Graph x < 5 on a number line

Answer: the last box for minutes is 16

And the first box for customers is 1

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

1st Box(First row)

We can set up a proportion to solve for the number of customers that would enter the store in 4 minutes:

3 customers is to 12 minutes as x customers is to 4 minutes

This can be written as:

3/12 = x/4

To solve for x, we can cross-multiply and simplify:

3/12 = x/4

3(4) = 12x

12 = 12x

x = 1

Therefore, we can expect 1 customer to enter the store in 4 minutes.

We can use the given ratios to find the time for 10 customers.

From the table, we can see that:

3 customers take 12 minutes.

1 customer takes 4 minutes (divide both sides of the ratio by 3).

So, 10 customers will take:

10 customers × 4 minutes per customer = 40 minutes.

Therefore, for 10 customers, the time is 40 minutes.

Answer: slope: undefined

y intercept: no y intercept

Step-by-step explanation:

The value of x which is the length of the base of the triangle in the question is; 29 meters

A triangle is a three sided polygon, with three interior angles.

Please find attached the possible diagram in the figure, (created with MS Word), which is a question from a mathematics textbook posted on the internet

The diagram indicates that the altitude or height of the triangle = 8 meters

The specified area of the triangle is; A = 261 square meters

The base length of the triangle = x

The formula for the area of a triangle, A, is; A = (1/2) ×Base length × Height

Therefore;

A = 261 m² = (1/2) × x × 18 m

x = 261 m² ÷ ((1/2) × 18 m) = 29 m

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Answer:

Step-by-step explanation:

Let x be the number

I hope this helps!

Answer:

13

Step-by-step explanation:

12 + 13 = 25

10+10=20

20+3+2=25

The $10 scale is a good scale to use for the y-axis. 12 months is sufficient to plot the graph and display the changes.

What is a coordinate system?

coordinate system, Setup of reference lines or curves that are used to pinpoint the locations of points in space The most popular two-dimensional system is called Cartesian (after René Descartes). Points are identified by their separation from a reference point, known as the origin, along a horizontal (x) and vertical (y) axis (0, 0).

Let the y-axis represent the money for groceries and the x-axis the number of months.

Given is that, the grocery bills range from $110 to $170.

We can thus view the changes in the grocery bills over 7 intervals by placing a scale of $10 on the y-axis.

Consequently, a $10 scale is a good scale.

Additionally, the y-axis shows the number of months. It will be sufficient to plot the graph and display the changes in grocery bills over the course of 12 months.

Therefore, 12 points are enough to represent a month.

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1. True. The PESTLE framework categorizes environmental influences into six main types: Political, Economic, Sociocultural, Technological, Legal, and Environmental factors.

These factors help analyze the external macro-environmental forces that can impact an organization's strategies and operations. 2. False. The PESTLE framework analyzes the macro-environmental factors and not the micro-environment of organizations. The micro-environment is examined through other frameworks like Porter's Five Forces, which focus on specific industry dynamics and competitive factors.

3. True. Economic forces, such as inflation, interest rates, exchange rates, and economic growth, are one of the types included in the PESTLE framework. Economic factors play a significant role in shaping business decisions and strategies.

4. False. An organization's strengths are not part of the types studied in the PESTLE framework. Strengths, weaknesses, opportunities, and threats (SWOT) analysis is a separate framework used to assess internal strengths and weaknesses of an organization.

5. True. The PESTLE framework provides a comprehensive list of influences on the possible success or failure of strategies. By considering the political, economic, sociocultural, technological, legal, and environmental factors, organizations can gain insights into the external forces that may impact their strategies and make informed decisions.

The PESTLE framework categorizes environmental influences into six main types, including political, economic, sociocultural, technological, legal, and environmental factors. It analyzes the macro-environmental forces, not the micro-environment of organizations. Economic forces are one of the types studied in the framework, while an organization's strengths are not included. The framework provides a comprehensive list of influences on the success or failure of strategies, allowing organizations to consider various external factors in their decision-making process.

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Answer:

203.5

Step-by-step explanation:

just divide 814 by 4

Answer:

203.5 miles per day

Step-by-step explanation:

divide 814 by 4= 203.5

Answer:

(x,y)=(19/5,-6/5) I'm not sure it's right, but hopefully it is

The linearized equation for the non-linear equation z = x² + 4xy + 6xy² in the region defined by 8 ≤ x ≤ 10, 2 ≤ y ≤ 4 is given by :

z ≈ 244 + 20(x - 8) + 128(y - 2).

When using the linearized equation to calculate the value of z at x = 8, y = 2, the error is 0.

1.1. To linearize the equation in the given region, we need to find the partial derivatives of z with respect to x and y:

∂z/∂x = 2x + 4y

∂z/∂y = 4x + 6xy

At the point (x₀, y₀) = (8, 2), we substitute these values:

∂z/∂x = 2(8) + 4(2) = 16 + 8 = 24

∂z/∂y = 4(8) + 6(8)(2) = 32 + 96 = 128

The linearized equation is given by:

z ≈ z₀ + ∂z/∂x * (x - x₀) + ∂z/∂y * (y - y₀)

Substituting the values, we get:

z ≈ z₀ + 24 * (x - 8) + 128 * (y - 2)

1.2. To find the error when using the linearized equation to calculate the value of z at x = 8, y = 2, we substitute these values:

z ≈ z₀ + 24 * (8 - 8) + 128 * (2 - 2)

= z₀

Therefore, the linearized equation gives the exact value of z at x = 8, y = 2, and the error is 0.

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A secant line is a line that intersects a circle in two different points. On the other hand, a chord is a segment whose endpoints lie on the circle.

To further discuss how a chord differs from a secant line, let's delve a bit deeper.

A chord is a line segment with endpoints that lie on the circumference of a circle. As an example, if line AB is drawn inside circle O, then AB is a chord.

A chord can be the diameter of the circle if it passes through the center.

A secant line is a line that intersects a circle at two different points. For example, when the line.

AB is drawn outside of circle O, it intersects the circle in two distinct points, C and D.

As a result, AB is a secant line.

Based on this explanation, it can be concluded that the difference between a chord and a secant line is that a chord is a line segment that connects two points on the circumference of a circle.

A secant line, on the other hand, is a line that intersects a circle in two different points.

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The predicted number of adults in Oak City whose main source of news is newspapers or the radio is 85

To predict the number of adults in Oak City whose main source of news is newspapers or the radio, we need to add the number of adults who answered "Newspapers" to the number of adults who answered "Radio".

According to the sample data

Number of adults who answered "Newspapers": 64

Number of adults who answered "Radio": 21

Therefore, the predicted number of adults in Oak City whose main source of news is newspapers or the radio we have to use the addition

64 + 21 = 85

Rounding this answer to the nearest whole number, we get

85 ≈ 85

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The given question is incomplete, the complete question is:

There are 44,000 adults living in Oak City. In examining attitudes toward the news, a research group asked a random sample of Oak City adults "What is your main source of news?" The results are shown below. Main Source of News Newspapers Number of Adults 64 Internet 80 Television 126 Radio 21 Other 40 Based on the sample, predict the number of adults in Oak City whose main source of news is newspapers or the radio. Round your answer to the nearest whole number.

Answer:

x = -2

Step-by-step explanation:

Answer:

Hence the positive numbers are 246, and 41

(246, 41)

Step-by-step explanation:

From the question,

Let the first positve number be \(x\)

and the other number be \(y\)

Hence,

\(x = 6y\) ....... (1)

Also,

That is,

\(x - y =205\) ........(2).

To solve for the two unknowns, substitute the value of \(x\) in equation (1) into equation (2).

Since,

\(x = 6y\)

Then

\(x - y =205\) becomes

\((6y) - y =205\\\)

Then,

\(6y - y = 205\\5y = 205\\\)

Divide both sides by 5

\(\frac{5y}{5} = \frac{205}{5} \\ y = 41\\\)

∴ the value of \(y\) is 41

Now, substitute the value of y into equation (1) to find \(x\)

Then,

\(x = 6y\) becomes

\(x = 6(41)\\x = 246\\\)

∴ the value of \(x\) is 246

Hence the positive numbers are 246, and 41

(246, 41)

Answer:

-68

Step-by-step explanation:

Using proportions, two ways of writing the fraction of these books that you read is:

4/12 and 1/3.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations, especially multiplication or division.

One example of application of proportions is for relative frequencies, as a relative frequency is given by the number of successes in the sample divided by the sample size.

In the context of this problem, it is found that:

Hence the relative frequency is:

4/12.

12 is divisible by 4, hence the fraction can be simplified as follows:

1/3.

The number of books is missing, and is of 12. (researching the problem on a search engine).

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ACTIVITY 3 :Spot the difference

Direction:Below are two sets of mathematical statements. Use these to answer the question and statements that follow. ​

Answer:

3

Step-by-step explanation:

5-(2*8)+14=

Parentheses first

5-16+14=

Then add and subtract from left to right

-11 +14

3

Answer:

1. y =x-2

2.y =½x ×5

3.y=x +5

4.y = 2x

_____________

1. 2

3. 4

is how my numbering works

!! for 2 and 3 these values are rounded

1) 693.5/18,250 = .038 x 100% = 3.8% commission

2) ~118.5%  --- divide tip/meal then x 100%

3) ~21.33%   divide sale price/over org., then subtract by 100%

Answer:

simply we can conclude here that,

p = A×100/100+TR

= 1100×100/100+5×2

= 110000/100+10

=110000/110

= 1 000

hence the principle of given amount is rs 1000

hope this helped you☺️

The lateral area of the pyramid is 192 cm².

To find the lateral area of a regular quadrilateral pyramid, we need to determine the area of all the lateral faces.

Given that the area of a lateral face is 48 cm², we can use this information to find the slant height of the pyramid's lateral face.

The slant height (l) of a regular quadrilateral pyramid can be calculated using the formula:

l = √(s² + h²)

where s is the side length of the base and h is the height of the pyramid.

In this case, we know the area of the base (B) is 36 cm². Since the base of a regular quadrilateral pyramid is a square, we can find the side length (s) of the base as follows:

s = √B

s = √36

s = 6 cm

Now, let's solve for the slant height (l). We'll use the given area of a lateral face (48 cm²):

48 = (1/2) × s × l

48 = (1/2) × 6 × l

48 = 3l

l = 48/3

l = 16 cm

Now that we have the slant height (l), we can calculate the lateral area (LA) of the pyramid using the formula:

LA = (1/2) × p × l

where p is the perimeter of the base.

In a regular quadrilateral pyramid, the perimeter (p) of the base is given by:

p = 4s

p = 4 × 6

p = 24 cm

Substituting the values, we get:

LA = (1/2) × 24 × 16

LA = 12 × 16

LA = 192 cm²

Therefore, the lateral area of the pyramid is 192 cm².

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Answer:

Step-by-step explanation:

Use notation x for the unknown variable:

Let the unknown number be x

Translate from words to math :

The sum of (add two things)

the cube of a number (x³) and (+)  the product (·) of the number (x) and 7

is equal to (=)  eight times(8·) the square of the number​(x²)

Write the mathematical equation:

x³+(x·7) = 8x²

Solve the equation to find x:

x³+7x = 8x², subtract 8x² from both sides

x³- 8x²+7x = 0, factor x

x(x²-8x+7) = 0, factor the quadratic equation (what 2 numbers have the sum 8, and product 7... numbers 1 and 7)

x(x-1)(x-7) = 0, find the roots (the solutions)

x= 0, x= 1, x= 7

Solution:

The equation given by the word problem is x³+7x = 8x²

The unknown number x, could be 0, 1, or 7

I think its the second one.  I hope it is

The time taken by both to mow the lawn is 36 minutes.

This is a question of time and work.

It is given that:-

Time taken by boy to mow the loan = 90 minutes.

Time taken by girl to mow the loan = 60 minutes.

We have to find the time taken by both of them together to mow the lawn.

LCM(60,90) = 180

Let the total work to be done to mow the lawn be 180 units.

Hence,

Efficiency of boy = 180/90 = 2 units

Efficiency of girl = 180/60 = 3 units

Total efficiency = 2 + 3 = 5 units.

Hence, time taken by both of them to mow the lawn = 180/5 = 36 minutes.

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The fill in the blanks are

1. 2PQ=PR  ⇒ given

2. PQ+QR=PR   ⇒ Segment addition postulate

3. 2PQ=PQ+QR  ⇒Transitive property

4. PQ=QR ⇒ subtraction property

5.Q is the mid-point of PR ⇒ definition of mid- point.

A congruence is a statement used in geometry that simply says that two objects are congruent, or have the exact same shape and size.

Given:

The given line segment PQR

2PQ=PR

Q is the mid point of PR.

According to given question we have

1. 2PQ=PR  ⇒ given

2. PQ+QR=PR   ⇒ Segment addition postulate

3. 2PQ=PQ+QR  ⇒Transitive property

4. PQ=QR ⇒ subtraction property

5.Q is the mid-point of PR ⇒ definition of mid- point

Multiplication Postulate If equal quantities are multiplied by equal quantities, the products are equal.

Subtraction Postulate If equal quantities are subtracted from equal quantities, the differences are equal.

Addition Postulate If equal quantities are added to equal quantities, the sums are equal.

Therefore , the fill in the blanks are

1. 2PQ=PR  ⇒ given

2. PQ+QR=PR   ⇒ Segment addition postulate

3. 2PQ=PQ+QR  ⇒Transitive property

4. PQ=QR ⇒ subtraction property

5.Q is the mid-point of PR ⇒ definition of mid- point.

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Assuming an annual appreciation rate of 5.4 percent, collection of 47 1952 silver dollars, purchased at face value, will be worth approximately $148.51 when you retire in 2057.

To calculate the future value of your collection, we can use the formula for compound interest: FV = PV * (1 + r)ⁿ, where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years. In this case, the present value is the face value of the silver dollars, which is equal to 47 * $1 = $47.

To find the future value in 2057, we need to calculate the number of years from the present to 2057, which is 2057 - current year. Assuming the current year is 2023, the number of years is 2057 - 2023 = 34.

Plugging in the values, we have

FV = $\(47 * (1 + 0.054)^{34\) = $\(47 * (1.054)^{34\) ≈ $148.51.

Therefore, your collection of 47 1952 silver dollars will be worth approximately $148.51 when you retire in 2057, assuming they appreciate at an annual rate of 5.4 percent.

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Answer:

The annual percentage yield (APY) is a measure of the return on an investment that takes into account the effect of compounding interest. To calculate the APY for an investment of $8000 at an interest rate of 4.75% compounded daily, you can use the formula:

APY = (1 + r/n)^(n*t) - 1

where r is the annual interest rate as a decimal (0.0475 in this case), n is the number of times the interest is compounded per year (365 for daily compounding), and t is the number of years (1 in this case).

Plugging these values into the formula gives:

APY = (1 + 0.0475/365)^(365*1) - 1 APY ≈ 0.0486

So, the APY for this investment is approximately 4.86%.

Step-by-step explanation:

The value of the angle θ₁, located in Quadrant IV with sin(θ₁) = -13/85, is such that cosθ₁ = 84/85.

In the given scenario, the angle θ₁ is located in Quadrant IV and sin(θ₁) is given as -13/85. We can use the trigonometric identity to determine the value of cosθ₁.

Using the Pythagorean identity sin²θ + cos²θ = 1, we can substitute sin(θ₁) = -13/85:

(-13/85)² + cos²θ₁ = 1

Simplifying:

169/7225 + cos²θ₁ = 1

cos²θ₁ = 1 - 169/7225

cos²θ₁ = (7225 - 169)/7225

cos²θ₁ = 7056/7225

Taking the square root of both sides, we get:

cosθ₁ = √(7056/7225)

Since the angle θ₁ is located in Quadrant IV where cosθ₁ is positive, the value of cosθ₁ is:

cosθ₁ = √(7056/7225)

Simplifying the square root:

cosθ₁ = 84/85

Therefore, the value of the angle cosθ₁ is 84/85.

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The complete question is:

The angle θ₁ is located in Quadrant IV and  sin(θ₁) = -13/85. What is the value of the angle cosθ₁?

Answer:

x = 4

Step-by-step explanation:

given 2 chords intersecting inside a circle , then

the product of the parts of one chord is equal to the product of the parts of the other chord, that is

9 × 4x = 8(4x + 2)

36x = 32x + 16 ( subtract 32x from both sides )

4x = 16 ( divide both sides by 4 )

x = 4

Answer:

∠PTQ = 124°

Step-by-step explanation:

∠QPT = 90° - 62° = 28°

∠PQT = 28°

∠PTQ = 180° - 28° - 28° = 124°