Zeno jumped 8 meters. Then he jumped half as far again (4 meters). Then he jumped half as far again ( 2 meters). So after 3 jumps, he was 8+4+2=14 meters from his starting place.
a) Zeno kept jumping half as far again. How far would he be after 4 jumps? 5 jumps? 6 jumps?
b) Before he started jumping, Zeno put a mark on the floor that was exactly 16 meters from his starting place. How close can Zeno get to the mark if he keeps jumping half as far again?

Calculate how much you would have in 20 years if you saved $3,000 a year at an annual rate of 8 percent with the company contributing $750 a year. Use Exhibit 1-B. (Round time value factor to 3 decimal places and answer to the nearest whole dollar.)

69/100 you would save since it decreased in value

The equivalent expression for the given expression is 3(4x + 3) will be 12x+3. Option A is correct.

The distributive property is the property that expresses the distributive law of algebraic multiplication. Similarly, in polynomial expression we can use the distributive property, for example, we can write a(c+b)  in the form of (ac+bc).

It is given that the expression is,3(4x + 3)

We have to find the equivalent expression for the given expression,

Expressions that function identically but have a different appearance are called equivalent expressions. When we enter the same value for the variable, two algebraic expressions that are equivalent will have the same result.

=3(4x + 3)

=12x+3

Thus, the equivalent expression for the given expression is 3(4x + 3) will be 12x+3. Option A is correct.

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Answer:

Yes

Step-by-step explanation:

Answer:

Your answer is 48.16 grams.

Austin needs to pour 48.16 grams of salt.

Here the total amount of salt is 71.26 grams.

But he pours 23.1 grams.

So when we minus 71.26-23.1, it is equal to 48.16 grams.

Therefore, Austin needs to pour 48.16 grams of salt.

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The value(s) of a where the tangent line to the graph of the function f(x) = -11x + is parallel to the line y = -19x - 18 is x=1,-1.

What is Slope of function?

Finding the rate at which the value of y (the dependent variable) changes in relation to x is what this method entails (independent variable). The slope itself identifies the line's slope and direction. Write the equation of the line in slope-intercept form to determine the slope from the equation. Utilize inverse procedures to find y, then write it as y=mx+b. Since the slope is the x variable's coefficient, or the number before x, you can thus readily observe the slope.

[tex]f(x)=-11 x+\frac{8}{x}$$[/tex]

Slope of function [tex]$\rightarrow f^{\prime}(x)=\frac{-21-8}{x^2}$[/tex]

Given line: y=-19 x-18

Slope [tex]$\rightarrow y^{\prime} \rightarrow-19$[/tex]

Since function and line both are parallel, hence slope of both will be equal.

[tex]$$\begin{aligned}-19 & =-11-\frac{8}{x^2} \\-8 & =\frac{-8}{x^2} \\x & =1,-1\end{aligned}$$[/tex]

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Answer:

Step-by-step explanation:

i believe the total would be 4

Answer: The set of integers greater than or equal to 2 is {2, 3, 4, 5, ...}. This set can be represented using set notation as:

{y: y is an integer and y ≥ 2}

This set includes all the integers that are greater than or equal to 2, including 2 itself. It does not include negative integers or fractions.

For example, the following are all elements of this set:

2, 3, 4, 5, 6, 7, 8, ...

The following are not elements of this set:

-1, 0, 1, 1.5, -3.14, ...

This set is infinite, because there are an infinite number of integers greater than or equal to 2.

Answer:

x > 1

Step-by-step explanation:

I  am solving this equation, not including the "_" in the equation.

-3(x+2)<-9

Multiply both sides by -1 to reverse the inequality.

3(x+2)>9

Divide by 3

x+2>3

Subtract

x>1

Answer:

5, -11. -3, 8. 10, 17. -15, 13.

Step-by-step explanation:

All you have to do is switch x and y

The side lengths of the triangle are 11.1, 21.4, and 18.5 units.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

The given sides of the right triangle are 3m, 2m+14, and 5m.

As per the Pythagorean theorem, it follows:

(2m + 14)² = (3m)² + (5m)²

4m² + 196 + 56m = 9m² + 25m²

30m² -56m - 196 = 0

15m² - 28m - 98 = 0

[tex]m=\frac{-(-28)\pm\sqrt{(-28)^2-4(15)(-98)}}{2(15)}\\\\m=\frac{28\pm\sqrt{6664}}{2(15)}\\\\m =\frac{28\pm81.6}{2(15)}\\\\m=3.7\text{ or } m=-1.8[/tex]

Since the lengths cannot be negative, the value of m is m = 3.7.

Therefore, the side lengths of the triangle are:

3m = 3(3.7)

= 11.1

2m + 14

= 2(3.7) + 14

= 21.4

and,

5m

=5(3.7)

= 18.5

Hence, the side lengths of the triangle are 11.1, 21.4, and 18.5 units.

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The one-way communication time between the Jupiter and Earth increases.

Radio waves are a type of electromagnetic radiation with the longest wavelengths in the electromagnetic spectrum, typically with frequencies of 300 Ghz and below.

Given is that Jupiter and Earth travel along their respective orbits.

As the Jupiter and Earth travel along their respective orbits, they start to get apart from each other. This leads to an increase in one-way communication time.

Therefore, the one-way communication time increases as the Jupiter and Earth travel along their respective orbits.

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Answer:

188 cents or $1.88

Step-by-step explanation:

We first want to find how many cents per one inch, and we do this by dividing 17 from 68 (68/17). This gets us 4 cents per inch. Now we need to multiply 4 by 47 (4 x 47). Now we get 188 cents. The equation for this would be y = 4x

Answer:

x > 65/7

Step-by-step explanation:

First, we make the equation positive.

-7/5x < -13

We have to switch the sign when multiplying or dividing a negative number.

7/5x > 13

Now, we multiply by 5 and divide by 7.

7x > 65

x> 65/7

The time taken for the population to reach 26.6 million is 2 years while the population in year 2000 is 18.5 million.

We can be able to  define population growth as the process by which the population of an area is increasing. We know that the increase or the decrease of population would have to be an exponential function.

Given that we have the function A =18.5e^0.1708t where A is the population after a given time from year 2000 and t is the number of years after year 2000. It then follows that 18.5 million refers to the population of the united states as at year 2000.

We now have;

26.6 =18.5e^0.1708t

26.6/18.5 = e^0.1708t

1.44 = e^0.1708t

ln(1.44) = 0.1708t

t = ln(1.44)/ 0.1708

t = 2 years

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The perimeter of the parallelogram is 24 units

From the question, we have the following parameters that can be used in our computation:

The parallelogram is added as an attachment

When the number of units on each side of the parallelogram is counted, we have the following representation

EH = FG = 7 units

EF = GH = 5 units

The perimeter of the parallelogram is the sum of the side lengths

So, we have the following representation

Perimeter = EH + EF + FG + GH

Substitute the known values in the above equation, so, we have the following representation

Perimeter = 7 + 7 + 5 + 5

Evaluate the sum

Perimeter = 24

Hence, the perimeter is 24 units

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Answer:

[tex]y = 5 - 3z[/tex]

Step-by-step explanation:

[tex]6z+2y=10[/tex]

divide by 2

[tex]3z + y = 5[/tex]

move the terms

[tex]y = 5 - 3z[/tex]

The amount of sample after 25 years and the half life are given as 51.8 g and 12.83 years respectively.

An exponentially decaying function has a general form f(x) = (1 -r)ˣ, where r is called the decay rate. it can be found by having any two values of x for which f(x) is known.

The given function for the decay of an isotope is given as A(t) = 200[tex]e^-0.054t[/tex].

Now, the given problem can be solved as follows,

(a) The amount of sample after 25 years is given as,

A(25) = 200[tex]e^{-0.054 \times 25}[/tex]

         = 200[tex]e^{-1.35}[/tex]

         = 200 × 0.259                      

         = 51.8

(b) The half life can be calculated as,

100 =  200[tex]e^{-0.054t}[/tex]

=> [tex]e^{-0.054t}[/tex] = 1/2

=> t = 12.83        

Hence, the sample left after 25 years will be 51.8 g and it will take 12.83 years for the sample to decay to half of its amount.

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Evan's error was that he subtracted  -2 1/2 from 4, and thus he got  6 1/2.  On adding he would be getting  1 1/2

A straight line of numbers is shown visually as a number line. This line is used to compare integers on an endless line that extends on both sides, either horizontally or vertically, at equal intervals. On a horizontal number line, the numbers grow as we walk to the right and decrease as we move to the left.

It is given that Evan added -2 1/2 and 4 but got 6 1/2

The mistake that Evan did was instead of adding, he substracted -2 1/2 from 4, and thus he got 6 1/2. This is because

4 -  (-2 1/2)

= 4 + 2 1/2

=  6 1/2

This is wrong as he was asked to add -2 1/2 and 4 not to subtract.

Therefore, on adding -2 1/2 and 4, we get,

= 4 - 2 1/2

= 1 1/2

Evan's error was that he subtracted  -2 1/2 from 4, and thus he got 6 1/2         .  On Evan's error was that he subtracted  from 4, and thus he got          .  On adding he would be getting  1 1/2

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Answer:1285.7 meters per second.

Step-by-step explanation: divide 900,000 meters by 700 seconds

Answer:

A plane travels 360,000 meters in 900 seconds

Step-by-step explanation:

Answer: 4.5 years or 54 months

Step-by-step explanation: Divide $4,000 by $75 a month to get 53.33 then round to 54. 54 months = 4.5 years.

The perimeter of the quadrilateral is √2+√8+√5+√13

We can use the distance formula to find the length of the segments that make up the quadrilateral.

We must find the length of the segments between the points (0,2),(1,3)(1,3),(3,1)(3,1),(2,−1)(2,−1),(0,2)

Recall the distance formula d=√(x2−x1)2+(y2−y1)2Applying this formula to the four pairs of points gives the following.

d=√(1−0)2+(3−2)2=√1+1=√2d=√(3−1)2+(1−3)2=√4+4=√8d=√(2−3)2+(−1−1)2=√1+4=√5d=√(0−2)2+(2+1)2=√4+9=√13

So the perimeter of the quadrilateral is √2+√8+√5+√13

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Answer:

no clue bro just help yourself

Step-by-step explanation:

add them

or multiply or divide or subtract and you'll get it

The equation of the tangent to the given curve x = t⁴ + 3 , y = t³ + t at the corresponding point is y = x - 2   .

In the question ,

it is given that ,

the parametric equation is x = t⁴ + 3 , y = t³ + t ,

differentiating with respect to t ,

we get ,

dx/dt = 4t³  and   dy/dt = 3t² + 1

On dividing dx/dt by dy/dt to get the slope ,

we get

dy/dx = (3t² + 1)/ (4t³)

Substituting in t=1

dy/dx = (3 + 1)/4 = 1

Slope (m) = 1 ;

Substituting t = 1 , in the parametric equation ,

we have , x = 4 and y = 2 .

So , (y - 2) = 1(x - 4)

y - 2 = x - 4

y = x - 2

Therefore , the equation of the tangent is  y = x - 2  .

The given question is incomplete , the complete question is

Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x = t⁴ + 3 , y = t³ + 3 ; t = 4 ?

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Step-by-step explanation:

that is a college question ?

oh my ...

to clarify :

perpendicular means intersecting or touching at a right angle (90°).

bisector means it is a line that cuts the other line in half.

1.

because of the bisector this means DF = FC = DC/2.

so, since FC = 17, so is DF (=y) = 17.

2.

for the same reason

2x - 3 = x + 8

x - 3 = 8

x = 11

the angle must be 90°.

so,

5y = 90

y = 18

3.

for the same reason

10 = 4a

a = 10/4 = 2.5

4.

for the given reasons of 1-3, this figure is a kite. that means the left side is a mirror image of the right side. so, all the lengths on one side are equation to the lengths of the other side.

x - 11 = 19

x = 30

5.

for the same reasons

3y + 5 = 26

3y = 21

y = 7

6.

the perimeter of EDP is then

EP + DP + ED = 19 + 19 + (9 + 9) = 56

because ED = EC + CD

and for the above reasons EC = CD = 9

so, ED = 9 + 9 = 18

7.

the perimeter of EDQ is then

EQ + DQ + ED = 26 + 26 + 18 = 70

8.

for the same reasons as above

x = 90°

9.

remember, the sum of all angles in a triangle is always 180°.

180 = 90 + 55 + y

y = 180 - 90 - 55 = 35°

10.

180 = y + M + z = 35 + (55+71) + z = 161 + z

z = 180 - 161 = 19°

The size of each angle of triangle, starting with the largest 90°, 45° and 45°.

Polygon which has three sides and three vertices is called as triangle.

Sum of all the angles of the triangle is 180°.

Given that a right angled triangle has two equal sides.

And the largest triangle of right angled triangle is 90°.

Right angled triangle which has two equal sides can be called right angled isosceles triangle.

And if one angle of isosceles triangle have angle is 90°. Then the rest of the two angle will be 45°.

Therefore, The rest of these two angles of the right angled triangle are 45⁰.

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Option-A is It comes in a variety of forms, making it possible to compare the effects of numerous groups and variables satisfy the statement.

Given that,

The most typical inferential statistical method used to evaluate trials is analysis of variance because

We have to find which of the options are suitable for the given statements.

Option-A is It comes in a variety of forms, making it possible to compare the effects of numerous groups and variables satisfy the statement.

Option-B is It comes in one form, and compared to two-sample tests, it is more accurate for comparing two groups does not satisfy the statement.

Option-C is It is the only statistical method that can test both within- and between-subjects factors does not satisfy the statement.

Option-D is The majority of academics are more focused on differences between one sample and the population as a whole does not satisfy the statement.

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Answer:

126 lineups

Step-by-step explanation:

This is a problem in combinatorics which asks in how many ways can a subset of 5 be formed from a larger set of 9

In general, if you were to see how many ways a subset of [tex]r[/tex] can be formed from a larger subset [tex]n[/tex] denoted by [tex]nC_r[/tex] we use the formula

[tex]nC_r = \dfrac{n!}{ r! (n - r)! }[/tex]

There are calculators that can compute this and I used a scientific calculator to do so.

[tex]9C_5 = 126[/tex]

Answer:

70

Step-by-step explanation:

Substitute the value -3 into the expression and simplify:

10(4 - -3)

10(4 + 3)

10(7)

70

The solution to the inequality n - 4/7 ≥ -2/3 is (a) n ≥ -2/21

From the question, we have the following parameters that can be used in our computation:

n minus four sevenths is greater than or equal to negative two thirds

By definition, inequalities are used to relate unequal values

Express the inequality properly

So, we have

n - 4/7 ≥ -2/3

Add 4/7 to both sides

So, we have

n ≥ -2/3 + 4/7

Evaluate the sum of the fractions

This gives

n ≥ -2/21

Hence, the solution is (a) n ≥ -2/21

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