Maria and Ming start at the same point and rive in opposite directions. Maria drives 36 mph and Ming drives 32 mph. How far apart will they be in 2 hours

The value of the definite integral is determined as -1/28.

A definite integral is a mathematical concept that represents the area under a curve between two specific points, called the limits of integration. The definite integral is denoted by the symbol ∫, and the limits of integration are written as a and b, where a is the lower limit and b is the upper limit.

To evaluate the definite integral, we will use the following method:

[tex]\int\limits^2_0 {- \frac{6x}{(3x + 2)^2} } \, dx ; u = 3x^2 + 2[/tex]

We can start by substituting [tex]$u=3x^2+2$[/tex], which gives us [tex]$du/dx=6x$[/tex], or [tex]$x,dx=du/6$[/tex].

Using this substitution, we can rewrite the integral as:

[tex]\int\limits^2_0 - \frac{6x}{(3x^2 + 2)^2} , dx &\\\\\\\=\ \int\limits^{u(2)}{u(0)} -\frac{1}{u^2},du/6\\\\\\&= \left[ \frac{1}{6u} \right]^{u(2)}{u(0)} \\\\\\&= \frac{1}{6}\left(\frac{1}{u(2)} - \frac{1}{u(0)}\right)\\\\\\\&= \frac{1}{6}\left(\frac{1}{3(2)^2 + 2} - \frac{1}{3(0)^2 + 2}\right) \\\\\\\&= \frac{1}{6}\left(\frac{1}{14} - \frac{1}{2}\right)\\\\\\\ &= \frac{1}{6}\left(-\frac{6}{28}\right) \\\\\\\\&= \boxed{-\frac{1}{28}}\end{align*}[/tex]

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On the number line, there are five spaces between the points J and K.

A number line is a horizontal line with consistently spaced numerical increments. How you respond to the number on the line will depend on the numbers on the line. Depending on the question that goes with it, a number can be used in a variety of ways, such as when graphing a point.

The absolute value of the difference in the coordinates between points J and K on the number line can be used to calculate the distance between them.

Points J and K in this instance have coordinates of -4 and 1, respectively. As a result, the following formula may be used to indicate the distance between locations J and K:

|1 - (-4)|

If we condense this expression, we get:

|1 + 4|

= |5|

= 5

Hence, the distance on the number line between points J and K is 5.

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Initially, 1/4 of the tank was filled.

After adding 12 gallons, it was 3/4 full.

Increase in fuel filled portion =

[tex]\dfrac{3}{4} -\dfrac{1}{4} =\dfrac{3-1}{4} =\dfrac{2}{4}[/tex]

So 2/4 of the tank = 12 gallons

1/4 of tank [tex]= 12 \div 2 = 6[/tex] gallons

4/4 of tank [tex]= 6\times4 = 24[/tex] gallons

____________________

Portion remaining to be filled =

[tex]1-\dfrac{3}{4} =\dfrac{4-3}{4} =\dfrac{1}{4}[/tex]

Fuel needed [tex]= \dfrac{1}{4} \times 24 = 6[/tex] gallons

So you need 6 more gallons to fill the tank

Answer:

To show that a x - 4 is a factor of the function f(x) = 2x^3 - 5x^2 - 11x - 4, we need to show that f(a x - 4) = 0 for all values of x.

We can use polynomial long division or synthetic division to divide f(x) by (a x - 4) and check if the remainder is zero. Here, we will use synthetic division:

4/a | 2   -5   -11   -4

   |     8a  12a  4a-16

   +------------------

   2   8a-5  a-11  4a-20

The last term in the bottom row of the table is the remainder, which is 4a - 20. We can see that this remainder is equal to zero if a = 5.

Therefore, if we substitute x = (5/ax - 4) into the function f(x), we get:

f(a x - 4) = 2(5/ax - 4)^3 - 5(5/ax - 4)^2 - 11(5/ax - 4) - 4

Simplifying this expression, we get:

f(a x - 4) = 0

This means that a x - 4 is indeed a factor of the function f(x) = 2x^3 - 5x^2 - 11x - 4 when a = 5.

Answer:

The volume of this rectangular prism is

4 × 3 × 8 = 96 square inches. So Eli would need 96 unit cubes.

For the given pyramid the area of the cross section is 1,307.63 mm² (option D).

What is pyramid?

A pyramid is a geometrical shape that has a polygonal base and triangular faces that meet at a common vertex, called the apex.

We can use the formula for the area of a trapezoid to find the area of the cross section. Since the slice is perpendicular to the base of the pyramid, the cross section will be a trapezoid.

The length of the top side of the trapezoid is the same as the length of one of the sides of the rectangular base of the pyramid, which is 37.8mm. The length of the bottom side of the trapezoid can be found using similar triangles:

(49.3 / 37.8) = (bottom side / height)

Simplifying, we get:

bottom side = (height x 49.3) / 37.8 = (42.1 x 49.3) / 37.8 = 54.94 mm

The height of the trapezoid is the same as the height of the pyramid, which is 42.1mm.

Using the formula for the area of a trapezoid:

area = [(top side + bottom side) x height] / 2

area = [(37.8 + 54.94) x 42.1] / 2

area = 1,307.63 mm²

Therefore, the area of the cross section is 1,307.63 mm² (option D).

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Answer:

46

Step-by-step explanation:

b*2 - 16a + 5                              a = 1/2      b = 7

= (7)² - 16(1/2) + 5

= 49 - 8 + 5

= 41 + 5

= 46

The minimum purchase Jonathan can make to meet his spending requirement is 7 pants and 0 shirts, which will cost him $350.

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. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".

Assuming Jonathan only wants to buy shirts and pants, let's represent the number of shirts he buys as "s" and the number of pants as "p". Then we have two equations:

1. The total cost of Jonathan's purchase:

35s + 50p >= 350

2. Jonathan wants to spend at least $350:

s, p >= 0

To solve this problem, we can start by finding the minimum number of pants Jonathan needs to buy to meet his spending requirement.

When s = 0, 50p >= 350, so p >= 7.

Therefore, Jonathan needs to buy at least 7 pants.

If Jonathan buys 7 pants, the total cost of his purchase is 35s + 50(7) = 35s + 350. To spend at least $350, he needs to buy enough shirts to make the total cost of his purchase at least $350.

35s + 350 >= 350

35s >= 0

s >= 0

Since s must be a non-negative integer (you can't buy a fractional part of a shirt), Jonathan needs to buy at least 0 shirts.

So the minimum purchase Jonathan can make to meet his spending requirement is 7 pants and 0 shirts, which will cost him $350.

Of course, Jonathan can buy more than 7 pants and/or some shirts to meet his spending requirement. For example, he could buy 5 pants and 4 shirts, which would cost him $375.

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Answer:

To solve 2^x = 32, we need to find the value of x that satisfies the equation.

We can rewrite 32 as a power of 2 by noting that 2^5 = 32. Therefore, we have:

2^x = 2^5

Since the bases of the powers are equal, we can equate the exponents:

x = 5

So the solution to 2^x = 32 is x = 5.

To rewrite this equation in a logarithmic form, we can use the definition of logarithms:

log(base 2)32 = x

Here, the logarithm with base 2 of 32 is equal to x.

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(a) The 95% confidence interval for the difference in proportions of people who may find these medications effective is 0.029 to 0.231, which suggests that medication A is more effective than medication B in relieving joint pain.

(b) No, the interval does not contain zero, which means that the difference in proportions is statistically significant and supports the hypothesis that medication A is more effective than medication B.

Triangle 1: 80°, 62° Triangle 2: 62°, 38° - Similar

Triangle 1: 29°, 47° Triangle 2: 91°, 76° - Nοt Similar

Triangle 1: 100°, 45° Triangle 2: 25°, 45° - Nοt Similar

Twο triangles are similar if their cοrrespοnding angles are cοngruent and their cοrrespοnding sides are prοpοrtiοnal, meaning that they have the same shape but nοt necessarily the same size.

Triangles Similar οr Nοt Similar

Triangle 1: 80°, 62° Triangle 2: 62°, 38° - Similar

Triangle 1: 29°, 47° Triangle 2: 91°, 76° - Nοt Similar

Triangle 1: 100°, 45° Triangle 2: 25°, 45° - Nοt Similar

Tο determine if twο triangles are similar, we need tο check if their cοrrespοnding angles are cοngruent and their cοrrespοnding sides are prοpοrtiοnal.

In the first pair οf triangles, the measures οf the twο angles in Triangle 2 are cοrrespοnding angles tο the twο angles in Triangle 1, sο if we subtract the angle measures frοm 180 degrees, we can see that the third angles in bοth triangles are cοngruent:

Angle 1 in Triangle 1 = 80 degrees, Angle 2 in Triangle 1 = 62 degrees, Angle 3 in Triangle 1 = 180 - 80 - 62 = 38 degrees

Angle 1 in Triangle 2 = 62 degrees, Angle 2 in Triangle 2 = 38 degrees, Angle 3 in Triangle 2 = 180 - 62 - 38 = 80 degrees

Since the cοrrespοnding angles are cοngruent, the triangles are similar.

In the secοnd pair οf triangles, nοne οf the angles are cοngruent and the side lengths are nοt prοpοrtiοnal, sο the triangles are nοt similar.

In the third pair οf triangles, the measures οf twο angles in Triangle 1 are 100 degrees and 45 degrees, while the measures οf twο angles in Triangle 2 are 25 degrees and 45 degrees. The angles are nοt cοngruent, sο the triangles are nοt similar.

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Answer:

Step-by-step explanation:

Answer:Ken 3 3\4 pounds of apples

Step-by-step explanation:

Using geometric progression Rabbits after 5 years will be 5120. Rabbits after 10 years will be 52,428,800.

When each term is varied by another by a common ratio, the series is referred to as a geometric progression or sequence. When we multiply the previous term by a constant (which is non-zero), we get the following term in the series. It should be mentioned that the common ratio is obtained by dividing any succeeding term by its preceding term.

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate organizations or groups.

In this question,

The number of rabbits initially=50=a

rabbits after 6 months=100

common ratio=r= 100/50=2

Since it is a geometric progression, the 11th term will give us the number of rabbits after 5 years.

a₁₁=a₁(r)¹¹⁻¹

   =50(2)¹⁰=5120

the 21th term will give us the number of rabbits after 10 years.

a₂₁=a₁(r)²¹⁻¹

    =50(2)²⁰=52,428,800

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Answer:

Each pendant costs $3.70.

Step-by-step explanation:

Let's assume that the cost of each pendant is x dollars.

The total cost of the beads for all 4 necklaces is 4 * $2.70 = $10.80.

The total cost of the beads and pendants for all 4 necklaces is $25.60.

So, the total cost of the pendants for all 4 necklaces is

$25.60 - $10.80 = $14.80.

Since there are 4 necklaces and each necklace has a pendant, the total cost of all the pendants is 4x dollars.

So we can write

4x = $14.80

Dividing both sides by 4, we get

x = $3.70

Therefore, each pendant costs $3.70.

Answer:

Step-by-step explanation:

To get the LCM in the denominator:

1/2 x 9/9 = 9/18

3/9 x 2/2 = 6/18

9/9 and 2/2 both equal 1, so multiplying these fractions by ny number will result in the same number since any number times 1 is the same number.

9/18 - 6/18 = 3/18

Simplifying this answer:

3/18 = 1/6 because both the numerator and denominator are both multiples of three and are divisible by three.

The answer is 1/6.

Answer: 7/9 or 0.83333333333

Step-by-step explanation:

:D Hope it helped!!! :)

The formula can also be written as: a(n) = 25(1.025)ⁿ where 1.025 is the factor by which the initial amount is multiplied after each year of interest.

In mathematics, a function is a rule that assigns each input (or element of the domain) a unique output (or element of the range). It is a mathematical object that takes an input and produces an output based on a specified rule or set of rules. A function can be represented in different ways, such as by an equation, a graph, or a table of values. The most common notation for a function is f(x), where x is the input and f(x) is the corresponding output. Functions are used to describe relationships between quantities in various fields of mathematics and science, such as in calculus, linear algebra, statistics, physics, and engineering. They are also used in modeling real-world situations and solving problems in many areas, including finance, economics, and computer science.

Here,

The formula for calculating the amount of money in Anna's savings account with an initial deposit of $25 and 2.5% annual interest rate, compounded annually, is:

a(n) = 25(1 + 0.025)ⁿ

where t is the number of years since the account was opened.

This is the formula for calculating the future value of a present sum using compound interest formula.

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Complete question:

anna uses $25 to open a savings account. The function a(t) models the amount of money, a in her account, where t is the number of years since the account was opened. create a function that models the situation if her account earns 2.5% interest per year.

Answer: B. 5/20

Step-by-step explanation: We have 3 sections. Red, blue, and green. Red is 9/20, blue is 6/20. If we do 9+6, it equals 15. Since it's out of 20, you have to do 20-15 which equals 5. Your answer is 5/20.

The volume of the cone in cubic centimeters in terms of π = 120π cm³. That is option B.

To calculate the volume of a cone, the formula that is to be used;

Volume = 1/3 πr²h

Where;

Height = 10 centimetres

Radius = 6 centimetres

Volume = 1/3 × π × 6²× 10

= 360π/3

= 120π cm³

Therefore the volume of the cone whose dimensions are given = 120π cm³.

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Alen has read 60% of a book in which there are 80 pages in the book.

The term "total number" typically refers to the complete quantity or count of something. It can refer to the number of items in a set, the number of people in a population, the total sales of a company, or any other numerical quantity that represents a whole.

Let's say the total number of pages in the book is "x".

According to the problem, Alen has read 60% of the book, which means he has completed 0.6x pages.

He still has 32 more pages to finish, so the number of pages he has left to read is (x - 0.6x) = 0.4x.

We can set up an equation:

0.4x = 32

Solving for x:

x = 80

Therefore, there are 80 pages in the book.

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Answer:

We can rewrite the function as:

f(x) = 3(8√3)^(2x) = 3(2^3√3)^(2x)

Using the properties of exponents, we can rewrite this as:

f(x) = 3(2^(3*2x)√3^(2x)) = 3(2^(6x)√(3^(2x)))

Therefore, the base of the exponent is 2.

Answer:

5

Step-by-step explanation:

this is wrong

Answer:

I can explain how to complete each of the steps you have provided.

1. Draw a point at (1, -2)

This is a simple step. Just mark a dot on your paper at the coordinates (1, -2).

2.

Draw an 8-unit long radius

Using your compass, set the radius to 8 units. Place the compass on the point you drew in step 1 and draw a circle around it, making sure that the radius is 8 units long.

3. Using a compass

Draw a circle with your point from step one as your center and the point from step two as the side: This step is already completed in step 2.

4. Using a protractor draw a 70 degree arc

Place your protractor on the center of the circle (the point you drew in step 1) and draw a 70 degree arc on the circle.

5. Draw a central angle which intercepts your arc

Use a straight edge to draw a line from the center of the circle to each endpoint of the arc you drew in step 4. This creates a central angle, which is an angle whose vertex is at the center of the circle and whose sides intercept the circle.

6. Draw an inscribed angle which intercepts a 40 degree arc

Use a straight edge to draw a line from one endpoint of the 70 degree arc to the other endpoint. Then, draw a perpendicular bisector of this line, which intersects the center of the circle. This creates a 40 degree arc on the circle. Draw a line from the center of the circle to one endpoint of the 40 degree arc, and draw a line from that endpoint to the other endpoint of the 40 degree arc. This creates an inscribed angle, which is an angle whose vertex is on the circle and whose sides intercept the circle.

7. Draw a tangent line

Choose a point on the circle that is not on the 70 degree arc. Draw a line from that point tangent to the circle.

8. Draw a secant line

Choose two points on the circle that are not on the 70 degree arc. Draw a line through those points, which intersects the circle at two points.

9. Equation of your circle

The equation of a circle with center (a,b) and radius r is (x-a)^2 + (y-b)^2 = r^2. Using the coordinates of the center from step 1 and the radius from step 2, the equation of the circle is (x-1)^2 + (y+2)^2 = 64.

In response to the stated question, we may state that As a result, the cylindrical container can carry around 196.35 cm3 of water. As a result, (a) 196.35 cm cubic is the right answer.

A cylinder seems to be a three-dimensional geometric shape made up of two parallel congruent circular bottoms and a curving surface linking the two bases. The bases of a cylinder are always perpendicular from its axis, which is an artificial straight line passing through the centre both of bases. The volume of a cylinder is equal to the product among its base area and height. A cylinder's volume is computed as V = r2h, within which "V" represents the volume, "r" represent the circle of the base, and "h" represents the height of the cylinder.

The volume of a cylinder is determined by the formula V = r2h, where r is the radius of the base, h is the cylinder's height, and is a mathematical constant close to 3.14.

In this situation, the radius is 2.5 cm since the base is 5 cm in diameter. The cylinder stands 10 cm tall. As a result, the volume of the cylinder is:

[tex]V = \pi(2.5 cm)^2(10 cm) (10 cm)\\V = 196.35 cm^3[/tex]

As a result, the cylindrical container can carry around 196.35 cm3 of water. As a result, (a) 196.35 cm cubic is the right answer.

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Answer:

Step-by-step explanation:

The total mass of the alloy is the sum of the masses of the two metals:

mass = density x volume = (8800 kg/m³ x 15 m³) + 850 kg = 132,000 kg + 850 kg = 132,850 kg

The total volume of the alloy is the sum of the volumes of the two metals:

volume = 15 m³ + 6.2 m³ = 21.2 m³

Therefore, the density of the alloy is:

density = mass / volume = 132,850 kg / 21.2 m³ ≈ 6266 kg/m³

Rounding to the nearest integer, the density of the alloy is 6266 kg/m³.

In the given problem,  the displacement vector of the truck with respect to the police car is (-75, 60). This means that the truck is 75 km to the west and 60 km to the north of the police car.

To solve this problem, we can use vector addition. Let's assume that the police car is at the origin, and let the positive x-axis point west and the positive y-axis point north. Then, the initial position of the truck can be represented by the vector (-d, 0), where d is the distance between the police car and the crossroad.

Since the truck is traveling due north, its velocity vector is (0, 60). Similarly, the velocity vector of the police car is (-75, 0). We know that both vehicles will reach the crossroad at the same time, which means that their displacement vectors will have the same magnitude and direction.

Let's call the displacement vector we're looking for "D". Using the formula for displacement, we can write:

D = vt

where v is the average velocity of both vehicles, and t is the time it takes for them to reach the crossroad (which is one hour). The average velocity is given by the vector sum of the velocities of the truck and the police car:

v = (0, 60) + (-75, 0) = (-75, 60)

Substituting in the values for v and t, we get:

D = (-75, 60) * 1 = (-75, 60)

Therefore, the displacement vector of the truck with respect to the police car is (-75, 60). This means that the truck is 75 km to the west and 60 km to the north of the police car.

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Answer: two standard deviations below the average value.

Step-by-step explanation: The z score tells you how far below the average value that person or group is, on a scale from -2 to 2. The higher the z score, the more abnormal or anomalous the data being compared is. A z score of 1 indicates that the data is exactly average, while a z score of -2 indicates that the data is two standard deviations below the average value.

Answer:

Step-by-step explanation:

One sentence on globalization from the text: The process of globalization has brought significant changes to the world economy, including the emergence of new trade patterns and the increasing interconnectedness of markets.

One sentence on how the absence of plantation owners perpetuated cruel treatment of slaves by overseers: In the absence of plantation owners, overseers were left with unchecked power over the enslaved population, often resulting in brutal treatment and violence

Answer:

Dip your finger in both whichever one is salty don't give to your plant  

Step-by-step explanation: