Please Show detailed algebraic work.

The table for the function d = 3t is

t (hours) d = 3t (miles)

0 0

1 3

2 6

The equation of the function is given as

d= 3t

The above is a linear function

To make a table for the function d = 3t, we can choose some values of t and then calculate the corresponding values of d using the given equation.

Since the equation represents distance traveled at a rate of 3 miles per hour, we can assume that t represents time in hours and d represents distance in miles.

Let's choose some values of t and calculate the corresponding values of d:

t (hours) d = 3t (miles)

0 0

1 3

2 6

3 9

4 12

5 15

The graph is attached

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All the answers related to null hypothesis are explained below.

Null hypothesis is used to test if there is any statistical significance between the two groups being compared.

1. The null hypothesis is that there is no difference in the number of counseling sessions attended by men and women.

2a. For a two-tailed .05test, you would reject the null hypothesis if the absolute value of the t-statistic is greater than the critical value of 1.96.

2b. For a one-tailed .05test, you would reject the null hypothesis if the t-statistic is greater than the critical value of 1.645.

2c. For a two-tailed .01test, you would reject the null hypothesis if the absolute value of the t-statistic is greater than the critical value of 2.58.

2d. For a one-tailed .01test, you would reject the null hypothesis if the t-statistic is greater than the critical value of 2.33.

3. Rejecting the null hypothesis means that the data is statistically significant and you are confident that the difference in the number of counseling sessions attended by men and women is not due to chance.

4. For a two-tailed test, a Type I error occurs when the null hypothesis is rejected when it should not have been. For a one-tailed test, a Type I error occurs when the null hypothesis is rejected when the difference between the two groups is not greater than the critical value.

5. Conceptually, something is considered to be statistically significant when it is unlikely that the observed results were due to chance.

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Answer:

ANswer ig

Step-by-step explanation:

1/12+1/3=1/12+[4]/12=5/12

6\12. 1\2

I have to add mor but that is all so I’m writing this

Answer:

To determine which is cheaper, we need to consider the total cost for a certain amount of time. Let's say we want to paint a picture that will take 5 hours to complete.

For Paint by Numbers:

Flat rate = $100

Hourly rate = $16/hour x 5 hours = $80

Total cost = Flat rate + Hourly rate = $100 + $80 = $180

For Paint it Right:

Flat rate = $38

Hourly rate = $24/hour x 5 hours = $120

Total cost = Flat rate + Hourly rate = $38 + $120 = $158

Therefore, Paint it Right is cheaper for this particular job. However, if the amount of time required for the job is different, the cost comparison may change.

Emila gοt a tοtal οf 2 + 7 = 9 marbles.

Let's first find οut which bags each friend gοt. Since each friend tοοk twο bags, we can subtract the marbles each friend gοt frοm the tοtal number οf marbles in the twο bags tο find οut the number οf marbles in the οther bag.

Amina gοt 5 marbles, sο the tοtal number οf marbles in her twο bags must be 1 + 4 οr 2 + 3. Let's assume she gοt bags with 1 and 4 marbles.

Then, the bags left fοr the οther friends are:

Bag 2: Breanna οr Chyna

Bag 5: Breanna οr Chyna

Bag 6: Deiοn οr Emila

Bag 7: Deiοn οr Emila

Bag 8: Available tο any friend

Bag 9: Available tο any friend

Bag 10: Available tο any friend

Breanna gοt 7 marbles, sο the tοtal number οf marbles in her twο bags must be 3 + 4. Therefοre, Chyna gοt bags with 2 and 5 marbles.

Chyna gοt 9 marbles, sο the tοtal number οf marbles in her twο bags must be 4 + 5. Therefοre, Deiοn gοt bags with 1 and 8 marbles.

Deiοn gοt 15 marbles, sο the tοtal number οf marbles in his twο bags must be 6 + 9. Therefοre, Emila gοt bags with 2 and 7 marbles.

Therefοre, Emila gοt a tοtal οf 2 + 7 = 9 marbles.

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The height of ladder is approximately 26.9 feet tall.

In order to get the length of the hypotenuse, divide the non-hypotenuse side that is close to the angle by cos(). If you prefer, you can multiply this length by tan() to obtain the length of the side that is perpendicular to the angle.

Let's tackle this issue using the Pythagorean theorem.

According to the Pythagorean theorem, the sum of the squares of the leg lengths in a right triangle equals

The length of the slide is the other leg, the distance from the ladder's bottom to its base is one leg, and the ladder itself is the hypotenuse.

b² = 18² + 20²

b² = 324 + 400

b² = 724

b = √(724)

b ≈ 26.9

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From the given information provided, the area of the square room with rectangular section is 72 square feet.

Let's assume that the rectangular section of the floor that is tiled has length "L" and width "W". Since the area of the rectangular section is 18 square feet, we have:

L × W = 18

Since the room is square, its length and width are equal, let's say it's "x". Then, the area of the room is x².

Since the rectangular section is a part of the room, we have:

L ≤ x and W ≤ x

Therefore, we can find the minimum possible value of x by assuming that L = W = √18 (the sides of the rectangle are equal, and equal to the square root of 18), which gives:

x = √18 + √18 = 2√18

So, the area of the room is:

x² = (2√18)² = 4(18) = 72 square feet

Question - A contractor tiles a rectangular section of floor in a square room. The tiles covers 18sq. feet. What is the area of room?

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Converting into whole number:

a. 5 5/10 = 5 1/2

b. 4 5/10 = 4 1/2

c. 5

d.  4/8 = 1/2

To convert a fraction into a whole number, you need to perform the division indicated by the fraction and express the result as a mixed number or a whole number.

Example: 55/10 means that 55 is divided by 10. When we divide 55 by 10, we get 5 with a remainder of 5. Therefore, we can express 55/10 as a mixed number: 5 5/10. However, we usually simplify the mixed number by reducing it to its lowest terms, which in this case is 5 1/2.

Similarly, we can convert the other fractions into whole numbers:

45/10 = 4 5/10 = 4 1/2

20/4 = 5

4/0.8 can be simplified first by dividing both the numerator and denominator by 0.8, which gives 5. Then we can express 5 as a fraction with a denominator of 10 by multiplying both the numerator and denominator by 2, which gives 5/10. Finally, we can reduce this fraction to its lowest terms, which is 1/2. Therefore, 4/0.8 = 1/2.

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There are 24 different possible ways a resident can receive an advertisement in the mail.

The counting principle states that if there are "a" ways to do one thing, and "b" ways to do another thing, then there are "a × b" ways to do both things. In this case, we need to multiply the number of different types of advertisements for each week to find the total number of different possible ways a resident can receive an advertisement in the mail.

Week 1: 2 different types of advertisements (postcard or leaflet)
Week 2: 3 different types of advertisements (flyer, catalog, or calendar)
Week 3: 2 different types of advertisements (brochure or poster)
Week 4: 2 different types of advertisements (business card or coupon)

Total number of different possible ways = 2 × 3 × 2 × 2 = 24

Therefore, there are 24 different possible ways a resident can receive an advertisement in the mail.

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The probability that a random sample of 55 students has a mean age of less than 19.2 age years is 0.3866 and the probability that a random sample of 55 students has a mean age between 18.8 and 23 years is 0.27808.

a. To find P(x < 19.2), we need to find the area under the normal distribution curve to the left of x = 19.2. We can use the formula for z-score to standardize the value of x:

z = (x - μ) / δ = (19.2 - 20.9) / 5.9 = -0.2881

Looking up the area to the left of z = -0.2881 in a standard normal distribution table or using a calculator, we find that the probability is approximately 0.3869. So P(x < 19.2) is 0.3866.

b. To find P(18.8 < x < 23.0), we need to find the area under the normal distribution curve between x = 18.8 and x = 23.0. Again, we can standardize the values of x and use a standard normal distribution table or calculator:

z1 = (18.8 - 20.9) / 5.9 = -0.3559

z2 = (23.0 - 20.9) / 5.9 = 0.3559

Looking up the area between z1 = -0.3559 and z2 = 0.3559 in a standard normal distribution table or using a calculator, we find that the probability is approximately0.27808. So P(18.8 < x < 23.0) is 0.27808.

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The total value of the remaining inventory is  $5,000. So correct option is B.

Inventory refers to the stock of goods or materials that a business or organization has on hand for the purpose of selling, manufacturing, or producing. It can include finished goods ready for sale, work in progress, or raw materials waiting to be processed or used. Proper management of inventory is essential to ensure that a business can meet customer demand while minimizing costs associated with carrying excess inventory or stockouts. Inventory management techniques involve tracking inventory levels, determining optimal reorder points, and controlling the flow of goods in and out of the inventory.

Using the FIFO method, we assume that the first jackets purchased are the first ones sold, so the value of the remaining inventory is calculated as follows:

The first 30 jackets are from the beginning inventory and cost $175 each.

The next 16 jackets (out of the 25 purchased in March) cost $150 each.

The next 10 jackets (out of the 35 purchased in June) cost $125 each.

The last 0 jackets (out of the 30 purchased in September) cost $100 each.

So the total value of the remaining inventory is:

30 x $175 + 16 x $150 + 10 x $125 + 0 x $100 = $5,000

Therefore, the answer is B. $5,000.

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Step-by-step explanation:

ASA stands for angle, side, angle

How is triangle ABC congruent to DEF

If any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.

In the diagram you shared, side BC is equivalent to line FD

Angle B = angle F

Angle C = Angle D

(Compare the markings on both triangles)

The relationship between triangle ABC and triangle DEF are congruent only by 2 angles and one side.

The proportional relationship defined by the table is given as follows:

y = 2x.

A proportional relationship is defined according to the equation presented as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

From the table, when the input variable x is increased by one, the output variable y is increased by 2, hence the constant of proportionality is given as follows:

k = 2.

Meaning that the equation is given as follows:

y = 2x.

The graph of the relation is given by the image presented at the end of the answer.

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a) The probability of drawing a red marble is 1/4.

b) There is a 3/8 chance of drawing an odd-numbered stone.

c) There is a 7/16 chance of drawing a red or odd-numbered marble.

d) The odds of drawing the blue, even-numbered marble are 3/8.

(a) The ratio of red marbles to all other marbles in the jar represents the likelihood of drawing a red marble.

(4) red marbles are present.

(4) + (12) = (16) marbles total

As a result, there is a 4/16 or 1/4 chance of drawing a red marble.

(b) The proportion of odd-numbered marbles to all marbles in the jar determines the likelihood of drawing an odd-numbered marble.

6 odd-numbered marbles make up the total (red marbles numbered 1 and 3, and blue marbles numbered 1, 3, 5, and 7)

There are 16 marbles in total.

The likelihood of drawing an odd-numbered stone is therefore 6/16 or 3/8.

(c) The likelihood of drawing a red or odd-numbered marble is calculated as the product of the odds of drawing each type of marble, less the likelihood of drawing a red or odd-numbered stone (i.e., marble number 1).

a red marble's chances of being drawn = 1/4

Probability of drawing an odd-numbered marble = 3/8

Probability of drawing a marble that is both red and odd-numbered = 1/16

Therefore, the probability of drawing a red or odd-numbered marble is (1/4) + (3/8) - (1/16) = 7/16.

(d) The proportion of blue and even-numbered marbles to all other marbles in the jar determines the likelihood that a blue and even-numbered marble will be drawn.

Six blue and even-numbered marbles make up the total (blue marbles numbered 2, 4, 6, 8, 10, and 12)

Total number of marbles = 16

Probability of drawing the marble is blue and even-numbered = 6/16 or 3/8

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Answer:

There are 60 seconds in a minute, so to convert meters per minute to meters per second, we need to divide by 60.

90 meters per minute ÷ 60 = 1.5 meters per second

Therefore, the car's speed is 1.5 meters per second.

Step-by-step explanation:

Step-by-step explanation:

There are 60 in a minute, so to convert meters per minute to meters per second, we need to divide by 60

90 meters per minute ÷ 60 = 1.5 meters per second

The ratio of x:y is -9:5 or 3:-2.

The given equation is 2x-3y=0 and x+5y=0.

Since x is greater than 0 and y is greater than 0, we can solve the equations for x and y

2x = 3y

x = 3/2y

and

x = -5y

Substituting x = 3/2y in the second equation,

-5y = 3/2y

-10y = 3

y = -3/10

Substiuting y = -3/10 in the first equation,

2x = 3(-3/10)

x = -9/5

Therefore, the ratio of x:y is -9:5. In the simplest form, the ratio can be written as -9:5 or 3:-2.

2x - 3y = 0

x + 5y = 0

2x = 3y

x = 3/2y

-5y = 3/2y

-10y = 3

y = -3/10

2x = 3(-3/10)

x = -9/5

Therefore, x:y = -9:5 or 3:-2

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The scale factor given in the map to measure the distance is 1 unit = 557 miles.

What is scale factor?

The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.

The map is given for United States of America.

The map shows different states with their locations.

The maps say that 1 unit measures 557 miles.

The scale factor is the means to measure the distance on the map.

The scale factor mentioned in the map is 1 unit.

The value of 1 unit is given as  557 miles.

Therefore, the scale factor is 1 unit = 557 miles.

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The true statement about the function notation are:

The definition of the graph is given as

The distance vs time graph

This is represented by F = d(t)

The function notation would be determined to be true or false by observation

This is so because the graph is not drawn to scale

Using the above as a guide, we have the following:

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Erin will need to purchase 48ft² of tile for her kitchen island.

In order to calculate the square footage of tile needed for Erin’s kitchen island, we will use the formula for the area of a rectangle: A = lw, where A is the area, l is the length, and w is the width.

The first step is to measure the length and width of the island. Let’s assume that the length is 16ft and the width is 3ft.

Next, we will use the formula to calculate the area of the island: A = lw

A = 16ft x 3ft

A = 48ft²

Finally, Erin will need to purchase 48ft² of tile for her kitchen island.

To double check our calculations, we can also calculate the area of each individual side of the island. For example, the area of the 16ft side is 16ft x 2ft = 32ft². The area of the 3ft side is 3ft x 7ft = 21 ft². When we add the areas together, 32ft² + 21ft² = 53ft². Since 53ft² is greater than 48ft², it is clear that calculating the area of the entire island is the correct solution.

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the error interval will be [15.29, 15.3).

What is error?

Error is the difference between an actual value and an estimate, or approximate, representation of that value in applied mathematics. The discrepancy between the population's average and the average of a sample taken from that population is a frequent example in statistics. The discrepancy between an irrational number's true value and the values of rational expressions like 22/7, 355/113, 3.14, or 3.14159 serves as an example of round-off error in numerical analysis. A truncation error happens when an infinite series is ignored for all but a small number of terms. For instance, the sum of the infinite series can be used to express the exponential function ex.

Find the error interval of 15.29:

[15.29, 15.3)

Hence the error interval will be [15.29, 15.3).

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Answer:

2,7c-3,6c =-9+4,5

-0,9c=-4,5

c=5

Answer:

c=5

Step-by-step explanation:

2.7c-4.5=3.6c-9

     +4.5         +4.5

2.7c = 3.6c -4.5

-3.6c  -3.6c

-0.9c = -4.5

-0.9c/-0.9= -4.5/-0.9

c= 5

Answer: 56

Step-by-step explanation:

66 x 2 = 132

132-76 = 56

(76+52) divided by 2 = 66

Hence the mean score for class B is 56.

Devon needs to save at least $162.50 per month for the next four years to have enough money to pay for his first year tuition at state university.

To calculate the minimum amount of money Devon must save to have enough money to pay for his first year tuition, we need to take into account the amount of money he has available now and the amount he plans to save each month for the next four years.

First, we can calculate the total amount of money Devon will have available for his first year of tuition by adding the $5,200 his parents will give him to the amount he plans to save over the next four years. If he saves the same amount each month, he will save $x per month for 48 months, which gives him a total of $48x. Therefore, the total amount of money he will have available is:

Total = $5,200 + $48x

We want to find the minimum amount of money he must save to have enough to pay for his first year tuition, which is $13,000. So we set up an equation:

$5,200 + $48x = $13,000

Solving for x, we get:

$48x = $13,000 - $5,200

$48x = $7,800

x = $7,800 / $48

x ≈ $162.50

Therefore, Devon needs to save at least $162.50 per month for the next four years to have enough money to pay for his first year tuition at state university.

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Using percentages we know that the population after 25 years would be 12.4 billion which is 12,40,00,00,000.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.

A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The symbol "%" is frequently written after the number to indicate percentages.

Now, we know that:

The population is 8 billion.

The increasing percentage is 2.2%.

Then, the population after 25 years would be:

= 8000000000/100 * 2.2

= 17,60,00,000

Now, after 25 years:

= 17,60,00,000 * 25

= 4,40,00,00,000

Total population after 25 years:

4,40,00,00,000 + 8000000000 = 12,40,00,00,000

Therefore, using percentages we know that the population after 25 years would be 12.4 billion which is 12,40,00,00,000.

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Answer: 18d

Step-by-step explanation:

To find the greatest common factor (GCF) of the terms in the polynomial 18d^4e^2 − 45d^2 + 36d, we need to factor each term into its prime factors and then identify the common factors with the highest exponent for each variable.

The prime factors of each term are:

18d^4e^2 = 2 x 3^2 x d^4 x e^2

45d^2 = 3^2 x 5 x d^2

36d = 2^2 x 3^2 x d

To find the common factors, we need to look for factors that appear in all terms. The common factors with the highest exponent for each variable are:

2^1, 3^2, and d^1.

Therefore, the GCF of the terms in the polynomial is:

2 x 3^2 x d = 18d

Hence, the GCF of the terms in the polynomial 18d^4e^2 − 45d^2 + 36d is 18d.

The length of the shaded arc is 68.71 metres squared.

The arc of a circle is defined as the part or segment of the circumference of a circle. Therefore, the length of the bolded arc can be found as follows:

length of an arc = ∅ / 360 × 2πr

where

Therefore,

r = 26 / 2 = 13 m

∅ = 360 - 57 = 303 degrees

length of an arc = 303 / 360 × 2 × 3.14 × 13

length of an arc =  24736.92 / 360

length of an arc = 68.7136666667

length of an arc = 68.71 metres squared

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The surface area of the pyramid is 105.6 square feet.

To find the surface area of this pyramid, we need to calculate the area of all its faces and add them up.

Since all sides of our hexagon are equal, we can simplify this formula to:

Surface Area of Hexagon = 6 x (3√3 / 2) x (Side length)²

Total Surface Area = Surface Area of Base + Surface Area of Triangular Faces

Total Surface Area = 6 x (3√3 / 2) x (Side length)² + 6 x (Side length x 15) / 2

We can simplify this expression further by factoring out 6 x (Side length)² from both terms:

Total Surface Area = 6 x (Side length)² x [(3√3 / 2) + 15]

To find the surface area of a right hexagonal pyramid with equal-length sides and triangular faces of height 15 ft, we use the formula above:

Total Surface Area = 6 x (Side length)² x [(3√3 / 2) + 15]

When the value of side length is 1, then total surface area is

=> Total Surface Area = 6 x (1)² x [(3√3 / 2) + 15] = 105.6 square feet.

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Therefore, the shopkeeper made a profit of Rs. 30,000 and the profit percentage is 6.25%.

Percent is a way of expressing a fraction or a proportion as a quantity out of 100. The term "percent" means "per hundred". So, when we say that something is 50 percent, we mean that it is 50 out of 100 or 50/100, which can also be simplified to 1/2. The symbol used to represent percent is "%". For example, if a store is offering a discount of 20%, it means that the customer can buy the item for 20% less than the original price, or in other words, the customer will pay only 80% of the original price. Percentages are used in many different areas of life, such as finance, mathematics, science, and statistics. They are used to represent proportions, changes, growth rates, and many other types of data.

Here,

The total cost of 300 bicycles is:

Cost of 1 bicycle = Rs. 1500

Cost of 300 bicycles = 1500 x 300 = Rs. 4,50,000

Transportation cost per bicycle is Rs. 75, so the total transportation cost for 300 bicycles is:

Transportation cost of 1 bicycle = Rs. 75

Transportation cost of 300 bicycles = 75 x 300 = Rs. 22,500

The total cost of purchasing 300 bicycles including transportation cost is:

Total cost = Cost of bicycles + Transportation cost

Total cost = Rs. 4,50,000 + Rs. 22,500 = Rs. 4,72,500

The shopkeeper spent Rs. 7500 on advertising.

So, the total cost of the shopkeeper is:

Total cost = Cost of bicycles + Transportation cost + Advertising cost

Total cost = Rs. 4,72,500 + Rs. 7500 = Rs. 4,80,000

The selling price of 1 bicycle is Rs. 1700, so the selling price of 300 bicycles is:

Selling price of 1 bicycle = Rs. 1700

Selling price of 300 bicycles = 1700 x 300 = Rs. 5,10,000

The profit or loss is calculated by subtracting the total cost from the total selling price:

Profit/Loss = Selling price - Total cost

Profit/Loss = Rs. 5,10,000 - Rs. 4,80,000 = Rs. 30,000

Since the shopkeeper made a profit of Rs. 30,000, we can calculate the profit percentage as follows:

Profit percentage = (Profit / Total cost) x 100

Profit percentage = (30,000 / 4,80,000) x 100

Profit percentage = 6.25%

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The expression can be written as the sum of two terms as 74.5 + 0.5d

Mathematical expressions are combinations of numbers, variables, and operators (such as +, -, ×, ÷, =) that represent a mathematical relationship or computation.

To write the given expression as the sum of two terms simplify the expression by multiplying and adding or subtracting like terms.

Here we have

The expression 75 + 0.5(d - 1) represents the fine for an overdue library book, where d is the number of days overdue.

Simplify expression as shown below

=> 75 + 0.5(d - 1)

= 75 + 0.5d - 0.5

= 0.5d + 74.5  

Now the expression is in the form of the sum of two terms

Therefore

The expression can be written as the sum of two terms as 74.5 + 0.5d

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