Prove angle FGH is congruent to angle HIF.


A.
1) Given
2) Given
3) Reflexive property of congruency
4) SAS
B.
1) Given
2) Reflexive property of congruency
3) Given
4) AAS
C.
1) Given
2) Reflexive property of congruency
3) Given
4) SSA
D.
There is not enough information to prove the triangles congruent.

Answer

8meters

Step-by-step explanation:

divide the diameter (16) by 2

=8

Answer:

......

Step-by-step explanation:

.......

Answer:

5.50b+6d≤80

Step-by-step explanation:

One bag of popcorn costs $5.50, so bb bags of popcorn cost 5.50b.5.50b. One drink costs $6, so dd drinks cost 6d.6d. The total 5.50b+6d5.50b+6d must be less than or equal to \$80:$80

Answer:

a) (0.576, 0.624)

Step-by-step explanation:

Given that the sample proportion (p) = 60% = 0.6, sample size (n) = 900, confidence (C) = 85%

α = 1 - C = 1 - 0.85 = 0.15

α/2 = 0.075

The z score of α/2 (0.075) corresponds with the z score of 0.425 (0.5 - 0.075) which is equals to 1.44, hence \(z_\frac{\alpha }{2} =1.44\)

The margin of error (E) is:

\(E=z_\frac{\alpha }{2} *\sqrt{\frac{p(1-p)}{n} } =1.44*\sqrt{\frac{0.6(1-0.6)}{900} } = 0.024\)

The confidence interval = p ± E = 0.6 ± 0.024 = (0.576, 0.624)

Answer:

96.5 feet. looked it up.

Step-by-step explanation:

Have a great day:)

Answer:

Given: the angle of depression= 20°

Height of Kyle from the ocean = 30 feet

To find: how far is the whale from kyles biboculars?

Step-by-step explanation:

Let the distance between them be y

sin20° = \(\frac{33 }{y}\)

=> 0.342 = \(\frac{33}{y}\)          [  sin20° = 0.342]

=> y =  33/ 0.342

=> y = 96.5 ft

So, the distance between them is 96.5 ft

what is angle of depression?

The angle of depression is the angle formed by the horizontal line and the horizontal line's observation of the item. When we know the angles and the distance of an object from the ground, it is primarily utilized to find the distance between the two objects. If the line of sight is directed downward from the horizontal line, then an angle is created with the horizontal line.

The angle produced between the horizontal line and the observer's line of sight is known as the angle of depression if the object being observed is below the observer's level. The angle of depression is shown in the image below as.

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Answer:

Bottom right

Step-by-step explanation

Answer:

first answer is correct

A. Up

Parabolas are graphs that make U-shapes and are formed from quadratic equations.

Vertical Parabolas

There are 2 different types of parabolas: vertical and horizontal.

If the x-value is squared, then the parabola is vertical. So, this graph must open up or down.

Positive A-Value

The a-value is the coefficient before the squared term. In a vertical parabola, the graph opens up if the a-value is positive. On the other hand, the graph opens down when the a-value is negative.

In this case, the graph is a vertical parabola that opens up. This means that the range will have a minimum value but no maximum.

Answer:

125

Step-by-step explanation:

looked it up

Answer:

(4\(\sqrt{3}\))/3

Step-by-step explanation:

From the diagram,

Applying

sinθ = Opposite/Hypotenuse................. Equation 1

From the diagram,

Given: θ = 60°, Opposite = 2, Hypotenuse = X

Substitute these values into equation 1

sin60°  = 2/X

make X the subject of the equation

X = 2/sin60°.................. Equation 2

But,

sin60° = \(\frac{\sqrt{3} }{2}\)

Therefore,

X = 2/( \(\frac{\sqrt{3} }{2}\))

X = (2×2)/\(\sqrt{3}\)

X = 4/\(\sqrt{3}\)

Rationalising the denominator,

X = (4/\(\sqrt{3}\))×(\(\sqrt{3}\)/\(\sqrt{3}\))

X = (4\(\sqrt{3}\))/3

Answer:

x_>-4

Step-by-step explanation:

Answer:

μ  p ^ =0.29

σ  p ^  =  Square root[    ( (0.29)(0.71) )/100   ]

Step-by-step explanation:

The mean of the sampling distribution of a sample proportion is equal to the population proportion.

μ p ^ =p

The population proportion reported is 29%, so p=0.29p.

\mu_{\hat p}=p=0.29μ  

μ p ^ = 0.29

Since σ  p hat = sqare root [ ( p(1-p) )/ n]

After subsitution we get σ  p ^  =  Square root[    ( (0.29)(0.71) )/100   ]

​

it can be concluded that the population standard deviation is within or less than 12.

To construct a hypothesis test to determine whether the population standard deviation of σ≦12 should be rejected for Costco, we can use a chi-square test for variance.

Step 1: State the null and alternative hypotheses:
- Null hypothesis (H₀): σ ≤ 12
- Alternative hypothesis (H₁): σ > 12

Step 2: Determine the level of significance (α = 0.05) and degrees of freedom (df = n - 1 = 11 - 1 = 10).

Step 3: Calculate the test statistic:
- χ² = (n - 1) * (s² / σ²) = 10 * (11.3² / 12²) = 10 * 0.94 = 9.4

Step 4: Determine the critical value:
- The critical value at α = 0.05 with df = 10 is χ²ₐ = 18.307

Step 5: Compare the test statistic with the critical value:
- Since χ² = 9.4 < χ²ₐ = 18.307, we fail to reject the null hypothesis.

Step 6: Conclusion:
- Based on the given sample data, there is not enough evidence to reject the hypothesis that the population standard deviation of σ≤12 for Costco.

Therefore, it can be concluded that the population standard deviation is within or less than 12.

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Answer:

d

Step-by-step explanation:

3/5

5 poster boards in total and 3 are colour so...

it is  3/5

Hope this helps!

If Rachana randomly selects two mugs from the set, the probability that she gets two different mugs is 0.1556 or 15.56%.

To solve this problem, we can use the concept of combinations. Since there are 10 mugs in the set, there are 10 choose 2 = 45 ways to select two mugs without considering order.

Out of these 45 ways, we need to count the number of ways Rachana can select two different mugs. Since there are 3 different types of mugs, Rachana can choose any one of the three types for the first mug. There are 10 mugs in the set, out of which 3 belong to the chosen type. Therefore, the probability of choosing a mug of the chosen type is 3/10.

For the second mug, Rachana can choose from the remaining 9 mugs. Since she needs to choose a different type of mug, she can choose any one of the 2 remaining types. There are 7 mugs left from the other 2 types. Therefore, the probability of choosing a mug of a different type is (7/9) * 2/3 = 14/27.

Therefore, the probability of selecting two different mugs is the product of the probabilities of selecting a mug of the chosen type and a mug of a different type. This is given by (3/10) * (14/27) = 7/45, which is approximately 0.1556 or 15.56%.

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Complete question is:

Rachana has a set of ten mugs the set up is made of 3 different mugs. If Rachana randomly selects two mugs from the set, what is the probability that she gets two different mugs?

At state 1, the mass of the liquid water (mf) can be calculated using the equation mf = (10 - 1.002 * m1) / 0.001, where m1 is the total mass of the water-vapor mixture and mg = 0.6 * m1.
- At state 2, the masses of the liquid water and vapor remain the same as they were at state 1. Therefore, mg2 = mg and mf2 = mf.

The mass of the water-vapor mixture in the rigid vessel can be determined using the volume and quality of the mixture.

1. Given:
  - Volume of the vessel (V) = 10 m^3
  - Quality (x) = 60%

To find the mass (m1), we need to calculate the mass of the liquid water (mf) and the mass of the vapor (mg) separately.

2. Calculate the mass of the liquid water (mf):
  - The quality (x) represents the fraction of the total mass that is in the vapor phase, while (1-x) represents the fraction in the liquid phase.
  - The total mass of the water-vapor mixture (m1) can be expressed as the sum of the mass of the liquid water (mf) and the mass of the vapor (mg):

      m1 = mf + mg

  - Since the volume of the vessel is constant, the specific volume of the liquid water (vf) and the specific volume of the vapor (vg) can be used to relate the volumes to the masses:

      V = vf * mf + vg * mg

  - Since the vessel contains only water and water vapor, we can use the compressed liquid and saturated vapor tables to find the specific volumes (vf and vg) at the given pressure of 400 kPa.

3. Find the specific volume of liquid water (vf) at 400 kPa:
  - Using the compressed liquid table, we can find the specific volume of the liquid water at the given pressure. Let's assume that the specific volume is 0.001 m^3/kg.

      vf = 0.001 m^3/kg

4. Find the specific volume of vapor (vg) at 400 kPa:
  - Using the saturated vapor table, we can find the specific volume of the vapor at the given pressure. Let's assume that the specific volume is 1.67 m^3/kg.

      vg = 1.67 m^3/kg

5. Substituting the values of vf and vg into the equation from step 2, we have:
  - 10 m^3 = (0.001 m^3/kg) * mf + (1.67 m^3/kg) * mg

6. Solve the equation to find mf and mg:
  - We have one equation with two unknowns, so we need another equation to solve for both mf and mg. We can use the given quality (x) to write another equation:

      x = mg / m1

  - Since we know the quality is 60% (or 0.6), we can rewrite the equation as:

      0.6 = mg / m1

7. Solve the system of equations from steps 5 and 6 to find mf and mg:
  - We can rearrange the equation from step 6 to solve for mg:

      mg = 0.6 * m1

  - Substitute this value into the equation from step 5 and solve for mf:

      10 m^3 = (0.001 m^3/kg) * mf + (1.67 m^3/kg) * (0.6 * m1)

  - Simplify the equation:

      10 m^3 = (0.001 m^3/kg) * mf + (1.67 m^3/kg) * (0.6 * m1)
      10 m^3 = 0.001 m^3/kg * mf + 1.002 m^3/kg * m1

  - We can see that the units of volume (m^3) cancel out, leaving us with:

      10 = 0.001 * mf + 1.002 * m1

  - Rearrange the equation to solve for mf:

      mf = (10 - 1.002 * m1) / 0.001

  - Substitute this value into the equation from step 6 to solve for mg:

      mg = 0.6 * m1

  - We now have the values of mf and mg at state 1.

8. Determine the values of mg and mf at state 2:
  - Given:
    - Pressure at state 2 (P2) = 300 kPa
    - Volume at state 2 (V2) = 10 m^3 (constant volume)

  - We need to determine the new masses (mg2 and mf2) at state 2 by using the pressure-volume relationship for water-vapor mixtures.

9. Use the pressure-volume relationship for water-vapor mixtures:
  - The pressure-volume relationship for a rigid vessel is given by:

      P1 * V1 = P2 * V2

  - Substituting the given values, we have:

      400 kPa * 10 m^3 = 300 kPa * 10 m^3

  - The volume cancels out, leaving us with:

      400 kPa = 300 kPa

  - This means that the pressure is the same at state 1 and state 2.

10. Since the pressure is constant, the masses of the liquid water and the vapor will remain the same at state 2 as they were at state 1.
  - Therefore, mg2 = mg and mf2 = mf.

To summarize:
- At state 1, the mass of the liquid water (mf) can be calculated using the equation mf = (10 - 1.002 * m1) / 0.001, where m1 is the total mass of the water-vapor mixture and mg = 0.6 * m1.
- At state 2, the masses of the liquid water and vapor remain the same as they were at state 1. Therefore, mg2 = mg and mf2 = mf.

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a) Mass at state 1 contains water-vapor mixture ≈ 19.67 kg.

b) Mass of gas (mg) at state 2 = 0 kg

Mass of liquid (mf) at state 2 = 10,000 kg.

To find the mass of the water-vapor mixture in the rigid vessel at state 1, we can use the ideal gas law for the vapor phase and the density of liquid water at the given conditions:

Given data at state 1:

Volume of the vessel (V) = 10 m³

Pressure (P) = 400 kPa = 400,000 Pa

Quality (x) = 60% = 0.60 (vapor fraction)

Density of liquid water (ρf) = 1000 kg/m³ (approximately at atmospheric pressure and 25°C)

a) Calculate the mass (m) at state 1:

Using the ideal gas law for the vapor phase:

PV = mRT

where: P = pressure (Pa)

V = volume (m³)

m = mass (kg)

R = specific gas constant for water vapor (461.52 J/(kg·K) approximately)

T = temperature (K)

Rearrange the equation to solve for mass (m):

m = PV / RT

The temperature (T) is not given directly, but since the vessel contains a water-vapor mixture at 60% quality, it is at the saturation state, and the temperature can be found using the steam tables for water.

Assuming the temperature at state 1 is T1, use the steam tables to find the corresponding saturation temperature at the given pressure of 400 kPa. Let's assume T1 is approximately 300°C (573 K).

Now, calculate the mass (m) at state 1:

m = (400,000 Pa * 10 m³) / (461.52 J/(kg·K) * 573 K)

m ≈ 19.67 kg

The mass (m) of the water-vapor mixture at state 1 is approximately 19.67 kg.

b) To find the mass of the gas (mg) and the mass of the liquid (mf) at state 2 (P2 = 300 kPa):

Given data at state 2:

Pressure (P2) = 300 kPa = 300,000 Pa

We know that at state 2, the quality is 0 (100% liquid) since the pressure is reduced by cooling the vessel. At this state, all vapor has condensed into liquid. Therefore, mg = 0 kg (mass of gas at state 2).

The mass of liquid (mf) at state 2 can be calculated using the volume of the vessel (V) and the density of liquid water (ρf):

mf = V * ρf

mf = 10 m³ * 1000 kg/m³

mf = 10,000 kg

The mass of gas (mg) at state 2 is 0 kg, and the mass of liquid (mf) at state 2 is 10,000 kg.

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The second-order partial derivative of the function h(u, v) = u/(u + 16v) with respect to v, denoted as hvv (u, v), is computed as 32u/(u + 16v)^3.

To find the second-order partial derivative of h(u, v) with respect to v (hvv), we need to differentiate the function with respect to v twice. Let's begin by finding the first-order partial derivative of h(u, v) with respect to v, denoted as hv (u, v).

To compute hv, we use the quotient rule. The numerator of h(u, v) is u, and the denominator is (u + 16v). Applying the quotient rule, we get:

hv (u, v) = (u)'(u + 16v) - u(u + 16v)' / (u + 16v)^2

= u - u = 0.

Since hv (u, v) is equal to 0, there are no v terms left when we differentiate again. Therefore, the second-order partial derivative hvv (u, v) is also 0.

In conclusion, the second-order partial derivative of h(u, v) = u/(u + 16v) with respect to v is hvv (u, v) = 0.

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Answer:

I hope it helped u.

Step-by-step explanation:

The required width of the rectangle is given as 26 units.

As mentioned in the question, A rectangle has a length of 3x + 9 and a width of 5x - 4. The perimeter of the rectangle is 106 units. The width of the rectangle.

Perimeter is the measure of the figure on its circumference.

Here,
Perimeter of the rectangle  = 2 [ length + width]
Perimeter of the rectangle = 2 [3x + 9 + 5x - 4]
Perimeter of the rectangle = 2 [8x - 5]
106 = 16x - 10
96 = 16x
x = 6
Now,
Width = 5x - 4
Width = 5 [6] - 4
Width = 30 - 4
Width = 26 units,

Thus, the required width of the rectangle is given as 26 units.

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Answer:

6x - 4 = 8x + 12

Step-by-step explanation:

Translate a small part of the sentence into an expression until you translate the entire sentence.

"Four less than six times a number is the same as eight times the number, x, increased by 12."

6x

"Four less than six times a number is the same as eight times the number, x, increased by 12."

6x - 4

"Four less than six times a number is the same as eight times the number, x, increased by 12."

6x - 4 =

"Four less than six times a number is the same as eight times the number, x, increased by 12."

6x - 4 = 8x

"Four less than six times a number is the same as eight times the number, x, increased by 12."

6x - 4 = 8x + 12

The number of different ways the prizes can be awarded among the 2 entries received is 2 if no one gets more than one prize.

The question states that there are five different prizes and the top five winners will get them, but no one can get more than one prize. Since there are only two entries received, the number of ways the prizes can be awarded is determined by the number of ways to select two winners from the two entries received

This is a combination problem where we have to select 2 items (winners) out of 2 items (entries) without regard to the order.

The number of ways to select k items out of n items without regard to the order is given by the binomial coefficient (n choose k), which is calculated as:

nCk = n! / (k!(n-k)!)

where n is the total number of items, k is the number of items selected and ! denotes factorial.

So in this problem, we have to calculate the number of ways to select 2 winners out of 2 entries, the binomial coefficient is:

2C2 = 2! / (2!(2-2)!) = 2*1/1 = 2

Therefore, the number of different ways the prizes can be awarded among the 2 entries received is 2 if no one gets more than one prize.

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Answer:

The mean of the following scores is the sum of the numbers divided by the amount of terms,

The set is equal to 47, divided by the amount of numbers (10) = 4.7

Answer = 4.7

Answer:

2. 216cm3

3. 748.75

Step-by-step explanation:

Cube v=Bh

To get Base area 9cm x 4cm=36cm2

36cm2 x 6cm=216cm3

The required any score between 87 and 93 is considered to be within 1 standard deviation of the mean.

The mean of the values is the ratio of the total sum of values to the number of values.

Here,
To find the range of scores that fall within 1 standard deviation of the mean, we need to add and subtract one standard deviation from the mean.

One standard deviation from the mean covers approximately 68% of the data if the data are normally distributed. Therefore, to find the range of scores within one standard deviation of the mean, we can use the following formula,

Range = Mean ± Standard deviation

Range = 90 ± 3

The range of scores that fall within 1 standard deviation of the mean is between 87 and 93.

Therefore, any score between 87 and 93 is considered to be within 1 standard deviation of the mean.

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Answer:

$1368

Step-by-step explanation:

Income from dividends = price per share x number of dividends purchased

$3.42 x 400 = $1368

Traveling at a speed of 1000 miles per hour for 7.5 * 10⁵ hours would result in traveling a distance of 7.5 * 10⁸ miles.

To calculate the distance traveled, we can multiply the speed by the time traveled.

Speed = 1000 miles per hour

Time = 7.5 * 10⁵ hours

Distance = Speed * Time

Distance = 1000 miles/hour * 7.5 * 10⁵ hours

To perform this calculation, we can multiply the numerical values and keep the scientific notation for the result:

Distance = 1000 * 7.5 * 10⁵ miles

Distance = 7.5 * 10⁸ miles

Therefore, traveling at a speed of 1000 miles per hour for 7.5 * 10⁵ hours would result in traveling a distance of 7.5 * 10⁸ miles.

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The constant of proportionality for the relationship represented by the graph is 5/3.

To find the constant of proportionality for the relationship represented by the graph, we need to use the formula k = y/x, where k is the constant of proportionality, y is the change in the dependent variable (in this case, YA), and x is the corresponding change in the independent variable.

Looking at the graph, we can see that when x increases by 3 (from 2 to 5), YA increases by 5 (from 15 to 20). So, we have y = 5 and x = 3.

Plugging these values into the formula, we get:

k = y/x
k = 5/3

Therefore, the constant of proportionality for the relationship represented by the graph is 5/3.

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Answer:

(2, 7)

Step-by-step explanation:

you just look at the point where the two lines intersect.

Answer:

2:5 is less than 7:15

Step-by-step explanation:

7:15 = 7/15 = .47 = .5

the other given ratios are,

9:15 = 3:5 = 3/5 = .6

2:5 = 2/5 = .4

3:5 =3/5 = .6

24:45 = 8:15 = 8/15 = .5

thus, the ratio which is less than 7:15 is 2:5

Answer:

c = 24

Step-by-step explanation:

To find a positive number such that the sum of and is as small as possible, we need to use optimization. This problem requires optimization over a closed interval. The given problem is as follows, Let x be a positive number. Find a positive number such that the sum of and is as small as possible.

To find a positive number such that the sum of and is as small as possible, we need to use optimization. This problem requires optimization over a closed interval. The given problem is as follows, Let x be a positive number. Find a positive number such that the sum of and is as small as possible. So, we need to minimize the sum of and . Now, let's use calculus to find the minimum value of the sum.To find the minimum value, we have to find the derivative of the sum of and , i.e. f(x) with respect to x, which is given by f '(x) as shown below:

f '(x) = 1/x^2 - 1/(1-x)^2

We can see that this function is defined on the closed interval [0, 1]. The reason why we are using the closed interval is that x is a positive number, and both endpoints are included to ensure that we cover all positive numbers. Therefore, the problem requires optimization over a closed interval. This means that the minimum value exists and is achieved either at one of the endpoints of the interval or at a critical point in the interior of the interval.

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