Write the first five terms of the arithmetic sequence. Find the common difference d and write the nth term of the sequence as a function of n.
a1
= 300, ак + 1 = ак - 20

The polynomial x^2-y^2-3.5(x+y) is factored completely to xy(x - y)

Algebraic expressions are defined as expressions that are made up of coefficients, variables, terms, factors and constants.

They are also composed of arithmetic operations, such as;

x^2-y^2-3.5(x+y)

expand the brackey

x² - y² - 3.5x + 3.5y

Factor the common terms

xy(x - y - 3.5 + 3.5)

collect lie terms

xy(x - y)

Hence, the expression is xy(x - y)

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Answer:

See below

Step-by-step explanation:

[tex]4\sqrt{5}+\sqrt{5}=(4+1)\sqrt{5}=5\sqrt{5}[/tex]

This sum is irrational because [tex]\sqrt{5}[/tex] was irrational to begin with.

Answer: the shadow will extend 43.75m

Step-by-step explanation:

Answer:

Step-by-step explanation:

The measure of the two greatest angles is 105° and 45°

Let the angles be 2x, 3x and 7x ...... (i)

According to the 'Angle Sum Property' of triangle,

2x + 3x + 7x = 180°

12x = 180°

x = 15°

Now, put value of x in (i)

2x = 2 × 15 = 30°

3x = 3 × 15 = 45°

7x = 7 × 15 = 105°

so, the two greatest angles are 105° and 45°

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Felix's English score would be around 72 points if he spends 7 hours a week studying English.

the answer is option b, 72 points.

What is a graph of an equation?

A graph of an equation is a visual representation of the relationship between the variables in that equation. In mathematics, an equation typically involves one or more variables, and the graph of that equation shows how the value of one variable changes as the value of another variable change.

Look at the horizontal axis of the graph to find the point that corresponds to 7 hours of studying per week. In this case, it is approximately halfway between 6 and 8, so we can estimate it to be around 7.

From that point, draw a vertical line up to the graph to find the corresponding English score.

Follow the line until it intersects with the blue line representing Felix's English scores.

From that intersection point, draw a horizontal line over to the y-axis to read the corresponding score.

Based on this analysis, we can estimate that Felix's English score would be around 72 points if he spends 7 hours a week studying English.

Therefore, Felix's English score would be around 72 points if he spends 7 hours a week studying English.

the answer is option b, 72 points.

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The quantity of cholesterol in an egg is 272 mg

The quantity of cholesterol in a cupcake is 18 mg

The quantity of cholesterol in a slice of pizza is 9 mg

Let the amount of egg be e

Let the amount of cupcake be c

Let the amount of pizza be p

By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 299 mg of cholesterol

e + c + p = 299

The child eats 3 cupcakes and 4 slices of pizza, he or she takes in 90 mg of cholesterol

3c + 4p = 90

By eating 3 eggs and 1 cupcake, a child consumes 834 mg of cholesterol

3e + c = 834

e + c + p = 299

3c + 4p = 90

3e + c = 834

solving the simultaneous equation gives

e = 270

c = 18

p = 9

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The company will be able to purchase enough pens while staying within the budget by purchasing 10 mugs only not more than that.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

A company has a budget of $305

Company needs to purchase either a mug or a pen for each of its 100 clients.

Price per Mug $5.55 Price per Pen $2.50

Now,

Price of pen = 100*2.50=250

When the number of employees are 10

=10*5.50=55.0

Mugs can be purchased

When the number of employees are 15

=15*5.50=82.5

Mugs cannot be purchased

Therefore, by algebra the answer will be 10 mugs only.

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The potential energy of the roller coaster car at the top of a hill is 661,068.8 J.

The correct answer choice is option D

Potential energy is a form of energy which is dependent on the relationship between different system components.

The gravitational constant, g = 9.8 m/s².

Mass, m = 1088 grams

Height, h = 62 meters

So, The amount of potential energy the car has;

PE = mgh.

PE = 1088 × 9.8 × 62

PE = 661,068.8J

Ultimately, the car has a potential energy of 661,068.8J.

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Answer:

Step-by-step explanation:

Let me explain each step in more detail.

Step 1: Calculate the Z-score

The Z-score is a measure of how many standard deviations a value is from the mean. To calculate the Z-score, we use the following formula:

Z = (x - μ) / σ

Where:

x = 9.8 ounces (the value we want to examine)

μ = 10.2 ounces (the mean of the distribution)

σ = 0.12 ounces (the standard deviation of the distribution)

Plugging in the values, we get:

Z = (9.8 - 10.2) / 0.12 = -3.33

This Z-score tells us that 9.8 ounces is 3.33 standard deviations below the mean of 10.2 ounces.

Step 2: Look up the cumulative probability from a Z-table

A Z-table is a table that lists the cumulative probabilities for various Z-scores. The cumulative probability tells us the probability of getting a value less than or equal to a certain Z-score. To use the Z-table, we need to know the Z-score and whether we want the cumulative probability to the left (for values less than) or to the right (for values greater than). In this case, we want the cumulative probability to the left because we want to find the probability of getting a weight less than or equal to 9.8 ounces.

The cumulative probability for a Z-score of -3.33 is approximately 0.0004. This means that there is a 0.0004 (or 0.04%) chance of getting a weight of 9.8 ounces or less in a bag of chips.

Step 3: Interpret the results

Since the cumulative probability is very small, it is highly unlikely that a bag of chips would contain 9.8 ounces or less of chips. Therefore, we can conclude that it is unusual for a bag of chips to contain 9.8 ounces or less.

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Answer: A proper subset of a set A is a subset of A that is not equal to A

Step-by-step explanation:

The solution of inequalities is (1.714 , 4.857).

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

y > 4x-2

2y-x ≤ 8

Now, solving the inequalities.

y > 4x-2 is given by purple region and 2y-x ≤ 8 is shown by Grey region.

The two lines of inequalities intersect at (1.714 , 4.857).

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Answer: 65

Step-by-step explanation:

17 + 48

The equation can be used to calculate the average speed at which Yusef drove is (c) r = 130/2.5

The formula to calculate average speed is:

Average speed = distance traveled / time taken

In this problem, Yusef drove 130 miles in 2.5 hours.

So, we can substitute the values in the formula:

Average speed = 130 miles / 2.5 hours

Simplifying this expression, we get:

Average speed = 52 miles per hour

Therefore, the correct equation to calculate the average speed at which Yusef drove is:

r = 130/2.5 or r = 52

Option C matches this equation, so the answer is C.

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16.7, 6.7 and 22 degrees respectively are the measures of a, c and m<C

The given diagram is a triangle with the following sides

Hypotenuse = AC = 18

m<A = 68 Degrees

We need to determine the measure of a, b and m<C

Using the trigonometry identity

sin 68 = a/18

a = 18sin68

a = 16.7

Similarly;

cos68 = c/18

c = 18cos68

c = 6.7

Since the sum of angles in a triangle is 180 degrees, hence:

m<C = 90 - m<A

m<C = 90 - 68

m<C = 22 degrees

Hence the measure of a, c and m<C is 16.7, 6.7 and 22 degrees respectively.

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The output of the equation for input of 2 is 1.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

The given equation is:

y = 3x - 5

Here, x is the input value and y is the output value.

Substituting input that is x = 2.

y = 3(2) - 5

y = 6 - 5

y = 1

Hence, the output of the equation for input of 2 is 1.

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Answer:

they all have flat sides except for the cylinder

Step-by-step explanation:

Its okay we all are bad on some things

a) The probability of rolling a 5 or a number greater than 3 is 1/2.

b) The probability of rolling a number less than 4 or an even number is 5/6.

c) The probability of rolling a 4 or an odd number is 2/3.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

In rolling a six-sided die, the total number of outcomes is 6.

The sample space is {1,2,3,4,5,6}

The probability formula is -

Probability = Number of outcomes corresponding to events / total number of outcomes.

(a)  Let A be the event of rolling a 5. Then A = {5}.

Let B be the event of rolling a number greater than 3. Then B = {4,5,6}.

The event of rolling A or B is given by A∪B = {4,5,6}.

So, apply the probability formula -

P(A∪B) = 3/6 = 1/2

Therefore, the probability value is 1/2.

(b)  Let C be the event of rolling a number less than 4. Then C = {1,2,3}.

Let D be the event of rolling an even number. Then D = {2,4,6}.

The event of rolling C or D is given by C∪D = {1,2,3,4,6}.

So, apply the probability formula -

P(C∪D) = 5/6

Therefore, the probability value is 5/6.

(c)  Let E be the event of rolling a 4. Then E = {4}.

Let F be the event of rolling an odd number. Then F = {1,3,5}.

The event of rolling E or F is given by E∪F = {1,3,4,5}.

So, apply the probability formula -

P(E∪F) = 4/6 = 2/3

Therefore, the probability value is 2/3.

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Since the samples of the study are independent, the condition for inference have been met

The body mass index for adults in the United States = 26.8

BMI stands for Body Mass Index

Body mass index of marathon runners = less than 26.8

The random samples = 35

The body mass index of the random samples = 22.7

Standard deviation = 3.1

Then the researchers will conduct a one sample t test for a population mean.

The one sample t-test is is defined as the hypothesis test that check whether the unknow population mean is different from the specific value

Here the samples are independent

Therefore, the condition for inference have been met

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The required equation that Nandita used to make the given graph is y = -3x + 2. Option B is correct.

In the equation intercept is the value of the linear function where either of the variables is zero.

Here,
From the graph, we need to identify the y-intercept and then match that intercept with each given in the options So,
From the graph, the y-intercept is ordered where the x coordinate of the pair is zero, So,
(0, y) = (0, 2)

Thus, the required equation among the option is y = -3x + 2.

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Answer:

The slope between the two points would be 5.

Answer: The slope would be 5

Step-by-step explanation:

The width of the container can be calculated by dividing the product of the length and height by the volume. The width is 28.1 ft.

[tex]30 ft x 7.5 ft = 225 ft^3[/tex]

[tex]1800 ft^3 / 225 ft^3 = 8[/tex]

[tex]225 ft^3 / 8 = 28.125 ft[/tex]

Width = 28.1 ft

To calculate the width of the shipping container, you need to divide the product of the length and height by the volume. The length of the container is given as 30 ft, and the height is given as 7 ft 6 inches or 7.5 ft. Thus, the product of the length and height is [tex]225 ft^3[/tex]. The volume of the container when it is full is given as [tex]1800 ft^3[/tex]. To find the width, divide the product of length and height by the volume. Thus,[tex]225 ft^3 / 1800 ft^3 = 8[/tex]. Then, divide the product of length and height by the result you got in the previous step, that is,[tex]225 ft^3 / 8 = 28.125 ft[/tex]. This is the width of the container. Round this value to the nearest tenth and you get 28.1 ft as the width of the container.

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Answer: X^2+6.8^2=10.6^2

Step-by-step explanation:

The pythagorean theorem can be used to find the missing sides of triangles.

The formula is:

a^2+b^2=c^2, where c^2 is always the hypotenuse (the biggest and diagonal line) and a^2 and b^2 are the other side lengths

In this problem, plug in the values. So in this case, you have:

a^2+6.8^2=10.6^2

Hope this helps

The equation of line is y = 14.24375x + 296.8875 , where x is the number of days and y is the total weight gain in x days

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 18 , 40.5 )

Let the second point be Q ( 50 , 496.3 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 496.3 - 40.5 ) / ( 50 - 18 )

Slope m = 455.8 / 32

Slope m = 14.24375

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 40.5 = 14.24375 ( x - 18 )

On simplifying the equation , we get

y - 40.5 = 14.24375x - 256.3875

Adding 40.5 on both sides of the equation , we get

y = 14.24375x + 296.8875

where x is the number of days

Hence , the equation of line is y = 14.24375x + 296.8875

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It should be noted that finding the mean gives the average value of a set of numbers, while finding the halfway point gives a value that is equidistant between the two extreme values in the set.

Finding the mean of a set of numbers involves adding up all the numbers in the set and then dividing the sum by the total number of numbers in the set. The mean represents the average value of the set.

Finding the value that is halfway between a set of numbers involves taking the two extreme values in the set and finding the arithmetic average (i.e., adding the two values and dividing by 2). This value represents the midpoint between the two extremes.

In summary, finding the mean gives the average value of a set of numbers, while finding the halfway point gives a value that is equidistant between the two extreme values in the set.

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Answer:

  B)  2:3

Step-by-step explanation:

If you have mercury : copper = 1 : 5 and tin : copper = 3 : 10, you want the ratio of mercury to tin.

The ratios can be compared or combined when common components are represented by the same number. Doubling the values in the first ratio, we will have two ratios that both have 10 parts copper.

  mercury : copper = 1 : 5 = 2 : 10

Then ...

  mercury : tin : copper = 2 : 3 : 10

You need 2 parts mercury to 3 parts tin.

  mercury : tin = 2:3 . . . . . . choice B

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a) The fraction of the stickers that Kate gave to her 6 friends was 1/2.

b) The fraction of Kate's stickers that each friend received from the 1/2 of stickers was 1/12.

The fraction is the portion or part of a whole.

Fractions can be proper, improper, and complex fractions, depending on the relative value of the numerator and the denominator.

The total number of stickers that Kate possesses = 1/1

The fraction Kate kept for herself = 2/5

The remaining portion of Kate's stickers = 3/5 (1 - 2/5)

The fraction Kate gave to her 6 friends to share equally = 5/6 of 3/5 = 1/2

The fraction of Kate's stickers that each friend received = 1/2 ÷ 6 = 1/12

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Speed of bicycle in miles per hour will be 12.85 mi/h.

What is the definition of speed?

The following is the definition of speed:

The rate at which the position of an item changes in any direction.

The ratio of distance travelled to time spent travelling is described as speed. Speed is a scalar number since it has just one direction and no magnitude.

Formula for Speed

The speed formula is as follows:

s=d/t

Where,

s denotes the speed in metres per second, d the distance travelled in metres, and t the time in seconds.

Now,

Given Diameter=18 inch

then distance covered by cycle in 4 rotation in one second =4*π*diameter

=4*22/7*18

=226.28

Then Speed=226.28 in/s

As 1 mike=63360 inch and 1 hour= 3600 seconds

then Speed in miles/hour=226.28*3600/63360

=12.85 mi/h

hence,

          Speed of bicycle in miles per hour will be 12.85 mi/h.

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The combination should be 20 of Brand A and 20 of Brand B.

When a linear function is exposed to various constraints, it is maximised or reduced using the mathematical modelling technique known as linear programming. In commercial planning, industrial engineering, and—to a lesser extent—the social and physical sciences, this method has proven helpful for directing quantitative decisions.

Given:

Each bag of type x costs P400 and contains 100 units of calcium and 400 units of protein.

Each bag of type y costs P600 and contains 200 units of calcium and 200 units of protein.

So, Max Z = 400x + 600 y

Constraints:

100x + 200 y ≤ 6000

or, 400x + 200y ≤ 12000

Solving the Equation:

300x = 6000

x= 20

and, y= 20

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Answer:

44 in^2

Step-by-step explanation:

V = L×W×H

Bottom rectangle prism

L= 6 W= 4 H= 1

V = 6×4×1

V=24

Top rectangle prism

L= 2 W= 2 H= 5

V=2×2×5

V= 20

Add both of the rectangle prisms

24+25= 44