Find an equation of the plane with the given characteristics. The plane passes through the points (4, 2, 1) and (-2, 7,5) and is parallel to the z-axis.

The first interval which would most clearly and simply show the distribution of this data include the following: B. 0 – 10.

A class width can be defined as the difference between the upper (maximum) and lower (minimum) boundaries of any class in a data set. This ultimately implies that, all classes must all have the same width in a frequency distribution table or histogram.

Mathematically, the class width of a data set can be calculated by using this formula:

Class width = max - min

Where:

Based on the data set provided above, the most appropriate class width or interval is given by;

Class width = 0 to 10

In conclusion, 0 to 50 would produce two rectangular bars while 0 to 100 is too big an interval.

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Complete Question:

The data set {7, 20, 51, 6, 30, 72, 31, 84, 28, 77, 98} is to be represented by a histogram. Which first interval would most clearly and simply show the distribution of this data?

0–5

0–10

0–50

0–100

Answer: b) 4lb

Step-by-step explanation:

Answer:Your answer is B

Step-by-step explanation:

64 oz is= to 4 lb

Answer: 26

Step-by-step explanation:

Answer:

26 is the answer because we have to subtract when the signs of the number are diffrent and add when it is same . so +18 - (-8) = 26

Answer: #1

Step-by-step explanation: if you look closely at the purple line you will see it falls into (y <3) and yeah

Answer:

47

Step-by-step explanation:

Answer:

Yes, its a function

Step-by-step explanation:

We have to make a 170 gallons mixture of antifreeze with a 40% antifreeze percentage.

We have to made it mixing products from two brands:

• First brand (F): 35% pure antifreeze

• Second brand (S): 85% pure antifreeze.

NOTE: To work with percentage and perform calculations, it is better to express the percentages in decimal form. We can do this by dividing the percentage by 100. Then, for example, 35% will become 0.35.

We will call F to the volume for the first brand and S to the volume of the second brand.

We know that the total mixture volume is 170 gallons. The volume is made of the mixture fo the volume of the first brand and the volume of the second brand. Then, this total volume is equal to the sum of F and S, so we can write:

We need another equation to have a complete system of equations (two equations for two unknowns).

We can use the antifreeze content to write one.

We know the the mixture has to have 40% pure antifreeze. Then, the volume of antifreeze will be 40% of the total volume of 170 gallons.

This volume of antifreeze will come from 35% of the volume of the first brand and 85% of the volume of the second brand.

Then, we can write:

We now have can use the first equation to express S in function of F:

We can now replace S in the second equation and solve for F:

We have found that the first brand will have a volume in the mixture of 153 gallons.

We can now calculate S as:

The second brand volume in the mix is 17 gallons.

Answer:

First brand: 153 gallons

Second brand: 17 gallons.

you can either graph it or solve it algebraically

move the parts of the equation to fit the sctructure of y = mx + b

2x + 4y = 20

4y = -2x + 20

divide by 4 on both sides to get 'y' by itself

y = -2/4x + 20/4

y = -1/2x + 5

this equation tells you the 'y intercept' and the slope

slope; -1/2

y intercept; 5

Answer:

Hence the positive numbers are 246, and 41

(246, 41)

Step-by-step explanation:

From the question,

Let the first positve number be \(x\)

and the other number be \(y\)

Hence,

\(x = 6y\) ....... (1)

Also,

That is,

\(x - y =205\) ........(2).

To solve for the two unknowns, substitute the value of \(x\) in equation (1) into equation (2).

Since,

\(x = 6y\)

Then

\(x - y =205\) becomes

\((6y) - y =205\\\)

Then,

\(6y - y = 205\\5y = 205\\\)

Divide both sides by 5

\(\frac{5y}{5} = \frac{205}{5} \\ y = 41\\\)

∴ the value of \(y\) is 41

Now, substitute the value of y into equation (1) to find \(x\)

Then,

\(x = 6y\) becomes

\(x = 6(41)\\x = 246\\\)

∴ the value of \(x\) is 246

Hence the positive numbers are 246, and 41

(246, 41)

Adam can see the horizon at a distance of \(\sqrt{6}mi.\)

Given that the height of Pam's eye level above sea level is \(324ft\) and the height of adam's eye level above sea level is \(400ft\).

The formula used to find the distance they see in miles is \(d=\sqrt{\frac{3h}{2}}\).

Let the height of Pam's is \(h\) and the height of adam's is \(h'\).

The distance of Pam from the horizon can be given as \(d=\sqrt{\frac{3h}{2}}\).

Substitute these values,

\(\begin{aligned}d&=\sqrt{3\times \frac{324}{2}}\\ d&=\sqrt{486}\\ d&=\sqrt{81\times 6}\\ d&=9\sqrt{6}\end\)

And the distance of adam from the horizon can be given as \(d=\sqrt{\frac{3h'}{2}}\).

Substitute these values,

\(d'=\sqrt{3\times \frac{400}{2}}\\ d'=\sqrt{600}\\ d'=\sqrt{100\times 6}\\ d'&=10\sqrt{6}\)

The net distance of adam from the horizon is

\(\begin{aligned}d_{\text{net distance}}&=d'-d\\ &=10\sqrt{6}-9\sqrt{6}\\&=\sqrt{6}\end\)

Hence, the adam can see the horizon at a distance of \(\sqrt{6}mi\).

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Answer:

B

Step-by-step explanation:

it said sooo

Answer:

4 days

Step-by-step explanation:

The distance between the focus and the directrix is 6 units. So the equation of the parabola is x^2 = 6y.

(1) Since the parabola is symmetrical about the Y-axis and its vertex is at the origin, the equation of the parabola can be written in the form y^2 = 4ax. We need to find the value of 'a' to determine the equation.

We know that the point M (-1,3) lies on the parabola. Substituting these values in the equation above, we get:

3^2 = 4a(-1)

9 = -4a

a = -9/4

So the equation of the parabola is y^2 = -9x.

(2) The focus of the parabola is (6,0). Since the vertex is at the origin, the axis of symmetry is the X-axis. Therefore, the equation of the parabola can be written in the form x^2 = 4ay. We need to find the value of 'a' to determine the equation.

The distance between the focus and the vertex of a parabola is given by the equation a = 1/4f, where f is the distance between the focus and directrix.

We know that the focus of the parabola is F(6,0), so the directrix is x = -6. Therefore, the distance between the focus and the directrix is 6 units.

Using the formula above, we get:

a = 1/4f = 1/4(6) = 3/2

So the equation of the parabola is x^2 = 6y.

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The given equation is a recursive formula where a subscript i equals the product of a subscript i-1 and 2, with the initial value of a subscript 1 being -4a.

The equation represents a recursive relationship between the terms of the sequence. Starting with the initial term, a subscript 1, the subsequent terms are determined by multiplying the previous term, a subscript i-1, by 2. This recursive formula can be written as a subscript i = a subscript i-1 * 2.

Given that a subscript 1 = -4a, we can use this initial value to find the subsequent terms of the sequence. To calculate a subscript 2, we substitute i = 2 into the formula:

a subscript 2 = a subscript 2-1 * 2 = a subscript 1 * 2 = -4a * 2 = -8a.

Similarly, for a subscript 3:

a subscript 3 = a subscript 3-1 * 2 = a subscript 2 * 2 = -8a * 2 = -16a.

By applying the recursive formula repeatedly, we can generate the terms of the sequence. Each term is obtained by multiplying the previous term by 2.

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Answer: 7 over 30 times t plus negative 21

Step-by-step explanation:

(2/5t - 7 + 2/3t) - (5/6t + 14)

(16/15t - 7) - (5/6t + 14)

16/15t - 7 - 5/6t - 14

7/30t - 7 - 14

7/30t - 21, which is the same as 7/30t + -21

Answer:

8

Step-by-step explanation:

Father : 50 years old

Son : 10 years old

Answer:

\(\large\boxed{(2, -3)}\)

Step-by-step explanation:

\(\textsf{We are asked for the Center Coordinates given a circle.}\)

\(\large\underline{\textsf{What is a Circle?}}\)

\(\textsf{A Circle is a curved shape that is commonly used to present a equidistant (same}\)

\(\textsf{distance apart) from a Center point.}\)

\(\textsf{When we create an equation for a circle, we should keep in mind of what the}\)

\(\textsf{coordinates of the center point are, and the Radius. For this problem an equation}\)

\(\textsf{has been given to us.}\)

\(\boxed{\begin{minipage}{20 em} \\ \underline{\textsf{\large Equation of a Circle (Standard Form);}} \\ \\ \tt \tt (x-h)^{2} + (\tt y-k)^{2} = r^{2} \\ \\ \underline{\textsf{\large Where;}} \\ \textsf{h represents the x-coordinate of the center.} \\ \textsf{k represents the y-coordinate of the center.} \\ \tt r^{2} \ \textsf{represents the radius of a circle squared.} \end{minipage}}\)

\(\textsf{*Note that if we are given the formula, the radius is already squared, unless}\)

\(\textsf{specified in the directions.}\)

\(\tt (x-2)^{2} + (y+3)^{2} = 9\)

\(\textsf{Our main focus should be h and k. Notice how both point values are negative.}\)

\(\textsf{The Center Point is represented as the opposite given to us in the formula.}\)

\(\underline{\textsf{Find the Opposite of -2 and 3;}}\)

\(\tt -2 \rightarrow \boxed{2}\)

\(3 \rightarrow \boxed{-3}\)

\(\underline{\textsf{Center Coordinates;}}\)

\(\large\boxed{(2, -3)}\)

Answer:

SA = 108π cm²

Step-by-step explanation:

The surface area (SA) of a sphere is calculated as

SA = 4πr² ( r is the radius )

Thus the SA of a hemisphere is

SA = \(\frac{1}{2}\) × 4πr² = 2πr²

The area of the circular base = πr²

Then total SA is

SA = 2πr² + πr² = 3πr² = 3π × 6² = 3π × 36 = 108π cm²

Answer:

11. ASA

12. SSS

13. SAS

14. SAS

15. Not congruent

16. SAS

Step-by-step explanation:

11.

12, Oppositely congruent

13. indirectly congruent

14. Indirectly congruent

15.

16. Directly congruent

Answer:

Common factor

Difference of cubes

Sum of cubes

Difference of squares

Step-by-step explanation:

Answer: A, B, C, and D

common factor

difference of cubes

sum of cubes

difference of squares

Answer:

1/4 x 3/5 = 3/ 20

decimal form = 0.15

The bank that pays the highest interest for this 4-year IRA account is Chase Bank.

It should be noted that interest rates simply means the cost of borrowing or the gain from savings.

In this case, Destiny wants to compare interest rates quoted by four local banks for a deposit.

Chase Bank: = 2 1/2% = 2.5%

Jefferson City Trust:l = 1.7%,

Bank of America = 2.12%

First State Bank = 1 3/4% = 1.75%

Therefore, the highest is Chase Bank as it gives 2.5%.

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Answer: 69.2%

Step-by-step explanation:

There are 101 Year 13 students out of a total number of 146 pupils.

To find this as a percentage, divide the total number of students by the year 13 students and then multiply by 100%:

= Year 13 students/ Total students * 100%

= 101 / 146 * 100%

= 0.692 * 100%

= 69.2%

The X value corresponding to z = -2.00 is 60. The X value corresponding to z = -2.00 is 60. This means that the observation with a z-score of -2.00 is 60 units below the population mean of 80.

To find the X value corresponding to z = -2.00, we can use the formula:
z = (X - µ) / σ
Substituting the given values, we get:
-2.00 = (X - 80) / 10
Solving for X, we get:
X = (-2.00 x 10) + 80
X = 60

The z-score measures the number of standard deviations an observation is from the mean. In this case, the given z-score of -2.00 indicates that the observation is 2 standard deviations below the mean.
To find the corresponding X value, we use the formula:
z = (X - µ) / σ
Where z is the standard normal distribution value, X is the corresponding raw score, µ is the mean of the population, and σ is the standard deviation of the population.
Substituting the given values, we get:
-2.00 = (X - 80) / 10
Solving for X, we get:
X = (-2.00 x 10) + 80
X = 60

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The given term seems to include various descriptors, such as "17b hydroxy," "2a," "17b dimethyl," "5a," and "androstan 3 one azine." These descriptors likely refer to specific chemical features or substitutions present in the compound.

The term "17b hydroxy 2a 17b dimethyl 5a androstan 3 one azine" appears to be a chemical compound or a steroid compound. However, without additional information or context, it is challenging to provide an accurate description or explanation for this specific compound.Chemical compounds are typically described using a combination of systematic names, common names, or molecular formulas. These names are based on standardized nomenclature systems developed by scientific organizations.

In this case, the given term seems to include various descriptors, such as "17b hydroxy," "2a," "17b dimethyl," "5a," and "androstan 3 one azine." These descriptors likely refer to specific chemical features or substitutions present in the compound.To provide a more detailed explanation, it would be helpful to have the systematic name, molecular formula, or additional information about the compound's structure, properties, or usage. With these details, it would be possible to provide a more accurate and informative description of the compound.

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Answer:

12/16 sorry if im wrong

Step-by-step explanation:

Answer: 2 and 19/56

Step-by-step explanation:

x = (16/7 + 2 11/28)/2

x = (64/28 + 67/28)/2

x = (131/28)/2

x = 131/56 or 2 19/56

Answer:

78kg

Step-by-step explanation:

76×5= 380kg

380-72-74-75-81= 78kg

The statements are always true regarding the diagram are m∠5 + m∠3 = m∠4, m∠3 + m∠4 + m∠5 = 180° and m∠2 + m∠3 + m∠5 = 180°. So, correct answers are A, B and E.

The given triangle and its exterior angles are shown in the diagram. We are also given the interior angles of the triangle, which are angles 2, 3, and 5, and their corresponding exterior angles, which are angles 1, 4, and 6. We need to determine which statements are always true regarding the diagram.

A) m∠5 + m∠3 = m∠4: This statement is true because angle 4 is the exterior angle at angle 3, and it is equal to the sum of angles 3 and 5. Therefore, m∠4 = m∠3 + m∠5, and we can substitute this into the given equation to obtain m∠5 + m∠3 = m∠3 + m∠5, which is always true.

B) m∠3 + m∠4 + m∠5 = 180°: This statement is also true because the sum of the exterior angles of a triangle is always 360°. Therefore, we have m∠1 + m∠4 + m∠6 = 360°. But m∠1 = m∠2, and m∠6 = m∠5, so we can substitute these in to obtain m∠2 + m∠3 + m∠5 = 360° - m∠4.

Since the sum of the interior angles of a triangle is 180°, we have m∠2 + m∠3 + m∠5 = 180° + m∠4, which can be rearranged to give the given equation.

C) m∠5 + m∠6 =180°: This statement is not always true. It depends on whether angle 6 is an exterior angle or not. If it is, then this statement is true because the sum of an exterior angle and its adjacent interior angle is always 180°. But if angle 6 is not an exterior angle, then this statement may not be true.

D) m∠2 + m∠3 = m∠6: This statement is not always true. It depends on whether angle 6 is an exterior angle or not. If it is, then this statement is true because angle 2 and angle 3 are adjacent interior angles to angle 6. But if angle 6 is not an exterior angle, then this statement may not be true.

E) m∠2 + m∠3 + m∠5 = 180°: This statement is true because the sum of the interior angles of a triangle is 180°, and angles 2, 3, and 5 are the interior angles of the triangle.

Therefore, the statements that are always true regarding the diagram are A), B), and E).

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Complete question is:

A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options.

A) m∠5 + m∠3 = m∠4

B) m∠3 + m∠4 + m∠5 = 180°

C) m∠5 + m∠6 =180°

D) m∠2 + m∠3 = m∠6

E) m∠2 + m∠3 + m∠5 = 180°

The values of the speed, distance, and time variables are found using kinematic equation for speed and presented as follows;

Question 1; The distance traveled in 25 minutes = Speed × Time

Question 2; The distance traveled in 25 minutes is 7.5 miles

Second part; To find the time it takes to travel to school located 9 miles from the house, while bicycling at a rate of 18 miles per hour

The time it takes is 30 minutes

Kinematic equations are equations used to predict or determine the motion parameters of an object moving with constant acceleration

Question 1; The speed of the bicycle = 18 miles per hour

The distance traveled in 25 minutes is obtained from the formula

\(Speed = \dfrac{Distance}{Time}\)

Therefore; Distance = Speed × Time

Question 2; 1 hour is equivalent to 60 minutes

Therefore; \(1 \ minute = \dfrac{1}{60} \ hour\)

\(25 \ minute = 25\times \dfrac{1}{60} \ hour = \dfrac{5}{12} \ hour\)

The distance traveled in 25 minutes is therefore;

\(Distance = 18\, \frac{miles}{hour} \times \dfrac{5}{12}\, hour = 7.5 , miles\)

The distance traveled by the bicycle in 25 minutes is 7.5 miles

Second part; A second problem involving the rate of 18 miles per hour is as follows; Given that the speed rate of the bicycle is 18 miles per hour, how long does it take to get to the school located at approximately 9 miles from the house.

The equation that can be used to solve the problem is the equation for speed which can be expressed as follows;

\(Speed, \, v = \dfrac{Distance,\, d}{Time,\, t}\)

Which gives the following equation to solve the problem for the time;

\(t = \dfrac{v}{t}\)

Therefore;

\(t = \dfrac{9\, miles }{18\, \frac{miles}{hour} } = 0.5 \, hours\)

The time it takes to ride the bike to school is 30 minutes

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