Consider the following position function. r(t) = (t⁵ + 5, t⁸ , t⁵ - 4) (a) Find the velocity of a particle with the given position function. v(t) = (b) Find the acceleration of a particle with the given position function a(t) = (c) Find the speed of a particle with the given position function. Iv(t) |v(t)| =

Answer:

"A) 12n + 14m + 4" would be the standard form.

Step-by-step explanation:

the expression written correctly in standard form would be "A) 12n + 14m + 4"

10m + 3(n + 8) + 4(m - 5) + 9n you need to first clear the parenthesis by applying distributive property:

10m + 3(n + 8) + 4(m - 5) + 9n = 10m + 3n + 24 + 4m - 20 + 9n

After that you combine like terms

= 10m + 4m + 3n + 9n + 24 - 20 = 14m + 12n + 4

"A) 12n + 14m + 4" would be the standard form.

An equation for the nth term of the arithmetic sequence: an =  n - 6.

ad 10th term a10 = 4.

The formula for the nth term of the

an = a + (n -1)d

In which,

The arithmetic sequence is given as-

−5,−4,−3,−2, ...

Then, the equation will be

d = a2 - a1

d = -4 - (-5) = 1

an = a + (n -1)d

an = -5 + n - 1

Put n = 10 in the equation.

a10 = 10 - 6

a10 = 4

Thus, the 10th term of the sequence is 4.

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The correct question is-

Write an equation for the nth term of the arithmetic sequence. Then find a10.

−5,−4,−3,−2, ...

Answer:

15/16

Step-by-step explanation:

Using the order of operations, we need to multiply in the parentheses first...

3/5*25/24=75/120, which simplifies to 5/8.

Next, we need to divide 5/8 by 2/3. To divide, we can actually multiply by the reciprocal, which is flipping the fraction that you are dividing by. In this case, we need to multiply 5/8 by the reciprocal of 2/3. The reciprocal of 2/3 is 3/2, so we need to multiply 5/8 by 3/2.

5/8*3/2=15/16

This is the final answer!

I hope this helped you out!! Have an amazing day φ(゜▽゜*)♪

Answer:

The percent of interest is 12.3% per year

Step-by-step explanation:

According to the question Elwood invested 5000 $ in market account

The market account gives the compound interest annually

let p be the interest per year then

At the end of 1st year

amount =(1+0.p) x 5000  = 1.p x 5000

similarly at the end of 2nd year

amount =(1+0.p) x(1+0.p)x 5000  = \((1.p)^{2}\) x 5000

similarly at the end of 3rd year

amount = 7100 $ = \((1.p)^3\) x 5000

⇒ \(\frac{71}{50}\) = \((1.p)^3\)  

1.392 =  \((1.p)^3\)

on further solving we get

1.p = \((1.42)^{1/3}\) = 1.123

thus 1.p = 1 + 0.p = 1.123

thus p = 0.123

thus the percent of interest is 12.3% per year

Answer:

drop down 1 a slower rate per year

drop down 2 670

Step-by-step explanation:

as in three years you get $7100

you take that and subtract it by your starting amount (5000)

7100-5000= 2100

then divide 2100 by the number of years (3)

to get your annual rate of 700$

then you take the 8 year total and subtract it from your 3 year total

10350-7100= 3250

Then divide that by 5 because that how many years it has been

to get the annual rate of 650

making the 5 year rate slower.

The to find the average rate over all 8 year you take 10350 and subtract it from your starting number 5000

10350-5000= 5350

then take 5350 and divide it by the number of years (8)

you then get you average rate of 668.75

668.75=670

Hope this helps!

Answer: 5

Step-by-step 10-5=5

Answer:

5 apples

Step-by-step explanation:

Liam has 10 apples and he gives 5 away to his friend cherry

10-5= 5

He has 5 apples left

keeping in mind that a function doesn't have any X-repeats, namely the x-values in the set aren't repeated, let's check the sets above.

Check the picture below.

Answer:

y = -4

Explanation:

Given the equation:

Thus, the number is -4.

The least expensive C.A.R.S. that can be built to those specifications has dimensions of approximately 4.3088 m x 2.1544 m x 1.7321 m and will cost about $265.47 to build.

Let's start by looking at the dimensions of the base. We know that the length of the base is twice its width. Let's represent the width of the base as "x." This means that the length of the base is "2x." The area of the base is simply the product of the length and the width, which is 2x * x = 2x².

Next, let's look at the dimensions of the sides. The height of the box is going to be represented by "h." The length of each side is going to be equal to the length of the base, which we already know is 2x. The width of each side is going to be equal to the width of the base, which is just x. So the area of each side is simply 2hx.

Now we can use the formula for the volume of a rectangular prism to find the value of "h" in terms of "x." The volume of the box is given as 10 m^3, so:

V = lwh = (2x)(x)(h) = 10

Simplifying this equation, we get:

2x²h = 10

Solving for "h," we get:

h = 5/x²

Now that we have an expression for "h" in terms of "x," we can use it to find the total surface area of the box, which is the sum of the area of the base and the area of the four sides. We can then use this expression to find the minimum cost for a given volume of the box.

The total surface area of the box is given by:

A = 2x² + 4(2hx)

Substituting the expression we found for "h" into this equation, we get:

A = 2x² + 4(2x)(5/x²)

Simplifying this equation, we get:

A = 2x² + 40/x

Now we can take the derivative of this expression with respect to "x" and set it equal to zero to find the value of "x" that will minimize the cost of the box. Differentiating and setting equal to zero, we get:

dA/dx = 4x - 40/x² = 0

Solving for "x," we get:

x^3 = 10

Taking the cube root of both sides, we get:

x ≈ 2.1544

Now we can use this value of "x" to find the dimensions of the least expensive C.A.R.S. that can be built to those specifications. The length of the base is twice the width, so:

Length = 2x ≈ 4.3088

Width = x ≈ 2.1544

Height = 5/x² ≈ 1.7321

So the dimensions of the least expensive C.A.R.S. that can be built to those specifications are approximately: Length = 4.3088 m Width = 2.1544 m Height = 1.7321 m

These dimensions will allow us to build a C.A.R.S. with a volume of 10 m^3, while using the least amount of material possible, which means that the cost will be minimized. We can verify this by calculating the total surface area of the box and the cost of the materials needed.

The total surface area of the box can be calculated by substituting the values we found for "x" and "h" into the expression we derived earlier:

A = 2(2.1544)² + 4(2)(5)/(2.1544)² ≈ 28.2742 m²

Now we can calculate the cost of the materials needed to build the box:

Cost = (Area of base)(Cost per square meter for base) + (Area of sides)(Cost per square meter for sides)

Cost = (2.1544²)(10) + (28.2742 - 2(2.1544²))(6) ≈ $265.47

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Answer:

D

Step-by-step explanation:

the numerator of the exponent is the exponent of x

the denominator is the the index of the root

Answer:

Answer: 9 hours. If austin prepared 20 kg of dough in 5 hours, this means he can prepare 4kg of dough an hour. This is because 20/5=4.

36 cm tall will their stacks be when they are the same height for the first time.

Given,

Two students in Mrs. Johnson's preschool class are stacking blocks:

The height of Reece's block = 4 cm

The height of Maddy's block = 9 cm

We have to find the height of the stacks when they are same height for the first time.

Here,

We have to find the least common multiple.

Least Common Multiple (LCM):

The smallest number that is a multiple of both of two numbers is called the least common multiple.

So here,

We have to find the least common multiple of 4 and 9.

Here, the least common multiple of 4 and 9 = 36

Then,

36 cm tall will their stacks be when they are the same height for the first time.

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Answer:

No solution

Step-by-step explanation:

Given equation:

\(w+5w+4=3(2w-1)\)

Distribute the parentheses:

\(\implies w+5w+4=3 \cdot 2w- 3 \cdot 1\)

\(\implies w+5w+4=6w- 3\)

Combine like terms:

\(\implies 6w+4=6w-3\)

Add 3 to both sides:

\(\implies 6w+4+3=6w-3+3\)

\(\implies 6w+7=6w\)

Subtract 6w from both sides:

\(\implies 6w+7-6w=6w-6w\)

\(\implies 7=0\)

As 7 ≠ 0 there is no solution.

Answer:  (x, y) = (3, 4)

This is the same as saying x = 3 and y = 4 pair up together

======================================================

Explanation:

Subtract the equations straight down.

After all that is said and done, we have this new equation

5x = 15

Divide both sides by 5 to get x = 3

Then we use this x value to find y

-5x+2y = -7

-5(3)+2y = -7

-15+2y = -7

2y = -7+15

2y = 8

y = 8/2

y = 4

Or,

-10x+2y = -22

-10(3)+2y = -22

-30+2y = -22

2y = -22+30

2y = 8

y = 8/2

y = 4

Either way, we end up with y = 4.

Overall, the solution as an ordered pair is (x, y) = (3, 4)

If you were to graph the two equations, they intersect at the location (3,4).

Answer:

Step-by-step explanation:

-5x + 2y = -7            --------------------(I)

-10x + 2y = -22       ------------------(II)

Multiply the whole equation (I) by (-1) and then add.

(I)*(-1)            5x - 2y = 7

(II)                -10x+2y= -22  {Now add. y will be cancelled}

                    -5x      = -15

                             x = -15/(-5)

x = 3

Plugin x = 3 in equation (I)

-5*3 + 2y = -7

-15 + 2y = -7

        2y = -7 +15

        2y = 8

          y = 8/2

            y = 4

Answer:

  5 : 2

Step-by-step explanation:

The ratio of perimeters of similar triangles is the same as the ratio of any pair of corresponding sides. That ratio is given as ...

  1.4 m : 56 cm = 140 cm : 56 cm = 5 : 2

The ratio of the perimeters of the triangles is 5 : 2.

_____

As a unit ratio, it is 2.5 : 1, or 2.5.

Answer:

f(-3)=3

Step-by-step explanation:

Plug in -3 for x.

f(-3)=-4(-3)-8

f(-3)=12-8

f(-3)=3

Hope this helps!

If not, I am sorry.

Answer:

2/5*180=72

360/72=5

as simple as that you just need to read on polygons

Step-by-step explanation:

pls give me brainlyist

Answer:

(1+β)/α = 2

(1+α)/β = 0

Step-by-step explanation:

We need to determine the zeros of the polynomial. This would be done by equating the polynomial to zero and using factorization method to find the variables

x²+4x+3 = 0

x²+x+3x+3=0

x(x+1) +3 (x+1) = 0

(x+1)(x+3) = 0

(x+1)= 0 or (x+3) = 0

x= -1 or -3

If α = -1, and β=-3

(1+β)/α = (1-3)/-1 = -2/-1

(1+β)/α = 2

(1+α)/β = (1-1)/-3 =0/-3

(1+α)/β = 0

The probability that student A or B can solve a problem chosen at random is 0.95.

Probability is calculated by dividing the number of favourable outcomes by the number of possible outcomes.

Random: An event is referred to as random when it is not possible to predict it with certainty. The probability that either student A or B will be able to solve a problem chosen at random can be calculated as follows:

P(A or B) = P(A) + P(B) - P(A and B) where: P(A) = probability of A solving a problem = 0.75, P(B) = probability of B solving a problem = 0.7, P(A and B) = probability of both A and B solving a problem. Since A and B are independent, the probability of both solving the problem is:

P(A and B) = P(A) x P(B) = 0.75 x 0.7 = 0.525

Now, using the above formula: P(A or B) = P(A) + P(B) - P(A and B) = 0.75 + 0.7 - 0.525 = 0.925

Therefore, the probability that student A or B can solve a problem chosen at random is 0.95 (or 95%).

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Answer:

c) 58x2

Step-by-step explanation:

Twice the number 29 is 58

So, 29 is related to 58

Therefore 29*4 = 58*2

Answer:

TRUE

Step-by-step explanation:

The probability of committing a type 1 error is called alpha (or the level of statistical significance)

Alpha is the probability of committing a type i error. The statement is True.

Alpha is also known as the level of significance. In hypothesis testing, the level of significance is used to determine the acceptance or rejection of a null hypothesis. It's calculated by dividing the critical value (the value beyond which we can reject the null hypothesis) by the standard deviation of the population. The level of significance is typically set to 0.05 or 0.01. If the p-value (the probability of getting the observed results by chance) is less than the level of significance, we reject the null hypothesis and conclude that the alternative hypothesis is true.

Therefore, it's true that alpha is the probability of committing a type I error, which occurs when we reject a null hypothesis that is actually true. A type I error is also known as a false positive. In other words, we conclude that there is a significant effect or relationship when there isn't one. The level of significance is a measure of how willing we are to make this type of error. If we set a high level of significance, we are more likely to make a type I error.

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The probability of no heads is given as follows:

P(No Heads) = 17.5%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of outcomes is given as follows:

200.

The desired outcomes, those without heads, are Tails, Tails, which happened 35 times, hence the probability is given as follows:

p = 35/200

p = 0.175

p = 17.5%.

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Answer: 1.35

Step-by-step explanation:

Answer:

\(\frac{23}{20}\) or \(1\frac{3}{20}\)

Step-by-step explanation:

(\(\frac{3}{4}\\\)·5)+(\(\frac{2}{5}\\\)·4)

\(\frac{15}{20}+\frac{8}{20}\)

\(\frac{23}{20}\)=\(1\frac{3}{20\\}\)

Three of them possess pairs corresponding to a Shamir secret sharing scheme, enabling any two people to determine the secret.

In this scenario, there are four people in a room. Three of them possess pairs corresponding to a Shamir secret sharing scheme, enabling any two people to determine the secret.

The remaining person is a foreign agent who has chosen a pair randomly. Thus, if any two of the three people with the valid pairs collaborate, they can successfully uncover the secret, as per the properties of the Shamir secret sharing scheme.

The presence of the foreign agent does not affect the security of the scheme unless they collaborate with another person possessing a valid pair.

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The Kutta-Joukowski theorem, which is represented by equation (3.140), was originally derived for the case of a lifting cylinder. However, it can also be applied to a two-dimensional body of arbitrary shape, as stated in section 3.16.

A more detailed explanation of the answer.
To make a physical argument for this generalization, we can draw a closed curve around the body.

The key is to draw the curve far enough away from the body such that the body appears as a very small speck in the middle of the domain enclosed by the closed curve.

By doing this, we are essentially treating the body as a point object at the center of the curve. Since the body is now a very small speck in comparison to the large domain, its specific shape becomes insignificant to the overall flow around it.

Therefore, the lifting force calculations derived from the Kutta-Joukowski theorem for the lifting cylinder should also apply to the two-dimensional body of arbitrary shape, as long as the body is small in comparison to the domain enclosed by the closed curve.

This physical argument allows us to accept that equation (3.140) can be applied in general to a two-dimensional body of arbitrary shape without requiring a mathematical proof.

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Answer:

2. x=4

3. y= -7

4. y = -7

5. w = 0

Step-by-step explanation:

2.

4x-15=1

4x=16

x=4

3.

2y+3= -11

2y=-14

y= -7

4.

2y+7= -7

2y = -14

y = -7

5.

3w+3=3

3w = 0

w = 0

Answer:

1. 150π sq.ft  2. 10π ft

Step-by-step explanation:

Equation: Area of a sector = \(\frac{x}{360}\) × π\(r^{2}\)

Where:

x = internal angle

r = radius of circle

Values from problem:

x = 60

r = 30

Plug values into equation:

Area of sector = \(\frac{60}{360}\) × π\(30^{2}\)

Simplify:

60 divided by 30 equals \(\frac{1}{6}\) and 30 squared equals 900 so...

\(\frac{1}{6}\) × 900π

900π divided by 6 equals 150π so...

\(\frac{900}{6}\) × π = 150π

150π sq. ft

Equation: Arc length = \(\frac{x}{360}\) × 2πr

Where:

x = internal angle

r = radius of circle

Values from Problem:

x = 60

r = 30

Plug values into equation:

Arc length = \(\frac{60}{360}\) × 2π30

Simplify:

60 divided by 360 equals \(\frac{1}{6}\), and 2π × 30 equals 60π so...

\(\frac{1}{6}\) × 60π

60π divided by 6 is 10π

\(\frac{60}{6}\)π = 10π

10π ft

Answer:

Step-by-step explanation:

From the given question:

a) The piecewise function for the Social Security tax s(x) is expressed as:

s(x) = x * 6.05% when x < $17,700

The 6.05% of the given amount is:

= (6.05/100) * 17700

= 1070.85

s(x) = 1070.85 when x ≥ $17,700

b) Ten years later, i.e. 1988; the percentage had increased to 7.51% & maximum taxable income also increased to $45000

The piecewise function for the Social Security tax s(x) is expressed as:

s(x) = x * 7.51% when x < $45,000

The 7.51% of the given amount is:

= (7.51/100) * 45000

= 3379.5

s(x) = 3379.5  when x ≥ $45,500

c) The difference in the Social Security and Medicare taxes paid is as follows:

In 1978, s(x) = 1070.85 when x ≥ $17,700

In 1988, s(x) = 3379.5  when x ≥ $45,500

The difference in the Social Security and Medicare taxes paid  = $3379.5 - $1070.85

The difference in the Social Security and Medicare taxes paid = $2308.65

In 1988 $ 1,578.65 less was paid than in 1978.

Given that in 1978, the Social Security and Medicare rate combined was 6.05%, up to $ 17,700 earned, while ten years later, the percent had increased to 7.51% and the maximum taxable income had increased to $ 45,000, to determine, if a person earned $ 50,000 in 1978, and $ 50,000 in 1988, what was the difference in the Social Security and Medicare taxes paid, the following calculations must be performed:

Therefore, in 1988 $ 1,578.65 less was paid than in 1978.

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The answer of the given question is  the radius of the cylinders is approximately 1 unit, based on the chosen point on the graph.

Radius is a fundamental geometric property of a circle, which is defined as the distance from the center of the circle to any point on the circle's circumference. It is a one-dimensional measurement and is usually denoted by the symbol "r". The radius is defined similarly as the distance from the center of the shape to its outer boundary.

The radius is an important parameter in many mathematical equations and formulas that involve circles or three-dimensional shapes, like calculating the area or volume of a circle, cylinder, or sphere.

To find the radius of the cylinders given the equation V = πR²h, we can rearrange the equation to solve for R. We know that the radius is constant for all cylinders in the graph, so we can use any point on the graph to find its value.

Let's choose a point on the graph where the height is h=1 and the volume is V=3.14 (using 3.14 as an approximation for π):

V = πR²h

3.14 = πR²(1)

3.14/π = R²

R = √(3.14/π)

R ≈ 1.0

So the radius of the cylinders is approximately 1 unit, based on the chosen point on the graph.

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Here is a graph of the relationship between the height and volume of some cylinders that all have the same radius, R. An equation that represents this relationship is V =πR²h (use 3.14.as an approximation for π). What is the radius of these cylinders?​

Therefore, the total distance Gabe will paddle is 2x + 400 meters. The exact value of x depends on the width of the river, which is not provided in the given information.

To find the total distance Gabe will paddle, we need to consider the distance he will travel from Q to P, then from P to R, and finally from R back to Q.

First, let's consider the distance from Q to P. Since Gabe will paddle in a diagonal line across the river, this distance can be calculated using the Pythagorean theorem.

The length of the bridge (PR) is given as 400 meters, which is the hypotenuse of a right triangle. The width of the river can be considered as the perpendicular side, and the distance Gabe will paddle from Q to P is the other side. Let's call this distance x.

Using the Pythagorean theorem, we have:

x^2 + (width of the river)^2 = PR^2

Since the width of the river is not given, we'll represent it as w. Therefore:

x^2 + w^2 = 400^2

Next, let's consider the distance from P to R. Gabe will paddle along a route beside the bridge, which means he will travel the length of the bridge (PR) again. So, the distance from P to R is also 400 meters.

Finally, Gabe will paddle back from R to Q along the shore. Since he will follow the shoreline, the distance he will paddle is equal to the distance from Q to P, which is x.

To find the total distance, we add up the distances:

Total distance = QP + PR + RQ

= x + 400 + x

= 2x + 400

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The area of the triangle is approximately 235.342 square units.

To find the area of the triangle, we can use the formula for the area of a triangle given two sides and the included angle.

The formula for the area of a triangle is:

Area = (1/2) * a * b * sin(B)

Given the values:

B = 54.3°

a = 22.7

b = 26.6

We can substitute these values into the formula to calculate the area:

Area = (1/2) * 22.7 * 26.6 * sin(54.3°)

Using a calculator, we can find the sine of 54.3° to be approximately 0.8187.

Substituting this value into the formula, we have:

Area = (1/2) * 22.7 * 26.6 * 0.8187

Calculating this expression, we get:

Area ≈ 235.342 square units

Therefore, the area of the triangle is approximately 235.342 square units.

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