Which expression when simplified is equivalent to 43,450,000

To determine the minimum speed of a particle moving in 3-space with position function r(t) = t^2 i + 6t j + (t^2 - 24t) k, we need to find the magnitude of the velocity vector, which is the derivative of the position vector with respect to time.

v(t) = r'(t) = 2ti + 6j + (2t - 24)k

The speed of the particle at any given time t is the magnitude of the velocity vector, which is:

|v(t)| = √(4t^2 + 36 + (2t - 24)^2) = √(4t^2 + 4t^2 - 96t + 576) = √(8t^2 - 96t + 576)

To find the minimum speed, we need to find the minimum value of |v(t)|. We can do this by finding the vertex of the parabolic function 8t^2 - 96t + 576, which corresponds to the minimum value of the function.

The vertex of a parabola of the form ax^2 + bx + c is at x = -b/2a. In this case, a = 8, b = -96, and c = 576, so the vertex is at t = -b/2a = 96/16 = 6.

So the minimum speed of the particle is:

|min speed| = |v(6)| = √(8(6)^2 - 96(6) + 576) = √(288) = 12√2

Therefore, the minimum speed of the particle moving in 3-space with position function r(t) = t^2 i + 6t j + (t^2 - 24t) k is approximately 16.97 units/sec (rounded to two decimal places). Option 4, min speed = 17 units/sec, is the closest answer.

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The dealer's claim that there are "more than 1,000 different combinations" of the 10 optional packages available for the new car is justified, as there are actually 1024 possible combinations.

To determine whether the dealer's claim is justified, we need to calculate the total number of possible combinations of packages that can be selected.

Since there are 10 optional packages, there are 2^10 (or 1024) possible combinations of packages. This is because for each package, there are two possible choices: either it is selected or it is not selected.

Therefore, the dealer's claim that there are "more than 1,000 different combinations" is indeed justified. The actual number of possible combinations is 1024, which is greater than 1,000.

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According to national surveys conducted in current years, slightly more than 60% of adults within the united states of america drink alcohol.

Whilst this percentage may fluctuate slightly from year to year, it has remained pretty constant nowadays. it's crucial to be aware, however, that no longer all adults who drink alcohol do so in the same manner. some may additionally drink alcohol only on occasion or in moderation, even as others may engage in heavy or binge consuming.

Heavy alcohol consumption can have extreme health results, along with liver disorder, most cancers, and mental fitness issues, so it's critical for humans to reveal their consuming habits and are seeking help if important. additionally, it is essential for public health officers to hold tracking alcohol intake charges and promoting secure and responsible alcohol use.

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To determine which is the better value, we need to compare the cost per ounce of each bag of tortilla chips.

Joaquin should buy the 18-oz bags of tortilla chips to make his nacho platter.

For the 13-oz bag at $2.99, the cost per ounce is:

2.99 / 13 ≈ $0.23 per ounce

For the 18-oz bag at $3.42, the cost per ounce is:

3.42 / 18 ≈ $0.19 per ounce

Therefore, the 18-oz bag is the better value, as it has a lower cost per ounce than the 13-oz bag. Joaquin should buy the 18-oz bags of tortilla chips to make his nacho platter.

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Answer: D

Step-by-step explanation:

Note that where the above is given, the slant is 18.52 inches

Given the above, we can use the formula for the surface area of a triangular pyramid, which is given by...

Surface area = base area + (1/2) × perimeter × slant

where the perimeter is the sum of the lengths of the three sides of the base, and the slant is the height of each triangular face.

We are given that the base area is 55 square inches and the perimeter is 3 × 9 = 27 inches. We are also given that the total surface area is 305 square inches. Substituting  we have

305 = 55 + (1/2) × 27 × slant

Simplifying and solving for the slant, we get:

250 = 13.5 × slant

slant = 18.52 inches

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The number of students who would have a pet out of a population of 134 is equal to 90.

Percent of students did not have pet = 33%

Total number of students = 134

Number of students who do not have a pet

= 33% × 134

= 0.33 × 134

= 44.22

Since we cannot have a fraction of a student.

Round 44.22 to the nearest whole number which is 44.

This means that 44 out of the 134 students surveyed did not have a pet.

The number of students who have a pet

= subtract the number of students who do not have a pet from the total number of students.

⇒ Number of students who have a pet = 134 - 44

⇒ Number of students who have a pet  = 90

Therefore, approximately 90 students out of a population of 134 have a pet.

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The length of the square is derived to be √20 using the Pythagoras rule and the area of the square is 20 cm²

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

Let the length of the square be x, thus considering the triangle formed with the radius as the hypotenuse, x as the height and x/2 as the base, then By Pythagoras rule we can evaluate for x as follows:

x² + (x/2)² = 5²

(4x² + x²)/4 = 25

5x² = 100 {cross multiplication}

x² = 20

x = √20

Area of the square = (√20)²

Area of the square = 20 cm²

Therefore, the length of the square is derived to be √20 using the Pythagoras rule and the area of the square is 20 cm²

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1. axis of symmetry = -3

vertex = ( -3,-5)

2. axis of symmetry = -2

vertex = ( -2,-13)

3. axis of symmetry = 1

vertex = ( 1,-1)

4. axis of symmetry = 4

vertex = (4,-5)

The vertex is the highest point if the parabola opens downward and the lowest point if the parabola opens upward.

The axis of symmetry is the line that cuts the parabola into 2 matching halves and the vertex lies on the axis of symmetry.

The vertex is calculated as -b/2a and we substitute the value in the equation to get the y axis. The equation must be in the form ax²+bx + c

The axis of symmetry is calculated as -b/2a

1. x²+6x+4

axis of symmetry = -6/2 = -3

the y cordinate vertex = -3)²+6(-3)+4 = 9-18+4 = -5

therefore the vertex = ( -3,-5)

2. 2x²+8x-5

axis of symmetry= -8/2(2) = -8/4 = -2

the y cordinate of vertex = 2(-2)² + 8(-2) -5

= 8-16-5 = -13

therefore the vertex = ( -2,-13)

3. x²-2x

axis of symmetry = -(-2)/2 = 2/2 = 1

the y cordinate of vertex = 1²-2(1) = 1-2 = -1

vertex = ( 1,-1)

4. x²-8x-9

axis of symmetry = -(-8)/2 = 8/2 = 4

the y cordinate of the vertex= 4²-8(4) -9 = 16-12-9 = -5

therefore the vertex = (4,-5)

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The size of all numbered angles​ are ∠1 = 80 degrees, ∠2 = 20 degrees  and ∠3 = 80 degrees

Given that we have

The figure

Also, we have

GEF = 80 degrees

By the theorem of corresponding angles, we have

∠3 = 80 degrees

Next, we have

∠2 = 180 - 80 - 80 degrees --- sum of angles in a triangle

So, we have

∠2 = 20 degrees

Lastly, we have

∠1 = 80 degrees --- sum of angles in a triangle

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Answer:

f(x) = (x + 1)((x - 1)^2)(x - 3)

3! = 6

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers from 1 up to n. For example

1! = 1

2! = 2 x 1 = 2

4! = 4 x 3 x 2 x 1 = 24

The factorial function is defined only for non-negative integers, but it is often extended to other types of numbers, such as complex numbers or even some non-integer real numbers, using techniques from complex analysis.

Factorials are used in a variety of mathematical contexts, such as combinatorics, probability theory, and calculus. For example, in combinatorics, factorials are used to count the number of ways to arrange a set of objects, or the number of ways to choose a subset of objects from a larger set. In calculus, factorials appear in Taylor series, which are used to approximate functions as a sum of powers of x.

Hence, the correct option is D.

The expression 3! (read as "3 factorial") is a mathematical shorthand for the product of all positive integers from 1 to 3. It is written as

3! = 3 x 2 x 1

Evaluating this expression gives

3! = 6

Hence, the correct option is D.

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Therefore, the length of arc AB is 3π units (or approximately 9.42 units if rounded to the nearest hundredth).

An arc is a curved segment of a circle. It is defined by two endpoints on the circle and the curve connecting them. The length of an arc is determined by the size of the angle it subtends at the center of the circle and the radius of the circle. Arcs are used in many geometric and trigonometric calculations, such as finding the length of an arc, the area of a sector, or the measure of an angle formed by two intersecting chords. In addition, arcs are commonly used in the design of structures and objects, such as arches, bridges, and curves in roads and railways.

Here,

The formula to find the length of an arc is:

length of arc = (angle measure in degrees / 360) x 2πr

where r is the radius of the circle.

In this case, the radius is 27 units and the angle measure is 20 degrees, so we can substitute these values into the formula to get:

length of arc = (20/360) x 2π(27)

length of arc = (1/18) x 54π

length of arc = 3π

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The rectangular prism that has all the given qualities can be found to be Option D.

The shape is said to be a rectangular prism which means that it could be Options B, D, and F.

The shape is made up of more than 5 cubes which means that Option F is out as it is only made up of 4 cubes.

The volume of the rectangular prism is less than 8 cubes which means that it cannot be Option B as this has 8 cubes as its volume.

In conclusion, the rectangular prism described is Option D.

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Answer:

Step-by-step explanation:

The relationship between magnitude (M) and intensity (I) of an earthquake is given by:

I ~ 10^(1.5M + 4.8)

We can use this relationship to compare the intensities of the two earthquakes:

I1/I2 = (10^(1.5M1 + 4.8))/(10^(1.5M2 + 4.8))

= 10^(1.5(M1 - M2))

Substituting the given magnitudes, we get:

I1/I2 = 10^(1.5(8.6 - 8.2))

= 10^(1.5(0.4))

≈ 2.24

Therefore, the intensity of the first earthquake was approximately 2.24 times greater than the intensity of the second earthquake.

The solution for E in the equation V - E + F = 2 is E = V + F - 2

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

V - E + F = 2

The above equation relates the number of vertices V, the number of edges E, and the number of faces F, of a polyhedron.

It is called the Euler's formula

So, we have

V - E + F = 2

Add E to both sides

V + F = 2 + E

Subtract 2 from both sides

V + F - 2 = E

So, we have

E = V + F - 2

Hence, the solution for E is E = V + F - 2

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The correct option is B, The null hypothesis to test if the population variances differ is population variance 1 differs from population variance 2.

Variance is calculated as the average of the squared differences of each data point from the mean. In other words, variance measures how far the data points are from their average value. A high variance indicates that the data points are spread out over a wider range, while a low variance indicates that the data points are clustered more tightly around the mean.

Variance is an important concept in statistical analysis because it helps to assess the reliability of data and to make inferences about the population from a sample. It is also used in many areas of research, such as finance, economics, and engineering, to measure the risk or uncertainty associated with a set of data. Variance is closely related to other statistical measures such as standard deviation, covariance, and correlation, and is often used in conjunction with these measures to gain a deeper understanding of the data.

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Complete Question:-

Before comparing means, we need to test the relationship of the population variances. what null hypothesis would you use to determine if the population variances differ?

a. population variance 1 equals population variance 2

b. population variance 1 differs from population variance 2

c. population variance 1 is less than population variance 2

d. population variance 1 exceeds population variance 2

The requried estimate of the real height of the man is 1.7 meters and the height of the tree is 10.2 meters.

Since the man is of average height, we can assume he is about 1.7 meters tall.

From the diagram, the man is approximately 1/6 the height of the tree. Therefore, the tree is about 6 times taller than the man.

Thus, an estimate for the real height of the tree is 6 times the height of the man, which is 6 x 1.7 = 10.2 meters.

Therefore, the requried estimate of the real height of the man is 1.7 meters and the height of the tree is 10.2 meters.

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The values of l and h for the four square pyramids and values of I, w, and h for the rectangular pyramid that will produce Identical volumes is w = 4l.

In Mathematics and Geometry, a square pyramid can be defined as a type of pyramid that has a square base, four (4) triangular sides, five (5) vertices, and eight (8) edges.

In this scenario, the base areas of each geometric figures can be calculated as follows:

Square pyramid, A = L².

Rectangular pyramid, A = lw.

Where:

Since the four (4) congruent square pyramids has a combined volume that is the same as the volume of one rectangular pyramid, a relation for the dimension is given by:

4l²h/3 = lwh/3.

w = 4l.

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Answer:

Step-by-step explanation:

Dan's weight can be any value between 82 kg and 96 kg

Let's call Steve's weight "x".

According to the problem, Dan weighs 14 kg more than Steve, so Dan's weight would be x + 14.

Together, their weight would be the sum of their weights

x + (x + 14) = 2x + 14

We know that their combined weight is less than 178 kg, so the inequality will be

2x + 14 < 178

Subtracting 14 from both sides

2x < 164

Dividing by 2

x < 82

So Steve's weight is less than 82 kg.

To find the possible range of Dan's weight, we can substitute x + 14 for Dan's weight

(x + 14) < (178 - x)

Simplifying

2x < 164

x < 82

x + 14 < 96

So Dan's weight is less than 96 kg.

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As per the mentioned informations, there are 4 slip planes associated with each of the 3 unique <111> directions, giving a total of 12 unique {110} slip planes in a body-centered cubic (BCC) crystal

In a body-centered cubic (BCC) crystal, there are 12 slip systems of the {110} type. Each of these slip systems is associated with a unique slip plane.

To understand why there are 12 slip systems, consider that the {110} plane has two perpendicular <111> directions, which are the directions of maximum atomic density in a BCC crystal. Each of these <111> directions can be associated with four equivalent {110} slip planes, which intersect at a line that lies along the <111> direction.

Therefore, there are 4 slip planes associated with each of the 3 unique <111> directions, giving a total of 12 unique {110} slip planes in a BCC metal.

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Answer:

------------------------------

Factor the given expression, using the difference of squares identity:

Factoring in below steps:

Answer:

f(3) = 23,750(0.09)^3 = 6412.5

Step-by-step explanation:

Given:

[tex]0.1(-90 + 50a)[/tex]

Apply the distributive law: [tex]a(b+c)=ab+ac[/tex]

[tex]0.1(-90 + 50a)=0.1(-90)+0.1\times50a[/tex]

[tex]=0.1(-90)+0.1\times50a[/tex]

Simplify [tex]0.1(-90)+0.1\times50a[/tex]:

[tex]\boxed{\bold{=-9+5a}}[/tex]

Answer:

To draw the two triangles and state what triangle is congruent to what triangle and how we know, we start by drawing two triangles, one with vertices M, L, and R, and the other with vertices Z, J, and B. We are given that ML is congruent to ZJ, LR is congruent to JB, and angle L is congruent to angle J.

We can use the Side-Angle-Side (SAS) congruence criterion to show that the two triangles are congruent. This criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

In this case, we have ML congruent to ZJ, LR congruent to JB, and angle L congruent to angle J. Therefore, we can conclude that triangle MLR is congruent to triangle ZJB by the SAS criterion.

Answer:

To determine the possible lengths of the third side of a triangle with sides measuring 5 meters and 8 meters, we can use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

So in this case, let's call the length of the third side "x". According to the triangle inequality theorem:

5 + 8 > x

or

x < 13

8 + x > 5

or

x > -3

Since the length of a side cannot be negative, we can disregard the second inequality. Therefore, the possible lengths of the third side, "x", are:

- 5 < x < 13

So the third side can measure any length between 5 and 13 meters, exclusive of 5 and 13.

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The answer is either A. IQR, because Sunny Town is symmetric or B. IQR, because Beach Town is skewed.

We know that,

A distribution refers to the pattern of how data is spread out or distributed across different values or intervals. It is a way to describe and analyze the shape, center, and spread of a set of data.

According to question:

To determine the location with the most consistent temperature, we need to measure the variability of the temperature data in both locations. The measure of variability that is appropriate for this purpose is the interquartile range (IQR), which measures the spread of the middle 50% of the data.

Therefore, the answer is either A. IQR, because Sunny Town is symmetric or B. IQR, because Beach Town is skewed, depending on the shape of the distributions. If the temperature data in Sunny Town is symmetric, then the IQR would be appropriate to measure the spread of the data. If the temperature data in Beach Town is skewed, then the IQR would also be appropriate to measure the spread of the data. However, if the temperature data in either location is not skewed, then the range would not be an appropriate measure of variability.

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