What is the area of a rectangular picture frame with twenty inches in length, and a width of fifteen inches?​

The general common factor (GCF) of the polynomial equation [tex]24x^9 + 21x^6 = 0[/tex] is 3x6, which, after factoring, is the common factor of the coefficients and the terms enclosed in brackets.

We must factor out the common terms from both the coefficients and the exponents in order to determine the GCF (Greatest Common Factor) for the polynomial equation 24x9 + 21x6 = 0.

The first step is to determine the coefficients' common factor, which is 3. The equation can be changed to read:

3(8x^9 + 7x^6) = 0

We now need to determine which term the parenthesized terms have in common the most. Since x is raised to a power in both terms, we may factor out x^6 to obtain:

3x^6(8x^3 + 7) = 0

The greatest common factor of the polynomial equation 24x^9 + 21x^6 = 0 is 3x^6.

We can verify this by dividing both terms in the equation by 3x^6. Doing so gives us:

(8x^3 + 7) = 0

This equation has no common factors, and we cannot factor it further. Thus, the GCF of the original polynomial equation 24x^9 + 21x^6 = 0 is 3x^6

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Therefore, the length of the altitude is 4.8 centimeters.

A triangle is a closed two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and can be classified based on the length of its sides and the size of its angles. The sum of the angles of a triangle is always 180 degrees. Triangles are used in various fields of mathematics and science, including trigonometry, geometry, and physics. They also have practical applications in fields such as construction, engineering, and architecture.

Here,

Let the altitude of the right triangle be 'h' and the hypotenuse be 'c'.

We know that the altitude of a right triangle divides the triangle into two similar triangles, which are also similar to the original triangle.

Therefore, we can set up the following proportion:

h/3.6 = 6.4/h

Simplifying, we get:

h² = 3.6 x 6.4

h² = 23.04

Taking the square root of both sides, we get:

h= √23.04

h = 4.8 centimeters

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The surface area and volume of the tent are 213.5 ft² and 148?75ft³ respectively.

A prism is a solid shape that is bound on all its sides by plane faces.

The surface area of prism is expressed as ;

SA = 2B + ph. Where p is the perimeter and h is the height of the prism. B is the base area

Base area = 1/2 bh

= 1/2 × 7 × 5 = 35/2

= 17.5ft²

perimeter = 7+6+6 = 21ft

SA = 2 × 17.5 + 21 ×8.5

SA = 35+178.5

SA = 213.5 ft²

Volume of prism is expressed as;

V = base area × height

= 17.5 × 8.5

= 148.75 ft³

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The area of the composite figure is equal to 278 square inches

The composite figure can be observed to be made up of two triangles, a rectangle and a parallelogram, so we shall calculate for the area and sum the results to get the total area of the composite figure as follows:

area of top triangle = 1/2 × 8 in × 11 in = 44 in²

area of the side triangle = 1/2 × 9 in × 4 in = 36 in²

area of the rectangle = 11 in × 9 in = 99 in²

area of the parallelogram = 11 in × 9 in = 99 in²

total area of the composite figure = 44 in² + 36 in² + 99 in² + 99 in²

total area of the composite figure = 278 in²

Therefore, the area of the composite figure is equal to 278 square inches

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Answer:

there are 2,598,960 ways to deal 5 different cards from a standard 52-card deck.

Step-by-step explanation:

The number of ways 5 different cards can be dealt from a standard 52-card deck is given by the combination formula:

C(52,5) = 52! / (5! * 47!)

which simplifies to

C(52,5) = (52 * 51 * 50 * 49 * 48) / (5 * 4 * 3 * 2 * 1)

= 2,598,960

Therefore, the lawnmower can cut grass for 2.5 hours on 5/6 of a gallon of fuel in the gas can

To find out how long the lawnmower can cut grass with 5/6 of a gallon of gas, we first need to figure out how many gallons of gas the lawnmower will use per hour:

1 hour of grass cutting = 1/3 gallon of gas

1 gallon of gas = 3 hours of grass cutting

So the lawnmower uses 1/3 gallon of gas per hour, which means that 1 gallon of gas will last for 3 hours of grass cutting.

Now we can use this conversion factor to figure out how long 5/6 of a gallon of gas will last:

5/6 gallon of gas * 3 hours of grass cutting per 1 gallon of gas = 15/18 hours of grass cutting

Simplifying this fraction by dividing the numerator and denominator by 3:

15/18=3/6

So 5/6 of a gallon of gas will last for 5/6 of 3 hours, which is equal to 2.5 hours of grass cutting.

As a result, 5/6 of a gallon of gas will last for 5/6 of 3 hours, or 2.5 hours of mowing the lawn.

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The area of the rhombus is 84 square units . Option C

The formula that is used for calculating the area of a rhombus is expressed with the equation;

A = a × h

Given that the parameters are;

From the information given, we have that;

If x = 12 units, y = 4 units, and h = 7 units.

Then the area of the rhombus will be;

Substitute the values into the equation

A = 12 × 7

Multiply the values

A = 84 square units.

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Another equivalent equation to the equation (4x • 7)(5x • 9) is 28x(45x) respectively.

Equivalent equations in algebra are those that have equivalent roots or solutions.

In order to produce an equivalent equation, the same quantity or expression must be added to or subtracted from both sides of the original equation.

If you multiply or divide an equation's two sides by the same non-zero number, the results are identical.

If x4=2x+7, we can add 4 to both sides to get the following equation, which is equivalent: x4+4=2x+7+4.

So, we have the equation:

(4x • 7)(5x • 9)

Then, another equation that will be equivalent to the given equation can be:

(4x • 7)(5x • 9)

(28x)(45x )

Then,

28x(45x)

So,

(4x • 7)(5x • 9) = 28x(45x)

Therefore, another equivalent equation to the equation (4x • 7)(5x • 9) is 28x(45x) respectively.

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Answer:

We can use the Central Limit Theorem to solve this problem since we are dealing with a sample size greater than 30. The distribution of sample means will be approximately normal with a mean of 74 beats per minute and a standard deviation of 12.5 / sqrt(4) = 6.25 beats per minute.

To find the probability that the mean pulse rate of 4 adult females is between 70 and 78 beats per minute, we need to calculate the z-scores for both values and then use a z-table or calculator to find the area under the normal curve between those two z-scores.

The z-score for 70 beats per minute is:

z = (70 - 74) / 6.25 = -0.64

The z-score for 78 beats per minute is:

z = (78 - 74) / 6.25 = 0.64

Using a standard normal distribution table or calculator, the area between these two z-scores is approximately 0.4115.

Therefore, the probability that 4 adult females have pulse rates with a mean between 70 and 78 beats per minute is approximately 0.4115 or 41.15%.

The resort should sell a number of 255 packages at a price of $2400 per person to maximize their monthly profit and the maximal profit is $613,400.

Maximal profit refers to the highest level of profit that a business or organization can achieve given certain constraints such as cost, demand, or pricing. It is the point at which a company or business generates the most revenue after accounting for all expenses associated with production and distribution of goods or services. To determine the maximal profit, a business will need to find the optimal balance between costs and revenue, while also taking into account factors such as competition and market demand. This involves analyzing a variety of financial metrics such as revenue, cost of goods sold, gross profit margin, and net profit margin, among others.

Let's begin by defining some variables:

P = price of the package

Q = number of packages sold

R = revenue

C = cost

Profit = revenue - cost

Based on the information given, we can create the following equations:

R = P * Q

C = 1600 + 2000 * Q

Profit = R - C = P * Q - (1600 + 2000 * Q)

We want to find the price that will maximize the monthly profit. To do this, we need to find an expression for profit in terms of P only. We can use the equation for C to substitute Q in the expression for profit:

C = 1600 + 2000 * Q

Q = (C - 1600) / 2000

Profit = P * Q - (1600 + 2000 * Q)

Profit =

Profit = P * ((C - 1600) / 2000) - C + 1600

Now we can find the derivative of profit with respect to P:

dProfit/dP = (C - 1600) / 2000

To find the value of P that maximizes profit, we need to set the derivative equal to 0:

dProfit/dP = 0

(C - 1600) / 2000 = 0

C = 1600

This means that profit is maximized when revenue equals cost, which makes sense. Substituting C = 1600 into the expression for profit, we get:

Profit = P * ((1600 + 2000 * Q - 1600) / 2000) - 1600

Profit = P * Q - 1600

Now we need to find the corresponding values of P and Q. We know that for every increase of $100 in price, there will be a decrease of 5 in the number of packages sold. This means that:

Q = 300 - (P - 2000) / 100 * 5

Substituting this into the expression for profit, we get:

Profit = P * (300 - (P - 2000) / 100 * 5) - 1600

To find the maximum profit, we can take the derivative of this expression with respect to P and set it equal to 0:

dProfit/dP = 300 - (P - 2000) / 20 = 0

P = 2400

This means that the price that will maximize the monthly profit is $2400 per person. To find the corresponding number of packages sold, we can substitute this into the equation for Q:

Q = 300 - (2400 - 2000) / 100 * 5 = 255

Therefore, the resort should sell 255 packages at $2400 per person to maximize their monthly profit. To find the maximal profit, we can substitute these values into the expression for profit:

Profit = 2400 * 255 - 1600 = $613,400.

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The expression simplified can be written as:

6x³y  -7xy²

The correct option is the first one.

Here we have the following expression:

(4x³y - 2xy² + 3xy) + (2x³y - 5xy² - 3xy)

To simplify it, we need to group the like terms (this is terms with the same variables and correspondent exponents).

Then we can rewrite the expression as:

(4 + 2)x³y + (-2 - 5)xy² + (3 - 3)xy

6x³y  -7xy²

That is the expression simplified.

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Answer:

A:6x3y − 7xy2

Step-by-step explanation:

i took the test and got it right

Answer:

x = 50

Step-by-step explanation:

2x = 60+40

simply 60 + 40 to 100

so 2x = 100

and then divide 2 to get it to the other side.

like this = x = 100/2

then divide 100 by 2 and get 50

so x=50

Considering the binomial random variable, the probabilities are:

a. 0.1611

b. 0.8915

c. 0.7588

d. 0.1085

e. 0.0576

The binomial distribution formula is:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where:

P(X = k) is the probability of getting k successes

n is the number of trials

p is the probability of success on one trial

(n choose k) is the binomial coefficient, which is equal to n! / (k! * (n - k)!)

k is the number of successes we want to find the probability for

Using this formula, we can find the probabilities for the given scenarios:

a. P(X = 4) = (10 choose 4) * 0.15^4 * (1 - 0.15)^(10 - 4) = 0.1611

b. P(X <= 1)

= P(X = 0) + P(X = 1)

= (10 choose 0) * 0.15^0 * (1 - 0.15)^(10 - 0) + (10 choose 1) * 0.15^1 * (1 - 0.15)^(10 - 1)

= 0.8915

c. P(X >= 1)

= 1 - P(X = 0)

= 1 - (10 choose 0) * 0.15^0 * (1 - 0.15)^(10 - 0)

= 0.7588

d. P(X > 1)

= 1 - P(X <= 1)

= 1 - (P(X = 0) + P(X = 1))

= 1 - ((10 choose 0) * 0.15^0 * (1 - 0.15)^(10 - 0) + (10 choose 1) * 0.15^1 * (1 - 0.15)^(10 - 1))

= 0.1085

e. P(X < 1)

= P(X = 0)

= (10 choose 0) * 0.15^0 * (1 - 0.15)^(10 - 0)

= 0.0576

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Thus, the statement  -3 to the -3 power written without using exponents is -1/27.

A number's power or exponent, in other words, tells how many times it must be multiplied by itself. Any integer, fraction, or decimal can serve as the basis in this situation. Moreover, the exponent might have either a positive or negative value.

Given that-

-3 to the -3 power

This can written as:

= (-3)⁻³

Now using the property of exponents,taking reciprocal of the number will remove the negative number.

= (1 /-3)³

= (1)³ / (-3)³

= 1/(-27)

= - 1/ 27

Thus, the statement  -3 to the -3 power written without using exponents is -1/27.

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The surface area of the trapazoid based prism is 289.6 ft². The right option is b. 289.6 ft².

A prism is a solid shape that is bound on all its sides by plane faces.

To calculate the surface area of the trapazoid based prism, we use the formula below.

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the right option is b. 289.6 ft².

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Answer:

Step-by-step explanation:

The Unit Circle is a circle with a radius of 1 unit that is centered at the origin of a coordinate plane. It is often used in trigonometry to understand the relationships between angles, coordinates, and trigonometric functions such as sine, cosine, and tangent.

Special angles in trigonometry are angles that have commonly used values for their trigonometric functions. These special angles are 0 degrees, 30 degrees, 45 degrees, 60 degrees, and 90 degrees, and their corresponding angles in radians (which are the preferred units for angles in the Unit Circle). These angles have well-defined coordinates on the Unit Circle, and their sine, cosine, and tangent values can be easily determined.

To find the coordinates of points on the Unit Circle for special angles, we can use the following steps:

Start with the angle in radians. For example, if we are finding the coordinates for the angle of 30 degrees, we convert it to radians by multiplying by the conversion factor pi/180 (since there are pi radians in 180 degrees): 30 degrees * (pi/180) = pi/6 radians.

Identify the coordinates on the Unit Circle that correspond to the angle in radians. For example, for an angle of pi/6 radians, we know that it is located in the first quadrant of the Unit Circle, and the coordinates of the point where the angle intersects the Unit Circle are (cos(pi/6), sin(pi/6)).

Use the values of cosine and sine for the special angle from trigonometric tables or from memory. For example, the cosine of pi/6 radians is sqrt(3)/2, and the sine of pi/6 radians is 1/2.

Substitute the cosine and sine values into the coordinates of the Unit Circle. For example, for the angle of 30 degrees or pi/6 radians, the coordinates on the Unit Circle are (cos(pi/6), sin(pi/6)) = (sqrt(3)/2, 1/2).

Use the tangent function to find the tangent value of the special angle. The tangent function is defined as the ratio of sine to cosine: tan(theta) = sin(theta) / cos(theta). For example, for the angle of pi/6 radians, the tangent value is (sin(pi/6)) / (cos(pi/6)) = (1/2) / (sqrt(3)/2) = 1/sqrt(3).

In summary, special angles in trigonometry are used to determine the coordinates of points on the Unit Circle, and the sine, cosine, and tangent values of these special angles can be found using trigonometric tables or from memory, and then applied to the Unit Circle to determine the coordinates and trigonometric function values for these angles.

Answer:

10 hours

Step-by-step explanation:

[tex] \frac{28}{7} = \frac{40}{h} [/tex]

[tex]28h = 280[/tex]

[tex]h = 10[/tex]

The vector (3, 8, 1) provides the system's solution.

As a result, the system's vector solution is (3, 8, 1).

A sort of data structure used in computer programming is the vector. It is a collection of data objects that can be any type, such as strings, numbers, or even other vectors. The storage and manipulation of collections of data elements, such as a list of numbers, words, or other data elements, is done using vector data structures. Sorting, searching, and data manipulation can all be done with vector data structures.

The matrix equation Axequalsb's augmented matrix for the linear system is as follows:

[tex]\left[\begin{array}{ccc}1&-2&4\\7&-4&3\\-6&2&5\\-3&16&-29\end{array}\right][/tex]

Part - 2:

Step 1: Write the system's solution as a vector after solving it.

We must first reduce the augmented matrix to its reduced row-echelon form in order to solve this system.

[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\-5&2&0\\-3&8&1\end{array}\right][/tex]

Step 2: We can now quickly find solutions for the unknowns.

[tex]x_1[/tex] equals

3

[tex]x_2[/tex] equals

8

[tex]x_3[/tex] equals

1

Step 3:

The vector (3, 8, 1) provides the system's solution.

As a result, the system's vector solution is (3, 8, 1).

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Answer: The negative sign in front of 7/8 indicates that the fraction is negative. To find an equivalent fraction, we can keep the same value but change the sign. Therefore, an equivalent fraction that is positive would be (-(7/8)) = (-7)/8.

Step-by-step explanation:

Answer:sorryy if this is late but its 2

Step-by-step explanation:

If the job takes Reba 1 hours, the cost would be $ 19 with either artist

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let's assume the number of hours that Reba takes to paint the window is h. Then, the total cost of the job with Reba would be:

Total cost with Reba = $19 ( h )  + $41

The total cost with Pete is already given as a flat rate of $60.

We want to find the number of hours that Reba would have to take to charge the same amount as Pete, so we can set the two expressions for the total cost equal to each other and solve for "h":

$ 19 ( h ) + $ 41 = $ 60

Subtracting $41 from both sides, we get:

$ 19 ( h ) = $ 19

Dividing both sides by $ 19, we get:

h = 1

So Reba would have to take 1 hour to charge the same amount as Pete.

To calculate the cost of the job with either artist if it takes Reba 1 hour, we can substitute h=1 into the expression for the total cost with Reba:

Total cost with Reba = $ 19 ( 1 ) + $ 41 = $ 60

Hence , this is the same as the flat rate quoted by Pete, so the cost of the job would be $60 with either artist if it takes Reba 1 hour

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Answer:

208

Step-by-step explanation:

4*4(2)+11*4(2)+11*4(2)=208

Find the small squares.

4^2+4^2=32

4*11*4=176

176+32=208

Answer:

Here are two example data sets that meet the given conditions:

Data Set 1:

Values: 10, 12, 14, 16, 18, 20

Mean: (10+12+14+16+18+20) / 6 = 15

MAD: Mean Absolute Deviation = sum(abs(x - mean))/n = ((|10-15| + |12-15| + |14-15| + |16-15| + |18-15| + |20-15|)/6) = 2.5

Story: This dataset may have originated from measuring the time taken to complete a series of tasks by a group of skilled workers. The values represent the time taken in seconds, and the low MAD value indicates that the workers' performance was consistent. The mean value of 15 seconds suggests that the workers were efficient, completing the tasks quickly and accurately.

Data Set 2:

Values: 3, 5, 7, 9, 11, 13

Mean: (3+5+7+9+11+13) / 6 = 8

MAD: Mean Absolute Deviation = sum(abs(x - mean))/n = ((|3-8| + |5-8| + |7-8| + |9-8| + |11-8| + |13-8|)/6) = 2.5

Story: This dataset may have originated from measuring the height of a group of plants grown under different conditions. The values represent the height in inches, and the low MAD value indicates that the plants' growth was consistent across all conditions. The mean value of 8 inches suggests that the conditions were not optimal for plant growth, as the mean height is lower than the expected average for this type of plant.

Both data sets have a similar MAD value of 2.5, indicating that the variation in the data is relatively low, and the differences in the mean values suggest that they came from different sources. In both cases, the means are more than one MAD apart, indicating that there are significant differences between the values in each set.

Answer:

Step-by-step explanation:

17.5

The options that are not seen as retirement plan(s) are: II, IV

II. Pension Plan

IV. Traditional IRA

A defined contribution plan is a retirement plan in which the contributions made by or on behalf of the employee are defined, but the ultimate benefit depends on the performance of the investments made with those contributions.

Based on this definition, the retirement plans that are not considered defined contribution plans are:

II. Pension Plan - Pension plans are typically defined benefit plans, where the ultimate benefit is based on a formula that takes into account the employee's salary and years of service, rather than the contributions and investment returns.

IV. Traditional IRA - Traditional Individual Retirement Arrangements (IRAs) are also not defined contribution plans. While they do involve individual contributions, the ultimate benefit is not solely based on the contributions and investment returns, but rather on various factors, such as the individual's age, income, and tax deductions.

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The required value of impulse is 88 N-s and the mass of the cart is 8.8 kg.

Newton's Second Law relates an object's acceleration as a function of both the object's mass and the applied net force on the object.

Given data:

The speed of cart is, v = 10 m/s.

We are given the Force-time graph for which the area of the force-time graph will provide the value of impulse. So from the graph, the maximum force is,

F = 22 N

And time interval is,

t = 4.5 s - 0.5 s

t = 4 s

So, the impulse is,

I = Area of graph

I = F × t

I = 22 × 4

I = 88 N-s

Now the standard expression for the impulse as per the impulse-momentum theorem is,

I = ΔP (Change in momentum)

I = m ×( v - u )

Here, u is the final velocity, and since the cart stops finally, then u = 0 m/s. And m is the mass of the cart.

Solving as,

88 = m ×( v - u )

88 = m ×( 10 - 0 )

m = 8.8 kg

Thus, we can conclude that the required value of impulse is 88 N-s and the mass of car is of 8.8 kg.

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Thus, the area of the given trapezium is found toe be 37.8 sq. cm.

A trapezium is a quadrilateral in two dimensions with one pair of parallel sides. The non-parallel sides of a trapezium are referred to as the trapezium's "legs," while the parallel sides are referred to as its "bases." The length of the legs or the measuring of their angles are used to categorise trapeziums.

Given data:

area of trapezium = 1/2(sum of parallel side) * height

area  of trapezium = 1/2(PQ + CR)*PA

area  of trapezium = 1/2*(3.15 + 6.3)*8

area  of trapezium = 1/2*(9.45)*8

area  of trapezium = 37.8 sq. cm

Thus, the area of the given trapezium is found toe be 37.8 sq. cm.

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Answer: To answer this question, we need to calculate the maximum possible speed of the train based on the given information and check if it is greater than 160 km/h.

First, let's use the given information to find the range of possible speeds of the train. The time taken by the train is given as 110 minutes, correct to the nearest 5 minutes. This means that the actual time taken by the train could be anywhere between 107.5 minutes and 112.5 minutes.

Converting the time to hours, we get:

Lower bound of time = 107.5 minutes = 107.5/60 hours = 1.792 hours

Upper bound of time = 112.5 minutes = 112.5/60 hours = 1.875 hours

Now, let's use the given distance of 270 km, correct to the nearest 10 km, to find the range of possible average speeds of the train. The lower bound of the distance is 265 km, and the upper bound is 275 km.

Lower bound of speed = 265 km / 1.875 hours = 141.3 km/h

Upper bound of speed = 275 km / 1.792 hours = 153.5 km/h

Therefore, based on the given information, the maximum possible speed of the train is 153.5 km/h, which is less than 160 km/h.

So, we can conclude that the average speed of the train could not have been greater than 160 km/h.

Step-by-step explanation:

Answer:

Step-by-step explanation:

when h=0

0=-1125d²+d

1125d²-d=0

d(1125d-1)=0

d=0

or 1125d-1=0

d=1/1125 meters