geometric mean between 1/2 and 2​

Answer:

The constant of proportionality cannot be determined with just one set of values. It is only possible to determine the constant of proportionality when two quantities are directly proportional to each other and we have at least two sets of values for them.

Answer:

1.6

Step-by-step explanation:

To find the constant of proportionality for the given point (5, 8), we need to have more information about the relationship between the two variables.

If the relationship is given as y = kx, where k is the constant of proportionality, we can find k by substituting the given point (5, 8) into the equation:

8 = k * 5

Solving for k, we get:

k = 8/5 = 1.6

Answer:

x = 67

Step-by-step explanation:

∠ C = ∠ FGD ( corresponding angles )

Consecutive angles in a parallelogram sum to 180° , then

∠ B + ∠  C = 180 , substitute values

73 + x + 40 = 180

x + 113 = 180 ( subtract 113 from both sides )

x = 67

Answer:

Step-by-step explanation:

<B = <GFE                       The parallelograms are similar.

<GFD + <GFE = 180         Consecutive angles in a parallogram = 180

<GFD = x + 40                 Given

FGE = 73                          Step One

x + 40 +   73 = 180           Substitution

x + 113 = 180                     Subtract 113 from both sides

x = 67  

To solve the exercise you can first find the measure of angles B and C in triangle ABC.

Since the triangle ABC is an isosceles triangle, then it is true that

On the other hand, the Triangle Sum Theorem, which says that the sum of the three interior angles in a triangle is always 180°.

So, the measure of angles B and C in triangle ABC will be

Then, you can see that none of the angles in triangle ABC is congruent with angle D.

Therefore, none of the angles in triangle ABC are congruent to angle D, so the triangles are not similar.

Answer:

A tribe was named after him: the Tribe of Judah, which gave rise to the name of "Judaism", so the correct anser is d, one of the original tribes

Step-by-step explanation:

Answer:

Step-by-step explanation:

1/6 ÷ 8

1/6 × 1/8

1/48

for each batch

Step-by-step explanation:

To find the percentage increase, we use the following formula:

percentage increase = (new value - old value) / old value * 100%

In this case, the old value is 25 and the new value is 86. So, we can plug these values into the formula:

percentage increase = (86 - 25) / 25 * 100% = 244%

Therefore, the percentage increase from 25 to 86 is approximately 244%.

Answer:

244% increase

Step-by-step explanation:

To determine the angle from the vernal equinox to the station at the time of measurement, we need to use the following formula:

Angle = (Sidereal Time at Greenwich + Longitude of the Station - Hour Angle of the Object) * 15 degrees/hour

First, we need to determine the Hour Angle of the Object, which is the amount of time since the object (in this case, the radar measurement) passed over the Greenwich meridian. We know that the radar measurement occurred 2.8 hours after noon on January 1, so the Hour Angle of the Object is:

Hour Angle = 2.8 hours * 15 degrees/hour = 42 degrees

Next, we can plug in the values we know into the formula:

Angle = (100 degrees + (-4 degrees) - 42 degrees) * 15 degrees/hour
Angle = 54 degrees * 15 degrees/hour
Angle = 810 degrees/hour

Therefore, the angle from the vernal equinox to the station at the time of the radar measurement is 810 degrees/hour.

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The direction of the greatest increase in heat from the point (2, 5) is in the direction of the vector (-21, -20).

To find the direction of the greatest increase in heat from point (2, 5), we need to find the gradient vector of the temperature function T(x,y) at that point, and then determine the direction in which the gradient vector points.

The gradient vector of T(x,y) is given by:

∇T(x,y) = (∂T/∂x)i + (∂T/∂y)j

where i and j are the unit vectors in the x and y directions, respectively.

Taking the partial derivatives of T(x,y) with respect to x and y, we get:

∂T/∂x = (x² - y²)/(x² + y²)²

∂T/∂y = -2xy/(x² + y²)²

Substituting x = 2 and y = 5, we get:

∂T/∂x = (4 - 25)/(29)² = -21/1681

∂T/∂y = -20/1681

Therefore, the gradient vector of T(x,y) at the point (2, 5) is:

∇T(2,5) = (-21/1681)i - (20/1681)j

The direction of the greatest increase in heat from points (2, 5) is in the direction of the gradient vector. We can normalize the gradient vector to get the unit vector in this direction:

u = (∇T(2,5))/|∇T(2,5)|

where |∇T(2,5)| is the magnitude of the gradient vector, given by:

|∇T(2,5)| = √((-21/1681)² + (-20/1681)²) = sqrt(841)/1681 = 1/41

Thus, the unit vector in the direction of greatest increase in heat from the point (2, 5) is:

u = (-21/1681i - 20/1681j)/(1/41) = -21i - 20j

Therefore, the direction of the greatest increase in heat from points (2, 5) is in the direction of the vector (-21, -20).

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The elasticity of labor refers to the responsiveness of the quantity of labor supplied to changes in the wage rate. If the elasticity of labor is 0.60, a 15 percent increase in the wage rate will induce a decrease in the quantity of labor supplied, but the extent of this decrease will depend on the magnitude of the elasticity. The correct option is c.

In this case, a 0.60 elasticity implies that a 15 percent increase in the wage rate will result in a 9.0 percent decrease in the quantity of labor supplied. This can be calculated using the formula for elasticity, which is the percentage change in quantity divided by the percentage change in price (or wage rate, in this case):

Elasticity of labor = percentage change in quantity / percentage change in wage rate

0.60 = percentage change in quantity / 15 percent

Percentage change in quantity = 0.60 x 15 percent = 9.0 percent

Therefore, the correct answer is (c) a 9.0 percent decrease in the quantity of labor supplied. This means that as the wage rate increases, workers may be less willing to supply labor, resulting in a decrease in the number of workers willing to work at that wage rate.

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Answer: r=0

Step-by-step explanation: Hope this help :D

Answer:

\(g = 15 - \frac{1}{30}m\)

Step-by-step explanation:

Given

\(Initial = 15\)

\(mpg = 30\) --- miles per gallon

Required

Determine an equation for this trip

First we have to get the number of gallons per mile from \(mpg = 30\)

\(\frac{miles}{gallon}=30\)

Inverse the equation

\(\frac{gallon}{miles}=\frac{1}{30}\)

This represents the rate in gallons/mile

So, the equation is:

\(g= Initial - Rate * m\)

\(g= 15 - \frac{1}{30} * m\)

\(g= 15 - \frac{1}{30}m\)

Answer:

$45,000

Step-by-step explanation:

Income = percentage of income she receives x income

50% x 90,000

0.5 x 90,000 = 45,000

Answer:

C) \(122+154i\)

Step-by-step explanation:

\((14-2i)(7+12i)\\\\(14)(7)+(14)(12i)+(-2i)(7)+(-2i)(12i)\\\\98+168i-14i-24i^2\\\\98+154i-24(-1)\\\\98+154i+24\\\\122+154i\)

Therefore, C is correct. Recall that \(i^2=-1\)

The result of the complex expression is 122 + 154i.

The correct option is D .

Given, complex expression (14 - 2i)(7 + 12i) .

Complex number pair : a ± ib

i = iota(imaginary)

a = real part

b = imaginary part

Here expression \((14 - 2i)(7 + 12i)\)

Open the brackets by multiplying,

Here,

\(i = \sqrt{-1}\\ i^2 = -1\)

Simplifying the complex expression.

\((14 - 2i)(7 + 12i)\\= 98 + 168i - 14i +24\\= 122 + 154i\)

Therefore the correct option is D.

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For the training adaptation of maximum strength, 1 to 5 repetitions per set is recommended.

The one-repetition maximum test, also called a one-rep max or 1RM, is used to find out the heaviest weight you can lift just once.

If Maximal strength is desired, it is best achieved by performing  repetitions at  85 to 100 % of the one-repetition maximum (1RM).

Formula to find the repetition is

weight used x (reps done x 0.33 + 1) =  1RM

so,

Reps done = {{1RM/weight used} - 1}/ 0.33

By this find the no of reps are recommended for maximum strength.

The maximum strength is achieved by doing the number of reps by 85 to 100% of the value of 1 RM.

So,

For the training adaptation of maximum strength, 1 to 5 repetitions per set is recommended.

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Answer:

1. Angle forming a linear pair sum to 180°

2. Transitive property of equality

3. Algebra

4. Definition of congruency

Step-by-step explanation:

The given statement and reasons are presented as follows;

Statement      \({}\)                          Reason

1. m∠GKH + m∠HKI = 180°    \({}\) 1. Angle forming a linear pair sum to 180°

m∠HKI + m∠IKJ = 180°

2. m∠GKH + m∠HKI = m∠HKI + m∠IKJ \({}\)2. Transitive property of equality

3. m∠GKH = m∠IKJ  \({}\)              3. Algebra

4. m∠GKH ≅ m∠IKJ               4. Definition of congruency

The explanation are;

1. The sum of angles on a straight line is 180°

2. The transitive property of equality can be written as follows;

Given a = c and b = c, therefore, a = b

3. The addition property of equality states that given a + b = c + b, therefore a = c

4. Two geometric figures are said to be congruent when they are equal.

Answer:

Because θ lies in quadrant II, 2θ must lie in quadrant IV. This means the tangent of 2θ is negative.

The adjacent side to θ is 7 because √(25²-24²)=7, so tanθ=7/24.

The double angle formula for tangent is tan 2θ = (2 tan θ) / (1 − tan² θ).

Substituting the value for tanθ in and keeping in mind that this is in quadrant IV, we get tan 2θ = -(2(7/24)/(1-(7/24)²)).  

Simplified, this becomes tan 2θ = -336/527.  

Therefore, the answer is C. -336/527.

Answer:

24

Step-by-step explanation:

3x4x2=24

When finding the answer to this problem, you times all of the options by each other.

Answer:

4

Step-by-step explanation:

We plug x in as -5 so we have: |-5+1|

|-5+1| = |-4| = 4

Step-by-step explanation:

You must first know the formular for gradient then use the applied formular for slope

Answer:

B

Step-by-step explanation:

original--15+10=25

sale--15+10*50%=20

25-20=5

5/25=1/5=20%

Answer:

$46.15

Step-by-step explanation:

Given information:

Define the variable:

Convert 4% into a decimal:

\(\implies 4\%=\dfrac{4}{100}=0.04\)

Therefore, the sum of the cost of the juice, the price of the jeans and the sales tax on the jeans must be equal to or less than $50:

\(\implies 2+x+0.04x\leq 50\)

\(\implies 2+1.04x\leq 50\)

Solving the inequality:

\(\implies 2+1.04x\leq 50\)

\(\implies 2+1.04x-2\leq 50-2\)

\(\implies 1.04x\leq 48\)

\(\implies \dfrac{1.04x}{1.04}\leq \dfrac{48}{1.04}\)

\(\implies x\leq 46.15384615\)

Therefore, the maximum price of the jeans Juan can afford is $46.15 (not including sales tax).

Answer:

10 times 16 = C

Step-by-step explanation:

c2 = a2 + b2 − 2ab cos C = 162 + 102 − 2(10)(16) cos 22°

The angle measures that satisfy cos theta = 1/2 are

To find all angle measures for which cos theta = 1/2, we can use the unit circle and look for the x-coordinate of the point where the angle intersects the unit circle.

The x-coordinate (cosine) is equal to 1/2 at two points on the unit circle:

However, the given angle measures are not all within one revolution (360 degrees or 2pi radians), so we need to find equivalent angles within one revolution.

To do this, we can add or subtract multiples of 360 degrees or 2pi radians from the given angles until they are within one revolution.

-120° = 360° - 120° = 240°

-60° = 360° - 60° = 300°

120° = 120°

600° = 600° - 1(360°) = 240°

660° = 660° - 2(360°) = 60°

So the angle measures that satisfy cos theta = 1/2 are -120° (or 240°), -60° (or 300°), and 660° (or 60°).

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We are given two options diagrams A and B and we are required to use choose either A or B for which option properly represents the scenario presented in the sub-questions of Question 3.

Question 3.1:

The amount of rain this year decreased by 10% compared to last year. This implies that if last year's amount of rain was X, then this year's rain has decreased by 10% of X. Mathematically, we have:

This means that last year's rain must be 100% while this year's rain has a 10% decrease in the rainfall.

The option that depicts this properly is OPTION A

Question 3.2:

The amount of sleet this year is 90% of last year's amount. This implies that if last year's amount of sleet is X, then this year's sleet amount must be 90% of X. That is:

This means that Last year's amount is again 100% while this year is 10% less than last year.

The option that depicts this properly is OPTION A

Question 3.3:

The amount of sunshine this year increased by 10% compared with last year's amount. This implies that if last year's sunshine is X and then this year's sunshine must be 10% greater than X. That is:

This means that last year's amount is 100% while this year's amount is 10% greater.

The option that depicts this properly is OPTION B.

Question 3.4:

The number of windy days this year is 110% of last year's number. This implies that this year's number has increased by 10% given that last year's number was 100%.

The option that depicts this property is OPTION B

Question 3.5:

The percentage change in Graph A is:

The answer is -10%

(Note: This is negative because it is a decrease from last year to this year)

Question 3.6:

The percentage change in Graph B is:

The answer is 10%

Final Answer

Question 3.1:

OPTION A

Question 3.2:

OPTION A

Question 3.3:

OPTION B

Question 3.4:

OPTION B

Question 3.5:

The answer is -10%

Question 3.6:

The answer is 10%

9514 1404 393

Answer:

Step-by-step explanation:

For dilations about the origin, such as these, the scale factor is always the ratio of any image point coordinate* to the corresponding preimage point coordinate. If the scale factor is k, the transformation can be written as ...

  (x, y) ⇒ (kx, ky)

__

  S(9,12) ⇒ S'(6, 8) . . . . scale factor is 6/9 = 2/3; relation is (x, y) ⇒ (2/3x, 2/3y)

  U(8, 18) ⇒ U'(4, 9) . . . scale factor is 4/8 = 1/2; relation is (x, y) ⇒ (1/2x, 1/2y)

  I(0,8) ⇒ I'(0, 7) . . . scale factor is 7/8; relation is (x, y) ⇒ (7/8x, 7/8y)

  X(16, 8) ⇒ X'(4, 2) . . . scale factor is 2/8 = 1/4; relation is (x, y) ⇒ (1/4x, 1/4y)

_____

* The origin is the one invariant point in a dilation, so the chosen coordinate cannot be zero.

The minimum distance that Malia needs on her last throw to win the game is less than 2.12 meters.

In this target game, Malia needs to have the lowest mean distance of all throws to win. The mean distance is calculated by adding up all the distances and dividing by the number of throws.

First, we need to calculate the mean distance of Malia's first 7 throws.

Mean distance = (2 + 3 + 4 + 2 + 5 + 3 + 4) / 7 = 3.14

Now, we know that Malia's mean distance must be less than 3.14 to win the game. Let's call the distance of her last throw x.

The mean distance of all 8 throws will be: (2 + 3 + 4 + 2 + 5 + 3 + 4 + x) / 8

To find the minimum distance that Malia needs on her last throw to win the game, we can set up an inequality:

(2 + 3 + 4 + 2 + 5 + 3 + 4 + x) / 8 < 3.14

Multiplying both sides by 8 gives us:

2 + 3 + 4 + 2 + 5 + 3 + 4 + x < 25.12

Simplifying gives us:

x < 25.12 - 23

x < 2.12

Therefore, the minimum distance that Malia needs on her last throw to win the game is less than 2.12 meters.

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Answer:

88% of his weight remains

Answer:

D. 8/15

Step-by-step explanation:

13/23 = .565217

11/20 = .55

9/17 = .52941176

8/15 = .53333333