Use the given conditions to write an equation for the line in point-slope form.
Slope = 6
7
, passing through (
8
,
7
)
.

Answer:

Bees dont comanly eat flowers. They take the pollen and necture inside the flower to polenate OTHER flowers.

Step-by-step explanation:

most bees use pollen and nectar as a food source. Worker bees gather both pollen and nectar from flowers to feed to the larvae and other members of the colony.

Hope this helps a little

Answer:

Actually bees do not eat flowers but they land on flowers to collect nectar while at the same time pollinating them

Step-by-step explanation:

Actually bees do not eat flowers but they land on flowers to collect nectar while at the same time pollinating them

The correct answer is d) f^(-1)(x) = x/3, as it represents the Inverse relationship of y = 3x.

To find the inverse of a function, we need to switch the roles of x and y and solve for the new y.

The given function is y = 3x.

To find its inverse, let's swap x and y:

x = 3y

Now, solve this equation for y:

Dividing both sides of the equation by 3, we get:

x/3 = y

Therefore, the inverse function of y = 3x is f^(-1)(x) = x/3.

Among the given options:

a) f^(-1)(x) = 1/3x

b) f^(-1)(x) = 3x

c) f^(-1)(x) = 3/x

d) f^(-1)(x) = x/3

The correct answer is d) f^(-1)(x) = x/3, as it represents the inverse relationship of y = 3x.

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Thomas is 49 years old.

What is equation?

Two expressions joined by an equal sign form a mathematical statement known as an equation. An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.

Given:

Huilan is 11 years older than Thomas.

The sum of their ages is 109.

We have to find the Thomas's age in years.

Let x be the Thomas age.

Then the age of Huilan is x + 11.

As the sum of their ages is 109.

⇒ x + (x + 11) = 109

         2x + 11 = 109

               2x = 98

                 x = 49

Hence, Thomas is 49 years old.

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Answer:

x>4

Step-by-step explanation:

Step 1: Subtract 9 from both sides.

x+9−9>13−9

x>4

The orthonormal set derived from the original set is {(-1/√10, 3/√10), (3/√2, 1/√2)}.

(a) We must prove that the dot product of the set of vectors (-1, 3), and (15, 5) in R² is zero in order to show that they are orthogonal.

Ac + bd is the formula for the dot product of the two vectors (a, b) and (c, d). Let's determine the dot product of the vectors provided:

(-1, 3) · (15, 5) = (-1)(15) + (3)(5) = -15 + 15 = 0.

The set (-1, 3), (15, 5) is orthogonal because the dot product of the two vectors is zero.

(b) We divide each vector by its magnitude (length) to create unit vectors in order to normalize the set and create an orthonormal set.

(A² + B²) provides the magnitude (length) of a vector (a, b). Let's determine the magnitudes of the vectors provided:

||(-1, 3)|| = √((-1)² + 3²) = √(1 + 9) = √10,

||(15, 5)|| = √(15² + 5²) = √(225 + 25) = √250 = 5√2.

By dividing each vector by its magnitude, we may normalize the vectors:

=((-1, 3) / √10, (15, 5) / (5√2))

= (-1/√10, 3/√10), (15/(5√2), 5/(5√2))

= (-1/√10, 3/√10), (3/√2, 1/√2).

The orthonormal set that results from the original set is therefore (-1/10, 3/10), (3/2, 1/2).

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We know 3 angles sum to 180 degrees {in a triangle]. Thus, we can write:

We are given Angles 2 and 3 and are told to find Angle 1. We substitute and do a bit algebra to figure Angle 1 out. The steps are shown below:

The last answer choice is correct.

If the height of the trapezium is 7 units. Then the area of the trapezium will be 31.5 square units.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezium, one pair of opposite sides are parallel.

The quadrilateral ABCD whose vertices are A(-2,-1), B(-2,-3), C( 5,6), and D(5,-1).

The lines AB and CD are parallel to the y-axis. Then the quadrilateral ABCD is a trapezium.

The height of the trapezium will be 7 units.

The area of the trapezium will be

Area = 1/2 (2 + 7) x 7

Area = 0.5 x 9 x 7

Area = 31.5 square units.

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The diameter of the ball is approximately 16.67 meters.

To find the diameter of the ball, we can use the relationship between the distance traveled and the number of revolutions.

The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter.

Given that the ball rolls a distance of 3.5 meters and makes 15.0 revolutions, we can calculate the circumference of the path it travels:

C = 3.5 m * 15.0 = 52.5 m

Since each revolution covers the circumference of the ball, we have C = πd. Plugging in the known value for C, we can solve for the diameter (d):

52.5 m = πd

Dividing both sides of the equation by π, we get:

d = 52.5 m / π

Using a calculator, we can evaluate this expression:

d ≈ 16.67 meters

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In this scenario, we have a uniformly charged thin rod extending along the x-axis from the origin (x = 0) to positive infinity (x = +∞).

The term "uniformly charged" means that the charge is distributed evenly throughout the entire length of the rod.

To analyze this situation, we can consider the following steps: 1. Determine the linear charge density (λ) of the rod. Since the rod is uniformly charged, λ remains constant along its entire length. λ is usually given in units of charge per length (e.g., coulombs per meter).

2. To find the electric field at a particular point along or outside the rod, we can break the rod into infinitesimally small segments (dx) and consider the contribution of the electric field (dE) from each of these segments.

3. Calculate the electric field (dE) produced by each segment at the desired point using Coulomb's equations , considering the linear charge density (λ) and distance between the segment and the point.

4. Integrate the electric field contributions (dE) from all segments along the entire length of the rod (from x = 0 to x = +∞) to find the total electric field (E) at the point of interest.

By following these steps, you can analyze the electric field and related properties of a uniformly charged thin rod extending along the x-axis from x = 0 to x = +∞.

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Answer: d  =  10.2

Step-by-step explanation:

Answer:

5^8/5^6 = 5^(8-6) = 5^2 = 25. Therefore, 5^8/5^6 simplified to a single power of 5 is 25.

Step-by-step explanation:

Answer:

the answer for that is 5^6-3 = 5^3 = 125

Step-by-step explanation:

The face value and place value of underlined digit 8, in the given number 77,84,201 is: Face value: 8  : Place value: 80000.

We have,

Place value can be defined as the numerical value that every digit in a  given number has based on its position.

It is the value of the position of digits.

Example:

The place value of 2 in 2526 is at the thousandth and tenth place.

here, we have,

From the information given, we have that;

77,84,201

the underlined digit in the given number is 8

In this number 77,84,201 ,

the place value of 8 is;

8,0000

In this number 77,84,201, the face value of 8 is;

8

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First, we find the length of ST and multiply it by the given ratio to get the length of SP. Then, we use the midpoint formula to find the coordinates of point P.1. S(6,4), T(-4, -8); 1 to 3

Let P be the point on the directed line segment ST such that SP : PT = 1 : 3. We need to find the coordinates of P.Step 1: Find the length of ST.

Let S(x1, y1) and T(x2, y2) be the coordinates of S and T respectively. Then we can use the distance formula to find the length of ST.

d(ST) = √[(x2 - x1)² + (y2 - y1)²]

d(ST) = √[(-4 - 6)² + (-8 - 4)²]

d(ST) = √(100 + 144)

d(ST) = √244d(ST) = 2√61

Find the length of SP.We know that

SP : PT = 1 : 3. Therefore,

SP = (1/4)ST.SP = (1/4)(2√61)SP = (1/2)√61

Use the midpoint formula to find the coordinates of P.Let (x, y) be the coordinates of P. Then we can use the midpoint formula to find

(x, y).x = (1/4)(2x2 + 2x1) = (1/4)(2(-4) + 2(6)) = 1y = (1/4)(2y2 + 2y1) = (1/4)(2(-8) + 2(4)) = -1

The coordinates of P are (1, -1).

Once we have the length of SP, we can use the midpoint formula to find the coordinates of P. In the first example, we found that the coordinates of P are (1, -1) if SP : PT = 1 : 3. In the second example, we will use the same method to find the coordinates of P when S(-6, 7) and T(9, 25) are the given points, and

SP : PT = 2 : 3.

We will also find the length of ST, the length of SP, and the coordinates of P.2. S(-6, 7), T(9, 25); 2 to 3Let P be the point on the directed line segment ST such that SP : PT = 2 : 3. We need to find the coordinates of P.Step 1: Find the length of ST.Let S(x1, y1) and T(x2, y2) be the coordinates of S and T respectively. Then we can use the distance formula to find the length of ST.

d(ST) = √[(x2 - x1)² + (y2 - y1)²]

d(ST) = √[(9 - (-6))² + (25 - 7)²]

d(ST) = √(225 + 324)

d(ST) = 3√61

We know that SP : PT = 2 : 3. Therefore,

SP = (2/5)ST.SP = (2/5)(3√61)SP = (6/5)√61

Use the midpoint formula to find the coordinates of P.Let (x, y) be the coordinates of P. Then we can use the midpoint formula to find (x, y).x = (2/5)(x2 + x1) = (2/5)(9 + (-6)) = -3/5 y = (2/5)(y2 + y1) = (2/5)(25 + 7) = 16

The coordinates of P are (-3/5, 16).

To find the coordinates of point P along the directed line segment ST so that SP to PT is the given ratio, we need to find the length of ST and multiply it by the given ratio to get the length of SP. Then, we use the midpoint formula to find the coordinates of point P.

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a)The initial height of the flare when it is fired is 2m.

b)The height of the flare after 1 s is 38.75m

c)The flare reaches its maximum height after 2 seconds.

d) The maximum height of the flare is 65m.

e) The flare hits the water after 8 seconds.

The given equation which is h = -5.25t² + 42t + 2, can be used to solve the following questions:

a) To get the initial height of the flare when it is fired, the value of t = 0 must be used in the given equation:

h = -5.25(0)² + 42(0) + 2h

= 0 + 0 + 2h

= 2

Therefore, the initial height of the flare when it is fired is 2m.

b) To get the height of the flare after 1 s, the value of t = 1 must be used in the given equation:

h = -5.25(1)² + 42(1) + 2h

= -5.25 + 42 + 2h

= 38.75

Therefore, the height of the flare after 1 s is 38.75m

c)The maximum height of the flare is reached when the flare is at its peak.

Therefore, the time when the flare reaches its maximum height is found by dividing -b by 2a, where the equation is in the form of y = ax² + bx + c.

The equation h = -5.25t² + 42t + 2 is in the form of y = ax² + bx + c,

where a = -5.25, b = 42, and c = 2.t = -b/2a = -42/2(-5.25)

= -2

Therefore, the flare reaches its maximum height after 2 seconds.

d) To get the maximum height of the flare, the value of t = 2 must be used in the given equation:

h = -5.25(2)² + 42(2) + 2h

= -21 + 84 + 2h

= 65

Therefore, the maximum height of the flare is 65m.

e)When the flare hits the water, the height, h, is 0.

Therefore, the time when the flare hits the water is found by setting h = 0 in the given equation and solving for t:

0 = -5.25t² + 42t + 2

Using the quadratic formula:\($$t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$\)

where a = -5.25, b = 42, and c = 2.

= \(\frac{-42 \pm \sqrt{42^2 - 4(-5.25)(2)}}{2(-5.25)} $$t\)

= 8.003 or t = 1.331

Since time cannot be negative, the time when the flare hits the water is after 8 seconds. Therefore, the flare hits the water after 8 seconds.

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Answer:

1. A

2. A

3. B

Step-by-step explanation:

Tom will arrive in London at 4.10 pm, after travelling 140 miles at an average speed of 50 mph.

The formula to calculate the time taken is: Time = Distance/Speed

Using Tom's assumption that the coach is travelling at an average speed of 50 mph, the time taken for the journey from Newport to London can be calculated as follows:

Time = 140 miles/50 mph = 2.8 hours

Therefore, Tom will arrive in London at 1.30 pm + 2.8 hours = 4.10 pm.

To put this in context, it means that the coach will travel at an average speed of 70 km/h, covering a distance of 224 km in 2.8 hours. This is equivalent to covering 80 km in an hour.

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Answer:

1/4, 7/12, 5/8, 2/3

Step-by-step explanation:

2/3 = 16/24   (Multiplied by 8)

7/12 = 14/24  (Multiplied by 2)

5/8 = 15/24   (Multiplied by 3)

1/4 = 6/24      (Multiplied by 6)

The value that would complete the table to make the relationship between the two quantity proportional is 4.

When two quantities are proportional, their relationship is constant for all values and as one quantity rises, the other rises as well.

A proportional relationship exists between two quantities if they can be written in the general form y = kx, where k is the proportionality constant. In other words, the ratio between these amounts never changes. In other words, no matter which pair of the two numbers you divide, you always obtain the same number k.

The value that would complete the table to make the relationship between the two quantity proportional is 4.

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the highest possible number of components that would manufacture them the most efficiently  =  33%

The correct option is C.

What is percentage?

a percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. percentage.

According to the given information:

the 50 electronics components that a factory must manufacture.

70 percent would be most efficiently manufactured by Machine A

30 percent would be most efficiently manufactured by Machine B,

If 36 percent of the components were manufactured by Machine A

the highest possible number of components that would manufacture them the most efficiently =

we know that :

A can manufacture:

50*70% = 35 components efficiently

B can manufacture:

50*30% = 15 components efficiently;

now :

A actually manufactured:

50*36% = 18 components (so all efficiently, since 35>18);

B actually manufactured:

50-18 = 32 components, out of which 15 were manufacture efficiently;

so,

the highest possible number of components that would manufacture them the most efficiently = 18 + 15

                                          =  33

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I understand that the question you are looking for is :

Of the 50 electronics components that a factory must manufacture, 70 percent would be most e¢ ciently manufactured by Machine A and the remaining 30 percent would be most efficiently manufactured by Machine B, though either machine could manufacture any of the 50 components. If 36 percent of the components were manufactured by Machine A and the remainder were manufactured by Machine B, what is thehighest possible number of components that were manufactured by the machine that would manufacture them the most efficiently?

(A) 30

(B) 32

(C) 33

(D) 35

(E) 36

f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I.

To find when a function is decreasing, you must first take the derivative, then set it equal to 0, and then find between which zero values the function is negative. Now test values on all sides of these to find when the function is negative, and therefore decreasing.

The derivative of a function may be used to determine whether the function is increasing or decreasing on any intervals in its domain. If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I.

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The diagonals of a quadrilateral are perpendicular and one pair of opposite sides is parallel.

A quadrilateral is a shape with four straight sides. The trapezoid is a quadrilateral with only one pair of parallel sides.

An isosceles trapezoid is a trapezoid with two of the sides having the same length.

It can be proven that a quadrilateral is either a rectangle or an isosceles trapezoid by the following statement:

The diagonals of a quadrilateral are perpendicular and one pair of opposite sides is parallel.

If a quadrilateral has perpendicular diagonals and one pair of opposite sides that are parallel, then it can be either a rectangle or an isosceles trapezoid.

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Answer:

False.The statement "The least-squares solution of Ax=b is the point in the column space of A closest to b" is false.

The least-squares solution of Ax=b is the solution to the system (ATA)x = ATb, where AT is the transpose of A. This solution minimizes the distance between Ax and b in the sense of the Euclidean norm.

While the least-squares solution is related to the column space of A, it is not necessarily the point in the column space of A closest to b. The least-squares solution can be thought of as a projection of b onto the column space of A, but this projection may not fall directly on a vector in the column space.

In general, the least-squares solution will be the point in the column space of A that is closest to b only if b is already in the column space of A. Otherwise, the solution will be a linear combination of the column vectors of A that is as close to b as possible.

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Answer:

It's 33.33%

Step-by-step explanation:

It's 3/9 = 1/3 = 0.3333 = 33.33%

The estimated standard error and measures of effect size such as r2 and Cohen's d larger variance increases the standard error but decreases measures of effect size. B.

Larger variance increases the standard error but decreases measures of effect size.

The standard error is a measure of how much the sample mean is likely to vary from the true population mean.

It is calculated as the standard deviation of the sample divided by the square root of the sample size.

If the sample variance is large, the standard deviation of the sample will also be large, resulting in a larger standard error.

Measures of effect size, such as r2 and Cohen's d, indicate the strength of the relationship between variables or the size of the difference between groups, respectively.

Larger sample variances indicate greater variability in the data, which can make it more difficult to detect significant effects.

This can result in smaller effect sizes, as the magnitude of the effect is reduced relative to the variability in the data.

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Answer:

O perímetro do outro triângulo deve ser ou de 30 unidades de comprimento, ou de 3.33 unidades de comprimento.

Step-by-step explanation:

Dois triângulos semelhantes possuem razão entre suas áreas igual a 9.

O perímetro tem grau um, enquanto a área tem grau 2. Isto implica que a razão entre os perímetros é a raiz quadrada da razão entre as áreas, então a razão entre os perímetros é de 3.

Se o perímetro de um deles é 10, o perímetro do outro deve ser:

Ou 10*3 = 30, ou \(\frac{10}{3} = 3.33\)

O perímetro do outro triângulo deve ser ou de 30 unidades de comprimento, ou de 3.33 unidades de comprimento.

Answer:

Step-by-step explanation:

103.8 seconds

68.11024 inches

Answer:

\(b_{n} =b_{1} r^{n-1} =100*1.2^{n-1}\)

Step-by-step explanation:

first number is \(b_{1} =100\)

the cammon ratio is \(r=\frac{120}{100} =\frac{144}{120}=1.2\)

so \(b_{n} =b_{1} r^{n-1} =100*1.2^{n-1}\)