6 (x – 3) = 4(x – 4) + 2 (x - 1)

The number of strides the runner will make during 1 hour run will be =

10,800.

To calculate the distance or number of strides made by the runner in an

hour, the graph given above is considered as follows;

The y-axis which represents the number of strides is plotted against the x-axis which is the number of hours.

From the graph

20 minutes= 3600 strides

60 minutes = X strides

make X the subject of formula;

x= 3600×60/20

= 216000/20

= 10,800

Learn more about distance here:

https://brainly.com/question/30694816

#SPJ1

Answer:

6

Step-by-step explanation:

E ( \(x_{A} ;y_{A}\) ) = (-2, -3)

G ( \(x_{B} ;y_{B}\) ) = (4, -3)

Objective : Find the distance between two given points EG

Formula : Distance between two points

\(d = \sqrt{( x_{B} -x_{A} )^{2} + ( y_{B} -y_{A} )^{2}}\)

Solution : \(d = \sqrt{( 4 -(-2) )^{2} + (-3-(-3))^{2}} = \sqrt{( 4 -(-2) )^{2} + (-3-(-3))^{2}} =\sqrt{36+0} =6\)

This represents the distance that Mr. Stein drove, given that Mr. Smith drove x miles. The value of x must be between 0 and 140, since Mr. Smith cannot drive more than 140 miles and less than 0 miles.

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It can be simplified, evaluated, or manipulated using algebraic rules and properties.

Let x be the number of miles Mr. Smith drove. Then, the number of miles Mr. Stein drove is \(140 - x\)  , since they drove a total of 140 miles and Mr. Smith already drove x miles.

the algebraic expression for how many miles Mr. Stein drove is:

\(140 - x\)

Therefore, This represents the distance that Mr. Stein drove, given that Mr. Smith drove x miles. The value of x must be between 0 and 140, since Mr. Smith cannot drive more than 140 miles and less than 0 miles.

Learn more about expression here:

brainly.com/question/14083225

#SPJ1

Answer:

x/5 = 5280/1

Step-by-step explanation:

this is a proportion set up and then cross multiple. You will get your answer for x. Which is 26, 400 feet.

Answer:

Alright, so, the ratio is 2:5

In total, there are 7

So, 56/7=8

8x2=16

8x5=40

So after moving 2 students,

14 on the van, 42 on the bus

(you can use the true/false now)

Answer:

1. False

2. True

3. True

4. False

Step-by-step explanation:

Going to the museum:

Total: 56 students

van:bus = 2:5

2x + 5x = 56

7x = 56

x = 8

2x = 16

5x = 40

16 students go by van

40 students go by bus

40 - 16 = 24

Going back to school:

14 students go by van

42 students go by bus

van:bus = 14/42 = 1:3

42 - 14 = 28

Questions:

1. False

2. True

3. True

4. False

An equation to find the total cost of y of x rides is y = 3x.

The cost to ride 10 rides is equal to $15.

In order to write an equation that model this situation, we would assign variables to the number of tickets and the total cost respectively, and then translate the word problem into algebraic equation as follows:

Next, we would translate the word problem into an algebraic equation based on the fact that each ride requires 3 tickets and a ticket costs $1.50 as follows;

y = 3x

For the cost of 10 rides, we have:

y = 10x

When x = 1.50, the total cost is given by:

y = 10(1.50)

y = $15.

Read more on equations here: brainly.com/question/3382177

#SPJ1

Answer:143

Step-by-step explanation:5 goes into 715 143 times

Answer:

-4/3

Step-by-step explanation:

Moving from C(-4, 4) and D(5, -8) we see that x (the 'run') increases by 9 and that y (the 'rise') decreases by 12.  Thus, the slope m is rise/run, or

m = -12/9 = -4/3

Answer:

Function f is translated to the right 2 units, and then up 1 unit to obtain function g.

To see this, note that g(x) = (x+1)³ - 2 = (x-(-1))³ - 2. Comparing this to f(x) = (x-2)³, we see that replacing x with x+3 in f(x) gives g(x) = (x+3-2)³ = (x+1)³, so this transformation moves the graph of f(x) three units to the left. Then, adding the constant -2 to f(x) translates the graph down 2 units. Finally, adding the constant 2 to the result of the previous step translates the graph up 2 units, so the graph of g(x) is obtained by first translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:

Function f is translated to the right 2 units.

Function f is translated up 1 unit.

Function f is translated to the right 2 units, and then up 1 unit to obtain function g.

To see this, note that g(x) = √x - 2 + 1 = f(x-2) + 1. This means that the graph of g(x) is obtained by translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:

Function f is translated to the right 2 units.

Function f is translated up 1 unit.

Step-by-step explanation:

Answer:

1. a=-9  b=13  c=-1

2. a=1  b=1  c=-11

The prove of the given trigonometric function is given below.

The given trigonometric function is,

(sin⁴(x) - cos⁴(x))/(sin²(x) - cos²(x))

Now proceed left hand side of the given expression:

We can write the expression  as,

⇒[(sin²(x))² - (cos²(x))²]/(sin²(x) - cos²(x))

Since we know that ,

Algebraic identity:

a² - b²  = (a-b)(a+b)

Therefore the above expression be

⇒(sin²(x) - cos²(x))(sin²(x) + cos²(x))/(sin²(x) - cos²(x))

⇒(sin²(x) + cos²(x))

Since we know that,

Trigonometric Identities come in handy when trigonometric functions are used in an expression or equation. Trigonometric identities hold for all values of variables on both sides of an equation. Geometrically, these identities include one or more trigonometric functions (such as sine, cosine, and tangent).

Then,

sin²(x) + cos²(x)² = 1 is an trigonometric identity

Hence,

(sin⁴(x) - cos⁴(x))/(sin²(x) - cos²(x)) = 1

Hence proved.

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ1

The given box plot represented by the data sets in option A and B.

From the given box plot, we have

Minimum value = 3

Maximum value = 18

First quartile (Q1) = 7

Third quartile (Q3) = 13

Median = 10

Option A:

3, 4, 8, 9, 9, 12, 12, 13, 13, 16, 18

Median = 12

First quartile (Q1) = 8

Third quartile (Q3) = 13

Option B:

3, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18

Median = 10

First quartile (Q1) = 7

Third quartile (Q3) = 13

Option C:

3, 4, 8, 9, 9, 10, 12, 13, 13, 16, 18

Median = 10

First quartile (Q1) = 8

Third quartile (Q3) = 13

Option D:

2, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18

Median = 10

First quartile (Q1) = 7

Third quartile (Q3) = 13

Therefore, the correct options are B and D.

Learn more about the box plot here:

https://brainly.com/question/1523909.

#SPJ1

Answer:

if you're talking about slope intercept then

y= 8/5x + 11/5

Answer:

Intercept on y-axis is

\(b=\frac{11}{5}\)

Step-by-step explanation:

Equation of line in slope intercept form is given as

\(y=mx+b\) ------(1)

where m is slope and b is y-intercept

Re-arranging g 8x-5y=-11 yields

\(y=\frac{8}{5} x + \frac{11}{5}\)----------(2)

Comparing equation (1) and equation (2)

\(b=\frac{11}{5}\)

Answer:

False

-As the size of the sample increases, the mean of the distribution of sample doesn't change.

Step-by-step explanation:

From central limit theorem, as the size of a sample size increases, the sample mean and sample standard deviation will be far much more closer in value to the population mean(μ) and standard deviation(σ).

Thus, as the size of the sample increases, there will be no changes to the mean of the distribution of the sample mean.

Answer:

8

Step-by-step explanation:

15 - 5 = 10

10 / 1.25 = 8

Answer:

$4.20 / 7 erasers = $0.60 per eraser

So each eraser in the package costs $0.60.

Answer:

see explanation

Step-by-step explanation:

If f(x) and \(f^{-1}\) are inverse functions, then

f(\(f^{-1}\))(x) = x

Thus substitute x = \(f^{-1}\) (x) into f(x)

f(\(\frac{x+6}{5}\) )

= 5 (\(\frac{x+6}{5}\) ) - 6

= x + 6 - 6

= x

Thus f(x) and \(f^{-1}\) (x) are inverse functions

The correct option for this question is D. 128 cm³

How to solve and what is a Rectangular Prism?

The figure described in the question is a rectangular prism with dimensions of 4 cm by 4 cm by 8 cm. To find the volume of the figure, we simply multiply these three dimensions together:

Volume = length x width x height = 4 cm x 4 cm x 8 cm = 128 cubic centimeters

Therefore, the answer is D. 128 cm³.

A rectangular prism, also known as a rectangular parallelepiped, is a three-dimensional shape that has six rectangular faces. A rectangular prism is formed by taking a rectangle and extruding it perpendicular to its plane.

It has three pairs of parallel faces, with opposite faces being congruent and parallel to each other. The length, width, and height of a rectangular prism are its three dimensions, and they are all perpendicular to each other. The volume of a rectangular prism can be found by multiplying its length, width, and height together.

To know more about Rectangular Prism visit:

https://brainly.com/question/21308574

#SPJ1

Answer:

The warranty period should be of 30 months.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Optimal-Eats blender has a mean time before failure of 37 months with a standard deviation of 5 months.

This means that \(\mu = 37, \sigma = 5\)

What should be the warranty period, in months, so that the manufacturer will not have more than 7% of the blenders returned?

The warranty period should be the 7th percentile, which is X when Z has a p-value if 0.07, so X when Z = -1.475.

\(Z = \frac{X - \mu}{\sigma}\)

\(-1.475 = \frac{X - 37}{5}\)

\(X - 37 = -1.475*5\)

\(X = 29.6\)

Rounding to the nearest whole number, 30.

The warranty period should be of 30 months.

The transformations that map the strip pattern onto itself is a horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180°. Option A is the correct option.

Here, we have,

the conditions for mapping the strip transformation pattern onto itself:

The strip pattern can be mapped onto itself in two different ways.

The first way is to translate the strip pattern horizontally and then rotate it by 180° degrees.

The second way is to reflect the strip pattern across a vertical line.

Hence, the transformations that map the strip pattern onto itself can be achieved through a horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180°.

Learn more about transformations map on

brainly.com/question/7721186

#SPJ1

complete question:

Which transformations map the strip pattern onto itself?

a horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180°

a horizontal translation only

a horizontal translation, a reflection across a horizontal line, and a glide reflection only

a horizontal translation and a 180° rotation only

The length of a 45° arc with a radius of 4 miles is approximately 3.14 miles, calculated using the formula for arc length.

To determine the length of a 45° arc given a radius of 4 miles, we can use the formula: Arc length = (angle measure / 360°) x 2πr, where r is the radius of the circle and π is a constant equal to approximately 3.14.

Substituting the given values into the formula, we get: Arc length = (45° / 360°) x 2π(4 mi)Arc length = (1/8) x 2π(4 mi)Arc length = (1/8) x 8π Arc length = π

The length of the 45° arc is approximately 3.14 miles.

Summary: To find the length of a 45° arc of a circle, we use the formula: Arc length = (angle measure / 360°) x 2πr. Given a radius of 4 miles, we can substitute the values into the formula to get the length of the 45° arc, which is approximately 3.14 miles.

For more questions on arc length

https://brainly.com/question/31341388

#SPJ8

The man still owes R87,726 in taxes.

To calculate the tax amount the man still owes, we need to determine his taxable income first.

Gross income: R500,000

Less: PAYE deductions (17% of gross income): R500,000 * 0.17 = R85,000

Taxable income: R500,000 - R85,000 = R415,000

Next, we can use the tax table information provided to calculate the tax owed based on the taxable income.

Tax owed: R93,135 + 36% of (taxable income - R393,200)

Tax owed: R93,135 + 0.36 * (R415,000 - R393,200)

Tax owed: R93,135 + 0.36 * R21,800

Tax owed: R93,135 + R7,848

Tax owed: R100,983

Finally, we subtract the rebate amount of R13,257 from the tax owed to find the amount the man still owes.

Tax owed - Rebate: R100,983 - R13,257 = R87,726

Therefore, the man still owes R87,726 in taxes.

The correct option is not provided among the given answer choices.

for such more question on tax amount

https://brainly.com/question/16950901

#SPJ8

In algebra, "seven times a number" is written as 7x, which is the multiplication of seven instances of the symbol x.

An equation that includes constants, variables, and a few algebraic operations is said to be algebraic. A good example of an algebraic expression is 3x2 2xy + d. So, three different types of fundamental building blocks make up an algebraic expression: Coefficient (i.e. numbers) (i.e. numbers)

A seven-times-a-number is represented by multiplying it by seven or adding it to another integer (since this is an abbreviated successive addition ).

If x is any number, then it may be written as follows seven times: Algebraic expressions (numbers or letters) are linked by fundamental operations including addition, subtraction, multiplication, and division in mathematical language.

To learn more about algebraic expression from given link

https://brainly.com/question/4541471

#SPJ1

Complete question -

Seven times a number in algebraic expression

Answer: 58

Step-by-step explanation:

Answer:

Question 1.  38.6 %   2.  61.4%

Step-by-step explanation:

(New Cost - Old Cost) ÷ old Cost × 100

    (305 - 220) ÷ 220 x 100

    =   85/220 x 100

    = 38.6 %

2.  New Cost 305 + 50 = $355    

(Now new cost - old cost) ÷ old cost ×  100

    (355 - 220)  ÷ 220 × 100  

    =  135/220 × 100

        61.4%  

Answer:

5-8i

Step-by-step explanation:

-7-6i and -12+2i

Treat it as a polynomial. We all know that i=square root of -1, but in this case, treat it as a polynomial.

-12+5=-7

2i-8i=6i

So 5-8i

Answer: x = -5, y = 4

Step-by-step explanation:

Align the two equations according to their terms:

\(\left \{ {{-3x-3y = 3} \atop {3x+6y = 9}} \right.\)

Add the two equations. Because -3x and 3x equals zero, they can be eliminated from the equation. This results in:

\(3y = 12\\y = 4\)

Plug in y = 4 into the first equation:

\(-3x - 3(4) = 3\\\)

Solve for x:

\(-3x-12 = 3\\-3x = 15\\x = -5\)

Check by plugging in both x and y:

\(-3(-5) - 3(4) = 3\\15 - 12 = 3\\3 = 3\)

So, x = -5 and y = 4

The perimeter of the given shape as represented in the task content is; 29 cm.

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

Read more on perimeter of a shape;

https://brainly.com/question/303508

#SPJ1

The surface area of the toy box is 712 square centimeters.

Surface area is the measure of the total area that the surface of an object occupies. In other words, it is the sum of the areas of all the faces or surfaces of the object.

For example, consider a rectangular prism with dimensions length (l), width (w), and height (h). The surface area of this object would be the sum of the areas of all six faces, which are:

Two rectangular faces with area lw

Two rectangular faces with area wh

Two rectangular faces with area lh

So the total surface area of the rectangular prism would be:

Surface area = 2lw + 2wh + 2lh

The concept of surface area is useful in various fields, such as architecture, engineering, and physics. For example, in construction, knowing the surface area of a structure can help estimate the amount of materials needed for construction, such as paint or roofing tiles. In physics, surface area is important in determining the heat transfer and rate of reaction of a substance.

The surface area of the toy box can be found by summing the areas of its six faces. From the given net, we can see that the toy box has dimensions of 14 cm by 10 cm by 9 cm.

The top and bottom faces have areas of 14 cm × 10 cm = 140 cm² each.

The front and back faces have areas of 14 cm × 9 cm = 126 cm² each.

The left and right faces have areas of 10 cm × 9 cm = 90 cm² each.

Therefore, the total surface area is:

2(140 cm²) + 2(126 cm²) + 2(90 cm²) = 280 cm² + 252 cm² + 180 cm² = 712 cm²

Thus, the surface area of the toy box is 712 square centimeters.

To know more about dimensions visit:

https://brainly.com/question/16666308

#SPJ1