What is the surface area of the cylinder with height 8 ft and radius 8 ft? Round your answer to the nearest thousandth.

Step-by-step explanation:

A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.

This means that a function f will map an object x to exactly one object f(x) in the set of potential outputs if the object x is in the set of inputs (referred to as the domain) (called the codomain).

The metaphor of a function machine, which accepts an object as its input and produces another object as its output based on that input, makes the concept of a function simple to understand.

Given a collection of possible outputs Y (codomain) and a set of inputs X (domain), a function is more precisely defined as f: X→Y which shows that f is a function from X to Y using this notation.

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The steps in solving two rational numbers is using the cross multiplication method and then do the arithmetic operation on the numerator

The rational expression is defined as the expression with both numerator and denominator has polynomials.

Consider two rational expressions

Add two expression using cross multiplication

a/b + c/d

Cross multiply the expression

a/b + c/d = (ad + cb) / bd

Subtract two expression using cross multiplication

a/b - c/d

Cross multiply the expression

a/b + c/d = (ad - cb) / bd

Therefore, the two rational expression can be solved by using the cross multiplication method and do the arithmetic operation

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The final amount compounded monthly at a rate of 8% over 6 years on a principal of $5300 is $8551.56

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.

The formula of compound interest as given in the questions is

A = P[(1 + r/n)^nt

Substituting the values into the formula

A = 5300(1 + 0.08/6)^12 * 6

A = 8,551.56

Erica will owe $8551.56

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The length of t will be;

⇒ t = 294.30 inches.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In ΔSTU, s = 250 inches, ∠U=17° and ∠S=52°.

Now,

Since, In ΔSTU, s = 250 inches, ∠U=17° and ∠S=52°.

Hence, ∠ T = 180 - (17 + 52)

∠ T = 180 - 69

∠ T = 111°

Now, We use the sin rule as;

⇒ t / sint = s / sin s

⇒ t / sin 111° = 250 / sin 52

⇒ t = sin 111° × 250 / sin 52

⇒ t = 0.93 × 250 / 0.79

⇒ t = 294.30 inches.

Thus, The length of t will be;

⇒ t = 294.30 inches.

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Answer: 296.2

Step-by-step explanation:

t/sin111 = 250/sin52

t=250 sin111/52 = 296.1826 = 296.2

For the given similar triangles the value of x is 16/7.

What is similar triangles?

If the respective sides of two triangles are proportional and the corresponding angles are congruent, then the triangles are said to be comparable. To put it another way, similar triangles have the same shape but may differ in size. In addition, if the corresponding sides of the triangles are identical in length, the triangles are congruent.

Let the triangles ΔABD and ΔADE are similar.

Since ratios of sides of similar triangles are in proportion.

⇒

[tex]\frac{AB}{AD} = \frac{BC}{DE}\\ \frac{4}{7} =\frac{x}{4} \\16 = 7x\\x = \frac{16}{7}[/tex]

Hence, the value of x is 16/7.

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Answer:

26

Answer choice 1.

Step-by-step explanation:

6 1/2 ÷ 1/4 is our equation.

6 1/2 as an improper fraction is 13/2

Our new equation is 13/2÷1/4

flip the divisor into a reciprocal and multiply:

13/2×4/1

simplify:

13/1×2/1

26/1

=26

Answer: The answer is A or 26

Step-by-step explanation: I have my ways ;>

We know that a function has a discontinuity if the left hand limit and right hand limit of the function are there but they are not equal.

According to the question,

We have the following information:

A function is given and we need to find if the given function is discontinuous or not.

There are two situations to find this whether the function is discontinuous or not. First, we need to know that the function has both the left hand limit as well as the right hand limit.

Second condition is to check whether if the limits are equal or not. If they are not equal then the function is discontinuous.

Hence, we know that a function has a discontinuity if the left hand limit and right hand limit of the function are there but they are not equal.

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Answer:

x = 0 , y = 0 , z = -3

Step-by-step explanation:

Solve the following system:

{x - 6 y + 4 z = -12 | (equation 1)

x + y - 4 z = 12 | (equation 2)

2 x + 2 y + 5 z = -15 | (equation 3)

Swap equation 1 with equation 3:

{2 x + 2 y + 5 z = -15 | (equation 1)

x + y - 4 z = 12 | (equation 2)

x - 6 y + 4 z = -12 | (equation 3)

Subtract 1/2 × (equation 1) from equation 2:

{2 x + 2 y + 5 z = -15 | (equation 1)

0 x+0 y - (13 z)/2 = 39/2 | (equation 2)

x - 6 y + 4 z = -12 | (equation 3)

Multiply equation 2 by 2/13:

{2 x + 2 y + 5 z = -15 | (equation 1)

0 x+0 y - z = 3 | (equation 2)

x - 6 y + 4 z = -12 | (equation 3)

Subtract 1/2 × (equation 1) from equation 3:

{2 x + 2 y + 5 z = -15 | (equation 1)

0 x+0 y - z = 3 | (equation 2)

0 x - 7 y + (3 z)/2 = -9/2 | (equation 3)

Multiply equation 3 by 2:

{2 x + 2 y + 5 z = -15 | (equation 1)

0 x+0 y - z = 3 | (equation 2)

0 x - 14 y + 3 z = -9 | (equation 3)

Swap equation 2 with equation 3:

{2 x + 2 y + 5 z = -15 | (equation 1)

0 x - 14 y + 3 z = -9 | (equation 2)

0 x+0 y - z = 3 | (equation 3)

Multiply equation 3 by -1:

{2 x + 2 y + 5 z = -15 | (equation 1)

0 x - 14 y + 3 z = -9 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Subtract 3 × (equation 3) from equation 2:

{2 x + 2 y + 5 z = -15 | (equation 1)

0 x - 14 y+0 z = 0 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Divide equation 2 by -14:

{2 x + 2 y + 5 z = -15 | (equation 1)

0 x+y+0 z = 0 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Subtract 2 × (equation 2) from equation 1:

{2 x + 0 y+5 z = -15 | (equation 1)

0 x+y+0 z = 0 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Subtract 5 × (equation 3) from equation 1:

{2 x+0 y+0 z = 0 | (equation 1)

0 x+y+0 z = 0 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Divide equation 1 by 2:

{x+0 y+0 z = 0 | (equation 1)

0 x+y+0 z = 0 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Collect results:

Answer: {x = 0 , y = 0 , z = -3

Step-by-step explanation:

Initial liquid volume is x.

3/4 of the liquid was removed:

Then 1/2 quarts added, the expression including the addition is:

Simplify to get equivalent expression:

Cindy's monthly payment of $609.63 will cost her $29,262.24 in 4 years at a 4% APR.

The total cost that Cindy will spend on the car which costs $27,000 is computed by multiplying the monthly payment by 48 months (the payment period).

The monthly payment can be determined using an online finance calculator that compounds the interest rate monthly for four years.

Cost of car = $27,000

Annual Percentage Rate (APR) = 4%

Payment period = 4 years (monthly)

N (# of periods) = 48 months (4 years x 12)

I/Y (Interest per year) = 4%

PV (Present Value) = $27,000

FV (Future Value) = $0

Results:

PMT = $609.63

Sum of all periodic payments = $29,262.24

Total Interest = $2,262.45

Thus, Cindy will spend $29,262.24 for a car that costs $27,000, if she repays monthly for 4 years.

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The ABCD parallelogram turns into a rhombus if all of its sides are equal.

All Sides are equal.

Diagonals bisect at 90°.

In our question,

AB = DC is given for a quadrilateral ABCD (parallelogram).

When a parallelogram's sides are uneven, symmetry is disrupted and its diagonals do not bisect at 90 degrees. However, when all of the sides are equal, the diagonal does bisect at 90 degrees and the parallelogram becomes a rhombus.

Therefore, when all of a parallelogram's sides are equal, it becomes a rhombus.

The complete question is:

You are trying to prove that quadrilateral ABCD is a rhombus. You know that both pairs of opposite sides are parallel (a parallelogram). Which additional fact would prove that ABCD is a rhombus?

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The cost of the membership is the initial joining fee plus the cost per month multiplied by the number of months.

If the cost after [tex]m[/tex] months is [tex]c[/tex] dollars, then [tex]c=20m+40[/tex].

Answer:

[tex]y^6[/tex]

Step-by-step explanation:

1) Use Product Rule: [tex]x^ax^b=x^{a+b}[/tex].

[tex]y^{1+3+2[/tex]

2) Simplify 1 + 3 to 4.

[tex]y^{4+2}[/tex]

3) Simplify 4 + 2 to 6.

[tex]y^6[/tex]

Thank you,

Eddie

The total monthly charges for the mobile plan if the usage is 120 minutes is $480.

Given that,

A mobile plan's total monthly costs, $C, are made up of a fixed fee of $ 20 and a variable fee that is based on usage. The cost is $0.20 per minute used.

We have to calculate the total monthly charges for the mobile plan if the usage is 120 minutes.

We know that,

A mobile plan fee is $20

For 1 min $0.20 for mobile plan

For 120 minutes

=120×0.2

=24

=24×20

=480

Therefore, the total monthly charges for the mobile plan if the usage is 120 minutes is $480.

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The fourth term of the polynomial (d - 4b)³ is D. -64d³.

A polynomial is an expression involving the operations of addition, subtraction, multiplication of variables.

Given the expression (d - 4b)³, we need to open the bracket, hence:

(d - 4b)³ = d³ + 3(d²)(-4b) + 3(d)(-4b)²

             = d³ - 12bd² + 48b²d - 64d³

Therefore, the fourth term of (d - 4b)³ is D. -64d³

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Triangle DEF is congruent to triangle GHI is correct.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. A triangle having vertices A, B, and C is known as triangle ABC. Any three points in Euclidean geometry that are not collinear result in a distinct triangle and a distinct plane.

A triangle is a polygon with three edges and three vertices. A triangle's total number of angles equals 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

The sum of two sides of a triangle is greater then the third side. Mathematically -

a + b > c

There are different types of triangles such as -

Equilateral, scalene, isosceles, and other triangles are used.

Given are three triangles ΔABC, ΔDEF, ΔIHG.

ΔDEF is congruent to ΔGHI as -

EF = IH (given)

∠E = ∠H (right angle)

FD = IG (given)

Using SAS congruent rule, ΔDEF ≅ ΔGHI

Therefore,  triangle DEF is congruent to triangle GHI is correct.

The complete question is : Which of the following statements are correct?

Select all that apply.

Triangle ABC is congruent to triangle DEF.

Triangle DEF is congruent to triangle GHI.

All three triangles are congruent.

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The responses for the confidence intervals of the 45 lbs weight and the set of data are;

3. D. (45.0472, 45.0928); The exercise equipment company can be 95% confident the population mean of their 45 lb weights lies between 45.0472 and 45.0928

4. C. The size of the confidence interval would increase because Raul would be multiplying by a larger z-score and dividing by a smaller sample size.

The confidence interval is the likelihood of a parameter of a population can be found within a range of values during a specified percentage or proportion of the time.

3. The confidence interval can be found using the formula;

[tex]CI = \overline x \pm z\cdot \dfrac{s}{\sqrt{n} }[/tex]

Where;

[tex]\overline x[/tex] = The mean of the sample = 45.07 lbs

s = The standard deviation of the sample = 0.09 lbs

n = The sample size

z = The confidence level = 1.96 at 95% confidence level

Therefore;

[tex]CI = 45.07 \pm 1.96\times \dfrac{0.09}{\sqrt{60} }[/tex]

45.0472 < μ < 45.0928

The correct option is therefore, option D

Therefore;

4. Decreasing the sample size, n, will decrease the value by which the term on the right of the ± is being divided, increasing the confidence interval.

Increasing the level of confidence will increase z, thereby also increasing the confidence interval.

The correct option is therefore, option C.

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Using half-life and disintegration constant, the sample that will remain 4 seconds 2.03g

This is the spontaneous decay of an active radioactive sample. The decay curve is exponential and it slope is constantly changing.

The half-life of this sample given can be used to find the disintegration constant of the sample.

The formula of half - life is given as

T₁/₂ = ln2 / λ

Substitute the values into the equation;

7.13 = 0.693 / λ

λ = 0.693 / 7.13

λ = 0.0972

The amount of sample left after 4 seconds will be

A = Ne⁻(λt)

A = 3e⁻(0.0972 * 4)

A = 2.03g

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Answer:

9 + 20p ≤ 125

Step-by-step explanation:

This does not include the tax.

The area of walk is 504 square feet

The area of rectangle is define as a  product of length L and width w

calculate the area of rectangle yard

Area = L x W,  

where A equal the Area, L equals the length and W equal width.

A = 35 x 55

A= 1925 square feet

Area of the rectangular yard is 1925 square feet

From the question, we have 3ft wide goes all the way along the fence inside.

Therefore, we subtract six feet from each of the value of length ( 35) and width (55) because each side has 3feet .

Area = L x W

A = 29 x 49

A = 1421 square feet

Area of new rectangle formed by allowing for three foot walk is 1421 square feet

Area of Walk

To get the area walk;  we subtract area of new rectangular formed from area of rectangular yard

Area of Walk = Area of Rectangular yard - Area of new rectangle

Area of Walk = 1925 - 1421

Area of Walk = 504 square feet.

Therefore, the area of walk is 504 square feet.

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In a normal distribution, a data value located 1.4 standard deviations below the mean has Standard Score: z = -1.4.

In a normal distribution, a data value located 2.3 standard deviations above the mean has Standard Score: z = 2.3.

In a normal distribution, the mean has Standard Score: z = 0.

In Mathematics, a standard score is sometimes referred to as a z-value or z-score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

Additionally, a standard score indicate the number of standard deviations above or below the mean in which a raw score or data item falls.

Generally speaking, a standard score is positive when the data value is above (greater than) the mean while it is negative when the data value is below (less than) the mean.

In a normal distribution, the standard score of the mean is given by:

Standard score, z = (x - μ)/σ

Standard score, z = (μ - μ)/σ

Standard score, z = 0/σ

Standard score, z = 0.

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Answer:

∠ R = 115°

Step-by-step explanation:

• each lower base angle is supplementary to the upper base angle on the same side, that is

∠ R + ∠ S = 180°

∠ R + 65° = 180° ( subtract 65° from both sides )

∠ R = 115°

Am pula mare!

Da aaaaaaaaaaa????

Answer: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Step-by-step explanation: Add 5 until you get to 50.

Answer:

a. YES

b. YES

c. NO

d. YES

Step-by-step explanation:

[tex]\frac{7^6}{7^3}[/tex] simplifies to [tex]7^3[/tex]

a:

Let's simplify this:

([tex]7^9[/tex])([tex]\frac{1}{7^6}[/tex])

Now:

[tex]\frac{7^9}{7^6}[/tex]

Which equals:

[tex]7^3[/tex]

So, YES

b:

Simplify this one:

[tex]\frac{1}{7^8} / \frac{1}{7^1^1}[/tex]

Or:

[tex](\frac{1}{7^8})(7^1^1)[/tex]

Which simplifies to:

[tex]7^3[/tex]

So, YES

c:

Simplifies to:

[tex]\frac{7^8}{7^4}[/tex]

Which equals:

[tex]7^4[/tex]

So, NO

d:

This simplifies to:

[tex]\frac{1}{7^3} * 7^6\\\\ \frac{7^6}{7^3} \\\\7^3[/tex]

So, YES

The motion of the dolphin, evaluated using the kinematic equations and Newton's second law of motion are;

Mathematically, Newton's second law of motion states that force is the product of mass and acceleration.

The mass of the dolphin = 230 kg

Height to which the dolphin leaps = 6.4 m

The distance the drag brings the dolphin to a stop = 6.4 meters

First part;

The time it takes the dolphin to stop can be found from the equation;

At the water surface;

m·g·h = 0.5·m·v² (conservation of energy)

g·h = 0.5·v²

v² = 2·g·h

Therefore;

v² = 2 × 9.81 × 6.4 = 125.568

In the water, the initial velocity is v, the velocity at 1.5 meters depth is u, we get;

u² = v² - 2·a·s

Therefore;

v² = 2·a·s

a = v²/(2·s)

a = 125.568/(2 × 1.5) = 41.856

a = 41.856 m/s²

v = u - a·t

t = (u - v)/a

Therefore;

t = (√(125.568))/41.856 ≈ 0.268

The time it takes the dolphin to stop is about 0.268 seconds

Second part

Newton's second law of motion states that force is directly proportional to the rate of change of momentum produced

Mathematically

Force = Mass × Acceleration

Force on the dolphin, F = 230 kg × 41.856 m/s²= 9626.88 N

The possible parts of the question, obtained from a similar question are;

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Tom's growth chart  is a continuous graph.

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Answer please anyone help same doubht

Step-by-step explanation:

Answer:

Refer to the photos taken.

Step-by-step explanation: