/20 (fraction)

0.95 converts to 95/100. This can be simplified to 19/20

Ascending Order (smallest to largest)

smallest - 19/20

middle - 1 1/4

largest - 1 4/5

I believe this is the right answer, but haven't done fractions in a while so may want to double check to make sure