The volume of the rectangular prism is given by V(X)=3x^3+x^2-2x+3. Find the missing measures if you know the length is given by (x+1). Find the height and width.

The amount of money it would cost to recarpet the rectangular hotel room is equal to $1,752.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LB

Where:

By substituting the given parameters into the formula for the area of a rectangle, we have the following;

Area of rectangular hotel room = 4 × 6

Area of rectangular hotel room = 24 yd²

Now, we can determine the cost as follows;

Cost of recarpet = $73.00 × 24 yd²

Cost of recarpet = $1,752.

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The arc length SR is 6.98ft

Arc length is the distance between two points along a section of a curve. An arc is a cut out section of a circumference of a circle.

The arc angle = sector angle in the diagram

The length of an arc is expressed as;

l = tetha/360 × 2πr

where r is the radius and tetha is the angle between the two radii.

l = 100/360 × 2 × 4 × 3.14

l = 314 × 8/360

l = 2512/360

l = 6.98( nearest hundredth)

therefore the length of the arc is 6.98 ft

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The transformed fuction shifted 4 units to the right of the parent function is g(x)= x + 2

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

Parent function, f(x)= x+6,

Transformation: shifted 4 units to the right

The rule of the above transformation is

g(x) = f(x - 4)

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

g(x)= x - 4 + 6,

Evaluate the terms

g(x)= x + 2

Hence, the transformed fuction is g(x)= x + 2

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The percentage of the can that is not occupied by tennis balls is approximately 80.14%.

We have,

The volume of the can = The volume of the cylinder - The volume of the three tennis balls.

The volume of the cylinder.

V(cylinder) = πr²h

where r is the radius and h is the height of the cylinder.

Since the can holds three tennis balls snugly, the height of the cylinder is equal to three times the diameter of a tennis ball.

= 3 × 2(3.5 cm)

= 21 cm.

V(cylinder)

= π (3.5 cm)² (21 cm)

= 2709.38 cm³

The volume of one tennis ball.

V (ball) = (4/3)πr³

where r is the radius of the tennis ball. Thus,

V(ball) = (4/3)π(3.5 cm)³ = 179.594 cm³

The total volume of the three tennis balls is:

V(3balls) = 3 V(ball)

= 3(4/3) π (3.5 cm)³

= 538.782 cm³

The volume of the can not be occupied by tennis balls.

V(not occupied) = V(cylinder) - V(3 balls)

= 2709.38 - 538.782

= 2170.598 cm³

The percentage of the can that is not occupied by tennis balls.

percentage = (V(not occupied / V(cylinder)) × 100%

= (2170.598 cm^3/2709.38 cm^3) × 100%

= 80.14%

Therefore,

The percentage of the can that is not occupied by tennis balls is approximately 80.14%.

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The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:

0: µ = 14 (null hypothesis)

1: µ ≠ 14 (alternative hypothesis)

Option B is the correct answer.

We have,

The null hypothesis states that the population mean for the number of hours spent studying by full-time students at 4-year colleges in the United States is equal to 14 hours per week,

while the alternative hypothesis states that it is different from 14 hours per week.

By using a two-tailed test, we are checking for any significant change in either direction, whether the average number of hours spent studying has increased or decreased from 14 hours per week.

Thus,

The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:

0: µ = 14 (null hypothesis)

1: µ ≠ 14 (alternative hypothesis)

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It can hold 200 unit³ of popcorn.

The amount of paper used is 150 unit².

We have,

b = 8 unit

h = 5 unit

l = 10 unit

So, Volume of Triangular prism

= 1/2 x b x h x l

= 1/2 x 8 x 5 x 10

= 40 x 5

= 200 unit³

and, the amount of paper used

= 6 x 5 + 8 x 5 + 10 x 5 + 1/2 x 6 x 10

= 30 + 40 + 50 x 30

= 150 unit²

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Answer: 11

Step-by-step explanation:

-3 x 11 = -33

The inequality representing your total sales is:

15x + 20y >= 150

Let x be the number of small bowls and y be the number of large bowls.

The inequality representing your total sales is:

15x + 20y >= 150

Two possible solutions are:

x = 10, y = 0: Selling 10 small bowls ($150) and no large bowls meets the sales requirement.

x = 3, y = 6: Selling 3 small bowls ($45) and 6 large bowls ($120) results in $165 in sales, which exceeds the minimum sales target.

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The image is reflected over the y-axis. Then the correct option is B.

Given that:

Point of the polygon VWXYZ, W(2, 4)

Point of the polygon V'W'X'Y'Z', W'(-2, 4)

The translation does not change the shape and size of the geometry. But changes the location.

The reflection does not change the shape and size of the geometry. But flipped the image.

The point W' can be obtained by reflecting the shape across the y-axis.

Thus, the correct option is B.

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The missing diagram is given below.

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

Answer:

all triangle angle measures should add up to 180.  So given that,

40+60+80=180

Therefore it can be done

Answer:

23,850 cubic inches

Step-by-step explanation:

I think I know your dad officer Chau he works at my middle school in Navarre. this was also kind of a basic and easy question I would recommend trying to figure it out yourself before turning to the internet.

Answer:

The amount of air needed to fill the basketball is approximately 533.16 cubic inches

Step-by-step explanation:

To find the amount of air needed to fill a basketball, we need to first calculate its volume. We can use the formula for the volume of a sphere, which is V = (4/3)πr^3, where π is approximately 3.14 and r is the radius of the sphere.

Since the diameter of the basketball is given, we need to first find the radius by dividing the diameter by 2:

r = 9.45 in / 2 = 4.725 in

Now we can plug in the value of r into the formula for the volume:

V = (4/3)πr^3 = (4/3)π(4.725 in)^3 = 533.16 in^3

Therefore, the amount of air needed to fill the basketball is approximately 533.16 approx cubic inches.

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Answer:

the probability of selecting a quarter or a nickel is 0.495 or 49.5%.

Step-by-step explanation:

The probability of selecting a quarter or a nickel can be found by adding the probability of selecting a quarter to the probability of selecting a nickel. Since the coins are chosen randomly, the probability of selecting a coin from the jar is the number of coins of that type divided by the total number of coins in the jar.

So, the probability of selecting a quarter is:

P(quarter) = number of quarters / total number of coins

P(quarter) = 80 / (70 + 100 + 80 + 50)

P(quarter) = 0.32

Similarly, the probability of selecting a nickel is:

P(nickel) = number of nickels / total number of coins

P(nickel) = 70 / (70 + 100 + 80 + 50)

P(nickel) = 0.175

To find the probability of selecting a quarter or a nickel, we add these probabilities:

P(quarter or nickel) = P(quarter) + P(nickel)

P(quarter or nickel) = 0.32 + 0.175

P(quarter or nickel) = 0.495

Therefore, the probability of selecting a quarter or a nickel is 0.495 or 49.5%.

About 49.87% of buyers paid between $150,000 and $156,000 for the new homes.

According to the 68-95-99.7 rule, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations of the mean, and 99.7% falls within three standard deviations of the mean in a normal distribution.

In this case, the mean price of a certain model of new homes is $150,000, and the standard deviation is $2000. Thus, we can calculate the price range of one standard deviation above and below the mean as:

Lower Bound = Mean - 1 × Standard Deviation = $150,000 - $2,000 = $148,000

Upper Bound = Mean + 1 × Standard Deviation = $150,000 + $2,000 = $152,000

Therefore, approximately 68% of buyers paid between $148,000 and $152,000 for the new homes.

To find the percentage of buyers who paid between $150,000 and $156,000, we need to calculate the z-scores for these values using the formula:

z-score = (value - mean) / standard deviation

For $150,000:

z-score = ($150,000 - $150,000) / $2,000 = 0

For $156,000:

z-score = ($156,000 - $150,000) / $2,000 = 3

Looking at the z-score table, we can see that the area under the normal curve between z = 0 and z = 3 is approximately 49.87%.

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The missing sides of the right triangle were obtained below.

Pythagoras' theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

We have that;

1) x = √26^2 - 10^2

x = 24

2) x = √20^2 + 14 ^2

x = 24.4

3) x = √50^2 - 30^2

x = 40

4) x = √15^2 + 5^2

x = 15.8

5) x = √12^2 + 20^2

x = 23.3

These are the sides that are missing.

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Answer:

Step-by-step explanation:

I’m sorry but I don’t know how I can solve you question

The Vector R will be 4.8 units in the direction of East of South. Then the correct option is B.

Given that:

Vector C is 3.5 units West

Vector D is 3.3 units South

The quantity which has magnitude, and direction, and follows the law of vector addition is called a vector.

Vector R is equal to Vector D - Vector C. Then we have

Vector R = Vector D - Vector C

Vector R = 3.3 units South - 3.5 units West

Vector R = 3.3 units South + 3.5 units East

Vector R = √((3.3)² + (3.5)²)

Vector R = 4.8 units

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The acceleration of the car at that time was 3 m/s².

We have,

From the kinematic equation to find the acceleration:

v = u + at

where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

Initial velocity u = 15 m/s

Final velocity v = 45 m/s,

Time t = 10 s

We can rearrange the equation to solve for acceleration:

a = (v - u) / t

Substituting the values, we get:

a = (45 m/s - 15 m/s) / 10 s

a = 3 m/s^2

Therefore,

The acceleration of the car at that time was 3 m/s².

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The complete question in english.

A car moving on a straight track increases its speed from 15 m/s to 45 m/s using a

po of 10 seconds. Assuming that the acceleration was uniform, calculate:

acceleration at that time.

Answer:

(1/2)(4)(3)(2) = 12 cubic yards

The correct answer is A.

[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=2 \end{cases}\implies V=\cfrac{4\pi 2^3}{3} \\\\\\ V=\cfrac{4(3.14) 2^3}{3}\implies V=33.49~yd^2[/tex]

Answer:

33.49 yds^3

Step-by-step explanation:

the volume formula for a sphere is 4/3 pi r^3

so just fill in r with 2 and the pi with 3.14 and it becomes 4/3 times 3.14 times 2^3 which would equal 33.49 yds ^3 (im pretty sure at least)

The sum of the interior angle of the regular hexagon is S = 720°

Given data ,

Sum of Interior angles of a polygon with n sides is

nθ = 180 ( n - 2 )

where n is the number of sides

θ = angle in degrees

when n = 6 for a hexagon , we get

nθ = 180 ( 6 - 2 )

nθ = 180 x 4

nθ = 720°

Hence , the sum of interior angles of a hexagon is 720°

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Answer: 9.66666667

Step-by-step explanation:

To find the number of days it would take to build a similar house, we would need to create a proportion.

Workers: 27:9

Days: 29:?

Let's simplify.

Workers: 3:1

Days: 29:?

Now, we divide 29 by 3 to see how many days it would take to build a similar house.

29/3=9.666666667 (9.6 repeating)

So, your answer would be 9.6

Hope this helps!

The requried amount of fencing needed t cover the pond in this backyard is 319.36 meters.

A figure of Robert's backyard has been shown, we have to determine the perimeter of his backyard,

The perimeter of backyard = 2L + 2[πw/2]
The perimeter of backyard = 2*78 + 2[π*52/2]
The perimeter of the backyard = 319.36 meters

Thus, the requried amount of fencing needed t cover the pond in this backyard is 319.36 meters.

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Factorization is a mathematical process of breaking down a number or an expression into smaller numbers or simpler expressions that can be multiplied together to get the original number or expression.

Expressions, which are essentially mathematical statements containing numbers and letters, can be factorized in algebra. For illustration, consider the phrase 2x + 4. Finding the expressions or numbers that are common to each term allows us to factorize the expression. Since 2 appears in both terms, we can remove it by factoring to get 2(x + 2).

Given equation =  [tex]2x^{2} + 7x + 6[/tex]
                         ⇒   [tex]2x^{2} + 4x + 3x + 6[/tex]

                         ⇒ [tex]2x ( x+2) +3(x+2)[/tex]

                         ⇒[tex](2x + 3) (x+2)[/tex]

Therefore the factors of the expression [tex]2x^{2} + 7x + 6[/tex] are [tex](2x + 3) (x+2)[/tex].

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Since first four points in this table have been plotted on the scatter graph, the points that shows where the last point should be plotted is C.

In Mathematics and Geometry, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

Based on the cartesian coordinate (grid) above, the coordinate points and quadrants should be identified as follows;

Point C ⇔  (130, 180) → quadrant I.

In conclusion, we can logically deduce that the each of the intervals on both the x-axis and y-axis is equal to 10 units.

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The probability is given as 7 / 60 for the favorite sport of the person being bicycling

The frequency of bicycling in the table is goven as 7

We have tp add the total of all of the values in order to get the given probability

Hence we would have

2 + 11 + 6 +20 + 7 + 14

= 60

The probability is given as 7 / 60

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The quadratic equation that has 5i and -5i as solutions is:

x²+ 25 = 0

The quadratic equation is the polynomial having the highest power of 2. If 5i and -5i are the solutions to the quadratic equation, then the quadratic equation can be written as:

(x - 5i)(x + 5i) = 0

Expanding this equation, we get:

x² - (5i)² = 0

x² - 25i² = 0

Since i² = -1, we can substitute -1 for i², giving us:

x² - 25(-1) = 0

x² + 25 = 0

Therefore, the quadratic equation that has 5i and -5i as solutions is:

x²+ 25 = 0

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Hello! Here are the recursive definitions of the given sequence:

A) The sequence is increasing by 7 for each term, so the recursive definition can be written as:

a1 = 3

an = an-1 + 7

So, the recursive definition of the sequence is: 3, 3+7=10, 10+7=17, 17+7=24, ...

B) The second option given, "anan-1 + 10 a1 = 3" is not a recursive definition of the sequence.

C) The third option given, "San = 10an-1" is also not a recursive definition of the sequence because it uses a different variable 'S' instead of 'a'.

The statement which is true about the end behaviour of the given quadratic function is;

As evident from the task content; the answer choice which correctly describes the end behaviour of the given quadratic function is to be determined.

By observation, the given quadratic graph opens upwards and on this note, its end behaviour is such that; As x approaches -∞, f(x) approaches ∞, and as x approaches ∞, f (x) approaches ∞.

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