Graph the line that represents a proportional relationship between d and t with the property that an increase of 5 units in t corresponds to an increase of 8 units in d.

What is the unit rate of change of d with respect to t? (That is, a change of 1 unit in t will correspond to a change of how many units in d?)

The unit rate is

?

Graph the relationship.

Yes this question can be proven by mathematical induction

What do you mean by induction in mathematics?

For each and every natural number n, a statement, theorem, or formula can be proved using the mathematical induction technique. By generalizing this into the "Principle of Mathematical Induction," which we would utilize to demonstrate any mathematical assertion.

Here, n ≥ 1

1/1.2 + 1/2.3 + 1/3.4 + .............. + 1/n(n +1)

We employ the idea of Sigma here.

S/1/r(r + 1) { r = 1 to n }

Sigma [1/(r + 1) - 1/(1/r)] { r = 1 to n }

put r = 1 \s1/1 - 1/(1 + 1) = 1 - 1/2

put r = 2 \s1/2 - 1/(2 +1) = 1/2 - 1/3

put r = 3 \s1/3 - 1/(3 +1) = 1/3 - 1/4

........................................................... put r = n 1/n - 1/(n + 1)

after adding

Sigma = [1/(r+1) - 1/(1/r)] {r = 1 to n } = 1 -1/2 + 1/2 -1/3 + 1/3 - 1/4 + ............1/n - 1/(n +1)

= 1 - 1/( n +1) = n/( n +1)

Consequently, 1/1.2 + 1/2.3 + 1/3.4 +... 1/n(n + 1) = n/(n + 1).

so it proved

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The person who runs fastest is Zach.

Ron runs 9 feet per second: 9 ft/s

Zach runs 410 feet in 49 seconds:

410/49 ft/s

=8.36 ft/s

= 8.4 ft/s (Approximately)

Katie runs 1 mile in 412 seconds:

1 mile = 5280 ft

5280/412 ft/s

=12.8 ft/s

Noah  runs 870 feet in 1 minute:  

= 870/60 ft/s

= 14.5 ft/s

Hence,

Ron 9 feet per seconds

Zach 8.4 feet per seconds

Katie  12.8 feet per seconds

Noah 14.5 feet per seconds

So, Zach is the fastest.

Therefore the fastest is Zach.

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A system of linear inequalities that represents this scenario is given by:

p + s ≥ 10

5.50p + 3.50s ≤ 117

An inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

In order to write a system of linear inequalities to represent the scenario, we would assign variables to the cost of the beginner class and advanced class, and then translate the word problem into algebraic equation as follows:

Since Latisha cannot buy more than (≥) 10 vegetables, the inequality to represent this is as follows:

p + s ≥ 10

Since Latisha's budget cannot exceed (≤) $117, the inequality to represent this is as follows:

5.50p + 3.50s ≤ 117

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Answer:

18$

Step-by-step explanation:

this is so i can reach twenty characters.

The researchers include the scenario where subjects wear no bracelet at all are when it comes to mosquitoes, volunteers in each block should live in similar conditions.

An experiment might involve giving a novel drug to rats to see how they respond to learning about it. When you visit a new coffee shop but are unsure of how the coffee will taste, that is an example of an experiment. the act of carrying out a test like that; experimenting. An experiment is a procedure used as part of the scientific method to test a hypothesis. The independent and dependent variables are the two most important variables in every experiment. To investigate the impact of the independent variable on the dependent variable, it is either controlled or altered.

Given,

A company makes a bracelet containing magnets that they claim improves balance and overall athletic performance. researchers recruit volunteers for an experiment.

The researchers include the scenario where subjects wear no bracelet at all are:

When it comes to mosquitoes, volunteers in each block should live in similar conditions.

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Answer:

y = [tex]\frac{4}{3}[/tex] x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, 4) ← 2 points on the line

m = [tex]\frac{4-0}{0-(-3)}[/tex] = [tex]\frac{4}{0+3}[/tex] = [tex]\frac{4}{3}[/tex]

the line crosses the y- axis at (0, 4 ) ⇒ c = 4

y = [tex]\frac{4}{3}[/tex] x + 4 ← equation of line

They will require 4 (4/11) days to complete the remaining work together.

Time is the duration during which any activity or work happens or continues.  Work is a task or set of activities to achieve a certain result

It takes Ann alone 10 days to translate a document.

Ann's work in one day = 1/10

In 2 days = 2 / 10

Work left = 8 / 10

Ben alone now takes 12 days to translate a document.

Ben's work in one day = 1/12

We will now use addition.

Combined work of both Ann and Ben in 1 day = 1 / 10 + 1 / 12 = 11 / 60

Time taken to complete the rest of the work = 8 / 10 ÷ 11 / 60

= 48 / 11 = 4.4 days.

As a result, they need 4 (4/11) days to finish the remaining work together.

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Answer:

Answer:

This is in Standard form.  Did you mean scientific form?

1.47 x [tex]10^{-4}[/tex]

Step-by-step explanation:

You move the decimal so that the number is between 1 and 10.  Then since in standard form the number is much less than 1.47, you determine how muhc less my how many places you need to move the decimal to put it back in standard form.  Since you would need to move the decimal 4 places to the left, the exponent would be -4

Answer:

Step-by-step explanation:

slope=change in y over change in x

6-2=4

6--2=6+2=8

-4/-8=1/2

Answer:2

Step-by-step explanation:

2*4=8

2*25=50

The probability that the vertical faces have the same color painted is 0.6875

There are 6 faces on a cube.

Each face of the cube will either be red or blue.

The probability that one face will have red color = probability that the face will have blue color = 1/2

It is given that the cube is placed on a horizontal surface and the 4 vertical faces have the same color.

The painting of the faces of the cube clearly follows a binomial distribution.

Therefore the probability to color the faces of a cube

= P(4 faces are red, 2 faces blue) + P(4 faces are blue, 2 faces red) + P(5 faces blue) + P(5 faces red) + P(All faces blue) + P(all faces red)

For any binomial distribution

ⁿCₓ X pˣ (1 - p)ⁿ⁻ˣ

where

n = no. of sample

x = random variable

p = probability of success

Hence we get

⁶C₄ X 0.5⁴ 0.5²   + ⁶C₄ X 0.5⁴ 0.5²   +    ⁶C₅ X 0.5⁵ 0.5    +   ⁶C₅ X 0.5⁵ 0.5

⁶C₆ X 0.5⁶    +    ⁶C₆ X 0.5⁶

= 15 X 0.015625    +    15 X 0.015625    +    6 X 0.015625    +    6 X 0.015625    +    0.015625

= 0.6875

Therefore we get the probability of having the four vertical faces of the same color to be 0.6875.

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Answer:

Step-by-step explanation:

to find area of a rectangle we use (L)(W) so we do that here for both of these rectangles first find the area of the black top

5x(3x)

15x^2 is the area of the blacktop

The “!ield” area is next

12x(7x)

84x^2 is the area now we just subtract the two numbers by subtracting coefficients but keeping the rest the same

84x^2-15x^2

69x^2 is the area of the rectangle that is not black top

B- the foundtain we find with the area of circle formula r squared times pi

3x(3x)pi

9x^2pi

Now we just subtract this from the area of the rectangle

69x^2 -9x^2pi is the area

Hopes this helps please mark brainliest

The degree measure of each angle in the triangle is

∠H = 59°

∠F = 39°

Angle sum property of triangle says that sum of all the triangle is always equal to 180°

∠G is given to us as 90°

So by applying the property we an say that

90 + (3x - 14) + (5x - 16) = 180

8x = 180 - 90 + 14 + 16

8x = 120

x = 15

∠H =  5x - 16

∠H = 5*15 - 16

∠H = 75 - 16

∠H = 59°

∠F = 3x - 14

∠F = 3*15 - 14

∠F = 45 - 14

∠F = 39°

Therefore ∠H = 59° and ∠F = 39°

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The total number of oranges in the pyramidal stack is 78.

The oranges are stacked by the grocer in a pyramid like shape,

The base of the pyramid is rectangular with a size of 5 by 8 oranges,

So, total number of oranges in the base can be found as,

= 5 x 8

= 40 oranges.

One orange has four oranges below it. So, if there are 40 oranges in the base, the upper layer will have one row of oranges reduced from each side of the rectangular base.

So, every next level will have (L-1)(B-1) oranges, where L and B are the length and breadth of every preceding rectangle.

Hence, Oranges in level 1 = 4x8

Oranges in level 2 = 3x7

Oranges in level 3 = 2x6

Oranges in level 4 = 1x5

Hence, total oranges are, (40+21+12+5) oranges.

Total oranges stacked are 78 oranges.

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The area of the garden is 7 square feet.

The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth. An example of a quadrilateral with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. A rectangle is a shape with only two dimensions. A rectangle's area (A) is calculated by multiplying its length ('a') by its breadth ('b'). Area of Rectangle is therefore equal to (a× b) square units.

Given,

Width = 3/4

Length = 9 + 1/3

Length = 28/3

Area:

Length × Width

3/4 × 28/3

84/12

7

The area of the garden is 7 square feet.

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Answer:

===========

Note:

Other sides are 2 and 11. This is not a correct question as sum of two smaller sides (2 + 6) is less than the longest one (11), hence there is no such possible triangle.

Reflection at point y = -6 will have coordinates as

preimage      image

Q(0, -9)          Q' (0, -6)

R(4, -9)           R' (4, -6)

S(6, -8)           S' (6, -5)

T(2, -8)           T' (2, -5)

The transformation involve is reflection and this is a type of transformation that produces the mirror image of the preimage

The transformation rule to get the mirror image is (x, y) → (x, y + 3)

The coordinates are applied as follows

Q(0, -9) → (0, -9 + 3) → Q' (0, -6)

R(4, -9) → (4, -9 + 3) → R' (4, 6)

S(6, -8) → (6, -8 + 3) → S' (6, -5)

T(2, -8) → (2, -8 + 3) → T' (2, -5)

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The equation of line: y = 2x - 9

slope = 2

y-intercept = (0, -9)

The graph of the line y = 2x - 9 is as shown below.

In this question we have been given a point (6, 3) and slope m = 2

We need to find an equation of line passing through (6, 3) with slope m = 2

Using formula of the point-slope form:

(y - y1) = m(x - x1)

(y - 3) = 2(x - 6)

y - 3 = 2x - 12

y = 2x - 12 + 3

y = 2x - 9

This is slope-intercept form of equation of line.

slope = 2

y-intercept = -9

Therefore, the equation of line: y = 2x - 9

slope = 2

y-intercept = (0, -9)

The graph of the line y = 2x - 9 is as shown below.

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Answer

[tex]60\sqrt{x} 2[/tex]

Step-by-step explanation:

Answer:

StartRoot 60 EndRoot

Step-by-step explanation:

Edge

Answer:

i don't know

Step-by-step explanation:

The probability that the sample mean selling price was more than $210,000 is 0.9772.

The given values are:

The mean selling price(μ) = $215000

Standard deviation(σ) = $25000

The random sample (n) = 100

We have to find the probability that the sample mean selling price was more than $210000.

z-score with z-bar= 210000

z = (x-bar - μ) / (σ/ √n)

 = ( 210000 - 215000) / (25000/ √100)

 = -5000/ 2500

 =-2

Using z-tables, the probability is:

Probability = P[z> -2]

                  = 1 - 0.0228

                  = 0.9772

Therefore the probability is 0.9772.

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The probability the selected dog is medium and brown by Sarah is 6/49.

Probability = favourable outcome/ total outcome

The table for the given question is attached.

Total dogs owned by Sarah = 7.

Total medium sized dogs = 2.

Total brown coloured dogs = 3

Probability( medium sized ) = 2/7

Probability( brown coloured ) = 3/7

Probability( medium sized and brown coloured ) = (2/7)×(3/7)

Probability( medium sized and brown coloured ) = 6/49

Thus, the probability the selected dog is medium and brown is 6/49.

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An inequality to find the number of batches of rolls Liz can make is 13n/4 ≤ 26 and she cannot make more than 8 batches of rolls.

In order to solve this word problem, we would assign a variable to the number of batches, and then translate the word problem into an algebraic inequality as follows:

Let the variable n represent the number of batches.

Since Liz has 26 tablespoons of yeast left in the jar and each batch of biscuits takes 3 1/4 -tablespoons, we have:

3 1/4 (n) ≤ 26

13n/4 ≤ 26

Cross-multiplying, we have:

13n ≤ 26 × 4

13n ≤ 104

n ≤ 104/13

n ≤ 8.

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Complete Question:

Liz wants to make several batches of biscuits. She has 26 tablespoons of yeast left in the jar and each batch of biscuits takes 3 1/4 -tablespoons. Write and solve an inequality to find the number of batches of rolls Liz can make.

Step-by-step:

1)Combine multiplied terms into a single fraction

1/7a+ 1/7

1a/7+1/7

2)Multiply by 1

3)Combine fractions with a common denominator

Solution

a+1/7

Hope That helps!

The x-intercept of the function represented on the graph is 3

The graph represents the given parameters

To determine the x-intercept of the graph, we set y = 0

This means that the x-intercept of the graph is the point, where the line of the graph crosses the x-axis

For the graph, we have

When y = 0, the function has a value of 3

This means that

x-intercept is 3

Hence, the x-intercept of the graph is 7

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The formula for the cost if the line rental is £20 and the price of calls made is £15 will be 20 + 15p.

It should be noted that an expression is used to illustrate the relationship given between the variables.

In this case, the monthly phone contract is made up of the fixed line rental and the price represented by p.

The appropriate expression to illustrate this information will be:

= Fixed cost + Calls made

= 20 + 15(p)

= 20 + 15p

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