Which equation is used to calculate an object's speed? speed= distance time speed=time distance speed= distance x time speed=time x distance

The linear function y = 2x + 5 shows that Sarah charges $5 as fixed amount before she begins selling newspapers.

The table representing amount of money which Sarah charges her customers to sell newspapers.

Let us consider 'x' represents the time per hour charges taken by Sarah from customers.

In the table,

For zero hours charges are $5.

It means Fixed charges taken by Sarah to sell newspaper.

Difference between the rate per hour is,

$7 - $5 = $2

$9 - $7 = $2

It represents for Sarah charges $2 per hour.

let us consider 'y' that represents total amount charges by Sarah.

Required linear function for selling news paper and charging amount is

y = $5 + 2x

⇒ y = 2x  + 5

Therefore, the linear function y = 2x + 5 represents option 1. Sarah charges $5 before she begins selling newspapers.

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We can answer the questions in the following way:

Barriers to economic development are all those things that hinder the growth and development of an economy of a nation.

Many factors act as barriers to economic development, like lack of education, healthcare, inadequate infrastructure, lack of access to capital, etc.

These barriers can hinder people's ability to achieve their full potential, and lead to lower levels of economic growth and development.

Taking care of these issues by the government is important to promoting sustainable economic development.

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Answer: $105

Step-by-step explanation:

I would take 5+2=7 then take 7×15=105

Answer is $105 to ship.

Answer:

C

Step-by-step explanation:

8 x 10^4 = 80,000

3 x 10^3 =   3,000

1  x  10 ^2 =    100

2 x 10^1 =         20

add it up

83,120

C is correct

Answer:

a. The present value of these receivables is $42,123.64

b. The total value at the end of 10 years is $69,257.02

c. The present value of these payments is $10,059.37

Step-by-step explanation:

The calculated value of the length of segment DF is 51.96 units

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

The right triangle

The length of segment DF is then calculated as

sin(60) = DE/DF

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

sin(60) = 45/DF

So, we have

DF = 45/sin(60)

Evaluate the quotient

DF = 51.96

Hence, the segment DF is 51.96 units

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The third term in the expansion of the expression (5x - 7y)³ is 735xy².

Given expression is,

(5x - 7y)³

We have to expand this.

We know that,

(a + b)³ = a³ - 3a²b + 3ab² - b³

Using this,

(5x - 7y)³ = (5x)³ - (3 × (5x)² × 7y) + (3 ×(5x) × (7y)²) - (7y)³

               = 125x³ - (3 × 25x² × 7y) + (3 × 5x × 49y²) - 343y³

               = 125x³ - 525x²y + 735xy² - 343y³

Here the third term is 735xy².

Hence the third term is 735xy².

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The probability that they both select a poodle is bigger. The probability is 0.074

In the store, there are 11 puppies, and 3 of them are poodles.

If Rebeca and Aaron chose at random, then the probabilities are; for Rebbeca, there is a 3/11 probability to get a poodle ( because there are 3 poodles of eleven dogs) and the probability for Aaron is 2/10 because now there are one less poodle (and in consequence one less puppy)

now, the joint probability of these two events happening is the product of each probability, this is:

p = (3/11)*(2/10) = 6/110, that we can simplify at 3/55 if we divide both denominator and numerator by 2.

If the dog is replaced after Rebeca picked hers, then Aaron also has a 3/11 probability of picking a poodle, and in that case, the joint probability is:

q = (3/11)*/3/11) = 9/121

now, p = 3/55 = 0.055 and q = 9/121 = 0.074

Thus, this means that the probability of both of them selecting a poodle is bigger when the dog is replaced (which makes a lot of sense)

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The line a and line d are perpendicular to each other.

Perpendicular lines and intersecting lines are the same because they both describe 2 lines that cross one another.

Perpendicular lines cross one another in a specific way.  The intersection of perpendicular lines forms 90 degree angles.

Constructing lines a and d:

After constructing the two lines; line a and line intersect or meet each other at 90 degrees to the horizontal.

Thus, we can conclude that the line a and line d are perpendicular to each other.

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Answer:line a and line d are perpendicular

saw the answers

Jocelyn would need to save $1333.33 each year with 7% interest.

To calculate how much Jocelyn needs to save for the down payment over the next three years, we first need to determine the total down payment required. If the down payment is stated as $4000, then that is the total amount needed.

Assuming that Jocelyn wants to make the down payment in three years, we can calculate how much she needs to save each year by dividing the total down payment by three:

$4000 / 3 years = $1333.33 per year

So Jocelyn would need to save approximately $1333.33 each year for the next three years in order to have enough for the $4000 down payment.

Correct Question :

JUST $4000 DOWN PAYMENT!

LOW 7% INTEREST RATE!

5 YEARS TO REPAY YOUR LOAN!

In order to afford the down payment, how much will Jocelyn need to save for each of the next three years

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The rational function f(x) = (x² + 1)/(x² + 2x + 2) has no vertical asymptotes and no holes.

We have,

A rational function is a function that can be expressed as the ratio of two polynomials.

It can have vertical asymptotes and/or holes in its graph, depending on the behavior of the denominator polynomial.

To construct a rational function with no vertical asymptotes and no holes, we need to ensure that the denominator polynomial does not have any real roots.

This means that the denominator polynomial should either have no roots or only complex roots.

One way to achieve this is to use a quadratic polynomial in the denominator that has no real roots.

For example, consider the function:

f(x) = (x² + 1)/(x² + 2x + 2)

The denominator polynomial x² + 2x + 2 has no real roots because its discriminant, 2² - 4(1)(2) = -4, is negative.

This means that the function f(x) has no vertical asymptotes.

To check if the function has any holes, we need to simplify the function by canceling out any common factors between the numerator and denominator.

However, since the numerator x² + 1 has no common factors with the denominator, there are no terms to cancel out.

Therefore, the function f(x) has no holes either.

Thus,

The rational function f(x) = (x² + 1)/(x² + 2x + 2) has no vertical asymptotes and no holes.

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Answer:

28(17) + π(7^2)

= 476 + 49π square meters

= 629.94 square meters

Answer: The scale factor used to create the image is 0.8

Step-by-step explanation: To determine the scale factor used to create the image, we can divide the corresponding side lengths of the dilated polygon D' by the corresponding side lengths of the original polygon D.

For example, the top and bottom sides of polygon D have a length of 8, while the corresponding sides of polygon D' have a length of 6.4.

So, the scale factor used to create the image is:

6.4 / 8 = 0.8

Therefore, the scale factor used to create the image is 0.8.

To accumulate $88,000 (future value) in 17 years in a fund that attracts an APR of 4%, the monthly deposit should be $301.89

The monthly deposit can be determined from the future value using an online finance calculator.

N (# of periods) = 204 months (17 years x 12)

I/Y (Interest per year) = 4%

PV (Present Value) = $0

FV (Future Value) = $88,000

Results:

PMT (Monthly Deposits) = $301.89

Sum of all periodic payments = $61,585.56

Total Interest = $26,414.44

Thus, when $301.89 is deposited monthly in a fund earning 4% APR, the future value can become $88,000.

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When x = 7, what is the second coordinate in a scatter plot is: D. 112.8.

The approximate value x=4 to the nearest whole number is; C. 1,168.

In this scenario, the x-values would be plotted on the x-axis (x-coordinate) of the scatter plot while the y-values would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an exponential equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the x-values and y-values, an exponential equation for the line of best fit is given by

[tex]y = 31.86e^{0.18x}[/tex]

when x = 7, the second coordinate in this scatter plot is given by;

[tex]y = 31.86e^{0.18(7)}[/tex]

y = 112.8

logy = 0.75821x+0.03442

logy = 0.75821(4) +0.03442

logy = 3.03284 +0.03442

logy = 3.06726

y = log⁻¹(3.06726)

y = 1167.5084 ≈ 1,168

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Answer:

Almost equals 28°

Step-by-step explanation:

cos(x)= 12/18

x= cos^-1 (12/18)

So it equals 48.1896°

Answer:

Step-by-step explanation:

no higher than 4

Answer:

Step-by-step explanation:

сosx*cosy+sinx*siny

Suppose a trapezoid is defined as a quadrilateral with at least 1 pair of parallel sides. Thus, trapezoids will change the venn Diagram by being classified as under 1 pair of parallel sides.

In geometry, a quadrilateral with at least one set of parallel sides is referred to as a trapezium in American or Canadian English, or a trapezium in British as well as other forms of English. In Euclidean geometry, a trapezium is a convex quadrilateral by definition. The bases of a trapezium are the parallel sides. Thus, trapezoids will change the venn Diagram by being classified as under 1 pair of parallel sides.

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Probability that a random sample of 45 oil changes result in a sample mean time less than 10 minutes is 0.0001

Given information:

The mean time is, = 16.2 min.

The standard deviation = 3.4 min.

Let X' is sample mean time :

Now the sample mean time is given by the equation

Z = (X' - μ) / (σ/√n)

Where, μ population mean time

(σ) is Standard deviation

(A) Probability of random sample of 45 oil changes:

p (X' < 10) = 1 - p (Z ≤ 12.33)

Z = (10 - 16.2) / (3.4 √45)

p (X' < 10) = 1 - 0.9999

p (X' < 10) = 0.0001

Hence,

As, the highest critical value of Z is given as 4.40 which has an area of 0.9999.

Thus, Probability that a random sample of 45 oil changes result in a sample mean time less than 10 minutes is 0.0001.

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Complete question is,

The shape of the distribution of the time required to get an oil change at a 15-minute oil-change facility is unknown. However, records indicate that the mean time is 16.2 minutes, and the standard deviation is 3.4 minutes.

(a) What is the probability that a random sample of n = 45 oil changes results in a sample mean time less than 10 ​minutes?

The number of lateral faces of a pyramid with a six-sided base depends on the type of pyramid.

We have,

The number of lateral faces of a pyramid with a six-sided base depends on the type of pyramid.

If it is a regular pyramid, meaning that the base is a regular hexagon and the apex is directly above the center of the base, then it will have six lateral faces, each of which is a triangle.

If the pyramid is not regular, then it will have more than six lateral faces, but the exact number will depend on the specific shape of the base and the position of the apex.

If the base of a pyramid has ten sides, again, the number of lateral faces depends on the type of pyramid.

If it is a regular pyramid, meaning that the base is a regular decagon and the apex is directly above the center of the base, then it will have ten lateral faces, each of which is a triangle.

If the pyramid is not regular, then it will have more than ten lateral faces, but the exact number will depend on the specific shape of the base and the position of the apex.

Thus,

The number of lateral faces of a pyramid with a six-sided base depends on the type of pyramid.

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The complete question:

How many lateral faces does a pyramid whose base is a six-sided figure have? What if its base had ten sides?

Answer:

  9

Step-by-step explanation:

You want the least common denominator for the fraction in the sum ...

 (2/3)² -1/3

When the sum is simplified, it is ...

  4/9 -1/3

The denominator 9 is a multiple of the denominator 3, so the least common denominator of these two fractions is 9.

__

Additional comment

Using that denominator, the sum is ...

  4/9 -3/9 = 1/9

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Part(a),

The exponential function that models the total spent on food and drinks as a function of the number of years since 1990 is:

[tex]T(x) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^x[/tex]

Part(b),

The predicted amount spent in 2000 is 964 billion dollars (rounded to the nearest integer).

Part(c),

The predicted total sales of food and drink in 2018 is 1756 billion dollars

Part(d),

If the exponential trend continues, the total sales will reach 2 trillion dollars approximately 32.72 years after 1990, which is around the year 2022.

(a) To model the total spent on food and drinks as an exponential function of the number of years since 1990, we can use the general form of an exponential function:

[tex]T = a \times b^t[/tex]

where T is the total spent in billions of dollars, t is the number of years since 1990, a is the initial amount spent in 1990, and b is the growth factor or base of the exponential function.

Using the given information, we can set up two equations:

T(0) = 641 (total spent in 1990)

T(13) = 1016 (total spent in 2003, which is 13 years after 1990)

Substituting these values into the exponential function, we get:

[tex]641 = a \timrd b^0[/tex] => a = 641

[tex]1016 = a b^{13[/tex] => [tex]b = (\dfrac{1016}{641})^{\frac{1}{13}[/tex]

Therefore, the exponential function that models the total spent on food and drinks as a function of the number of years since 1990 is:

[tex]T(x) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13})^x[/tex]

(b) To predict the amount spent in 2000, we need to substitute t = 10 (since 2000 is 10 years after 1990) into the exponential function:

[tex]T(10) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^{10[/tex] ≈ 964

Therefore, the predicted amount spent in 2000 is 964 billion dollars (rounded to the nearest integer).

(c) To predict the total sales of food and drink in 2018, we need to substitute t = 28 (since 2018 is 28 years after 1990) into the exponential function:

[tex]T(28) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^{28[/tex] ≈ 1756

Therefore, the predicted total sales of food and drink in 2018 is 1756 billion dollars (rounded to the nearest integer).

(d) To estimate when the total sales will reach 2 trillion dollars, we need to solve for t in the exponential function when T(t) = 2000 (since 2 trillion dollars is equivalent to 2000 billion dollars):

[tex]2000 = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^t[/tex]

[tex]ln(\dfrac{2000}{641}) = t \times ln((\dfrac{1016}{641})^{(\frac{1}{13})[/tex]

[tex]t = \dfrac{ln(\dfrac{2000}{641})} { ln((\dfrac{1016}{641})^{(\frac{1}{13})) }}[/tex]

t = 32.72

Therefore, if the exponential trend continues, the total sales will reach 2 trillion dollars approximately 32.72 years after 1990, which is around the year 2022.

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Answer:

Step-by-step explanation:

110

The linear equations and the values of the variables of the equations are;

A linear equation is an equation that can be presented as; y = mx + c, where m is the slope and c is the y-intercept.

1. Please find attached, the graph of the equations y = 2x and y = 3x + 2, created with MS Excel, showing the solution point (-2, 4)

The solution is x = -2, y = 4

2. Please find attached, the graph of the equations y = 2x and y = 3x + 2, created with MS Excel, showing the solution point (0, 3)

The solution is x = 0, y = 3

3. The equations are solved using substitution as follows;

y = 2 - 6·x

9·x + 2·y = 3

Therefore;

9·x + 2×(2 - 6·x) = 3

4 - 3·x = 3

3·x = 4 - 3 = 1

x = 1/3

y = 2 - 6·x

y = 2 - 6 × 1/3 = 0

y = 0

4. 8·x + 7·y = 43

2·x + y = 7

Therefore;

y = 7 - 2·x

8·x + 7·y = 43

8·x + 7 × (7 - 2·x) = 43

49 - 6·x = 43

6·x = 49 - 43 = 6

x = 6/6 = 1

x = 1

y = 7 - 2·x

y = 7 - 2 × 1 = 5

y = 5

5. y = 8 + 5·x

Therefore where 7·x + 9·y = -32, we get;

7·x + 9 × ( 8 + 5·x) = -32

52·x + 72 = -32

52·x = -32 - 72 = -104

x = -104/52 = -2

x = -2

y =  8 + 5·x

y =  8 + 5 × (-2) = -2

y = -2

6. x = 4 - 2·y

x = 1 - 3·y

Therefore; 4 - 2·y = 1 - 3·y

3·y - 2·y = 1 - 4 = -3

y = -3

x = 1 - 3·y

x = 1 - 3 × (-3) = 10

x = 10

7. The cost for Company is C = 5·x + 48

The cost for Company 2 is C = 11·x

Therefore; 5·x + 48 = 11·x

11·x - 5·x = 48

6·x = 48

x = 48/6 = 8

The amount of data in GB at which the cost of both options are the same is 8 GB

y = 11 × 8 = 88

B. The amount of data at which the cost of both options are the same indicates that when using a small data amount, the cost of Company 2 is much more affordable, however, after 8 GB, the cost of using Company 1 becomes more affordable, hence going with Company 2 is not a good idea

8. Let x represent the number of students who can ride in a van and let y represent the number of students who can right in a bus, we get;

5·x + 3·y = 196

x + 6·y = 266

x = 266 - 6·y

Therefore;

5·x + 3·y = 196

5 × (266 - 6·y) + 3·y = 196

1330 - 27·y = 196

1330 -196 = 27·y

1134

y = 1134/27 = 42

y = 42

x = 266 - 6·y

x = 266 - 6 × 42 = 14

x = 14

9. Let x represent the number of bottles the shampoo and let y represent the number of bottles of the conditioner bought, therefore;

x + y = 19

Let a represent the cost of a shampoo and let b represent the cost of a conditioner

a·x + b·y = 147

The cost of a shampoo, a = (147 - b·y )/x

Cost of a conditioner, b = (147 - a·x )/y

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The fraction 9/10 is more than 78/100.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, and exponentiation) that are combined in a meaningful way.

To compare these two fractions, we can convert them to have a common denominator. In this case, the common denominator is 1000.

9/10 = (9/10) x (100/100) = 900/1000

78/100 = (78/100) x (10/10) = 780/1000

Now we can see that 900/1000 (which is equivalent to 9/10) is greater than 780/1000 (which is equivalent to 78/100).

Therefore, 9/10 is more than 78/100.

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Step-by-step explanation:

If radius is 8cm    then diameter =  16 cm

circumference of a circle = pi * d = pi * 16 cm = ~ 50.27 cm

Answer:

  (b)  0.083

Step-by-step explanation:

You want the probability that a part is New and Passed the test, given the distribution of parts as shown in the table.

"This group" consists of all the parts described by the table. That is a total of ...

  5 + 23 + 2 + 30 = 60

parts.

Of those 60 parts, the number that is found in the table cell (New, Passed) is 5. This means 5/60 = 1/12 ≈ 0.083 of the total number of parts shown were New and Passed the test.

The probability of choosing one of those parts at random is 0.083.

__

Additional comment

This is not "coordinate algebra". It is probability.

The number of students who participated in the survey, based on the histogram showing the number of hours students watch television on the weekend, is 125.

A histogram is a pictorial or graphical representation of categorical data, proportional to the frequency of a variable and whose width is equal to the class interval.

The number of students who watched between 0 - 4 hours = 20

The number of students who watched between 5 - 9 hours = 40

The number of students who watched between 10 - 14 hours = 30

The number of students who watched between 15 - 19 hours = 20

The number of students who watched between 20 - 24 hours = 15

The total number of students who participated = 125

Thus, using the histogram, the total number of students who participated in the survey was 125.

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