1) What would be another way to name plane M?
(picture attached)

A. plane KJH
B. plane J
C.plane HJG
D.plane GJN

The estimated age of the archaeological sample  as calculated from the given data is  = 2622.58333 years

Half life given is 5730

t₆.₅ = Ln2/k

k= ln 2/ 5730

The rate constant ,

k = 0.00012 year⁻¹

Given that 73 % of the 14C remains

then |A1|/|A2|  = 0.73

As we know ,

|A1|/|A2| = e ⁻₍kt₎

Hence, on solving the equation we get ,

ln(0.73)= -0.00012t

t = -0.31471/ -0.00012

 = 2622.58333 years

Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential (or, rarely, non-exponential) decay.

For example, the medical sciences refer to the biological half-life of drugs and other chemicals in the human body. The converse of half-life (in exponential growth) is doubling time.

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Personal car would be the best option to manage both tasks efficiently. While the train is a reliable mode of transportation, it may have fixed schedules that might not align perfectly with Patrick's needs.

On the other hand, using his personal car provides more flexibility and allows him to tailor the departure time according to his daughter's coding class schedule.

If Patrick decides to take the train, he would need to check the train schedule to see if there are convenient departure and arrival times for both the soccer game and the coding class. This option would require planning and coordination to ensure he arrives at the game on time and can pick up his daughter afterward.

Using his personal car gives Patrick the freedom to leave at a time that accommodates both the soccer game and the coding class. He can drop off his daughter at her coding class, attend the soccer game, and then pick her up afterward without being restricted by train schedules.

Considering the circumstances, Patrick might find it more convenient to use his personal car to manage both tasks effectively and ensure he can attend his son's soccer game while also ensuring his daughter arrives at her coding class on time.

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Answer:

Zero

Step-by-step explanation:

A number divisible by 2 must be positive.  Example: 2, 4, 6, 8

A number divisible by 5 must have either 5 or 0 in the ones place.  Example: 15, 200, 3985, 4500

A number divisible by 9 must have numbers that add up to one of the multiples from nine.  Example:  279 (2+7+9=18), 612 (6+1+2=9)

The digit that all numbers have in common is zero.  Zero is considered positive, is one the numbers required for 5, and, with other numbers, can be divisible by 9.

The range of the relation that is represented in the mapping shown in the diagram attached below is: {3, 5, 11, 21}.

If we are given a mapping that represents a relation, the input values (x-values) make up the domain of the relation while the output values (y-values) make up the range of the relation.

In the mapping shown in the diagram attached below, we have the following:

The domain of the relation is: {-1, 0, 1, 2, 3}

The range of the relation is: {3, 5, 11, 21}

Thus, we can conclude that, the range of the relation that is represented in the mapping shown in the diagram attached below is: {3, 5, 11, 21}.

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A scatterplot shows the number of miles driven versus the gallons of gasoline remaining in the gas tank of a car. Which correlation best describes the relationship shown on the scatterplot?

Answer:

Negative correlation

Step-by-step explanation:

The kind of relationship which exists between two variables can be obtained whwn plotted in a graph such that we can visually access the data and note its trend. Datasets with fit lines trending downward will always have a slope value which is negative. In the scenario above, gallon of gasoline falls as the number if miles driven increases. This is a very reasonable relationship. And thus correlation between Both variables will be negative

Answer:

n=10.3

3n-30.9=0

Step-by-step explanation:

Answer:

n= -10.3

Step-by-step explanation: I took the test

Answer:

The solution to the equation is:

\(x=4,\:x=\frac{3}{2}\)

Step-by-step explanation:

Given the equation

\(3\left(x-4\right)\left(2x-3\right)=0\)

Using the zero factor principle

if ab=0, then a=0 or b=0 (or both a=0 and b=0)

\(x-4=0\quad \mathrm{or}\quad \:2x-3=0\)

now solving

\(x - 4 = 0\)

adding 4 to both sides

\(x - 4 + 4 = 0 + 4\)

simplifying

\(x = 4\)

and also solving

\(2x - 3 = 0\)

adding 3 to both sides

\(2x - 3 + 3 = 0 + 3\)

simplifying

\(2x = 3\)

divide both sides by 2

\(\frac{2x}{2}=\frac{3}{2}\)

simplifying

\(x=\frac{3}{2}\)

Therefore, the solution to the equation is:

\(x=4,\:x=\frac{3}{2}\)

Answer:

4 or 3/2

Step-by-step explanation:

I had this question on a quiz, I got it correct.

Answer:

It would be to ask all the students in the grade.

Step-by-step explanation:

Answer:

it D answer D and it will be correct I just did this test guys well if it isnt D then its all students in each grade I just did this test lol

Step-by-step explanation:

Answer:

it is 6

Step-by-step explanation:

The simple multiplier of the economy represented by the system of equation above is: 4/7.

The simple multiplier is the ratio of the change in equilibrium output to a change in autonomous expenditures, such as government spending or investment.

To find the simple multiplier in the economy, we need to first determine the equation for equilibrium output, which is where aggregate demand (AD) equals aggregate supply (AS).

Setting y in both equations equal to each other, we get:

710 - 30p + 5g = 10 + 5p - 2s

Simplifying and rearranging, we get:

35p = 700 + 2s - 5g

p = (20/7) + (2/35)s - (1/7)g

Now that we have the equilibrium price, we can substitute it back into the AD equation to find the equilibrium output (y):

y = 710 - 30[(20/7) + (2/35)s - (1/7)g] + 5g

y = (400/7) + (6/7)s + (4/7)g

The simple multiplier is then equal to the change in equilibrium output divided by the change in government purchases:

simple multiplier = Δy/Δg = 4/7

Therefore, the simple multiplier in the economy is 4/7.

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Answer:

area of rectangle: 64.4

area of sector: 8.3

Step-by-step explanation:

area of rectangle: 7 × 9.2 = 64.4

area of sector:

radius = 9.2 ÷ 2 = 4.6

area of circle: 3.14 × 4.6² = 66.4

66.4 × \(\frac{1}{8}\) = 8.3

The area of the considered composite figure is 97.6212 cm²

A composite figure is formed by composition of more than one figure. If there is no positive intersection of the figures' area, then the area of the composite figure is the sum of the areas of the composite figures.

Sector of a circle is like slice of a circular pizza. Its two straight edge's having an angle, and edge's length(the radius of the circle) are two needed factors for finding the area of that sector.

Since the whole circle with radius 'r' units have 360 degrees angle on center of the circle, and its area is \(\pi r^2 \: \rm unit^2\), thus, as the angle lessens, this area gets lessened.

360 degree =>  \(\pi r^2 \: \rm unit^2\) area

1 degree =>  \(\pi r^2 \: \rm unit^2\)/360 area

x degree =>\(\dfrac{x \times \pi r^2}{360} \: \rm unit^2\) area

Thus, area of a sector with edge length 'r' units and interior angle 'x' degrees is given as:

\(A = \dfrac{x \times \pi r^2}{360} \: \rm unit^2\)

For the given case, the composite figure is made up of two parts, one is sector of a circle with radius of 9.2 cm with angle 45 degrees, and a rectangle of dimensions 7 cm by 9.2 cm.

The edge length of the sector is 9.2 cm, and the angle the sector has got is 45 degrees internally (on the side whose area is needed, and not outward angle).

Thus, we get:

Area of sector = \(\dfrac{45 \times \pi \times (9.2)^2}{360} \approx 33.2212\:\rm cm^2\)

And area of rectangle is its length times width = \(7 \times 9.2 = 64.4 \: \rm cm^2\)

Thus, the area of the composite figure is evaluated as:

Area of composite figure = Area of sector + Area of rectangle

A ≈ 33.2212 + 64.4 sq. cm  = 97.6212 sq. cm

Thus, the area of the considered composite figure is 97.6212 cm²

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Answer:

Center: (0, 6); radius = 4

Step-by-step explanation:

x^2 + y^2 - 12y + 20 = 0

We must complete the square in y.

x^2 + y^2 - 12y = -20

x^2 + y^2 - 12y + 36 = -20 + 36

x^2 + (y - 6)^2 = 16

(x - 0)^2 + (y - 6)^2 = 4^2

Center: (0, 6); radius = 4

Answer: The meaning of the statement “ x vary inversely as y “ is “x is inversely proportional to y".

Final Answer // x=5yx is equal to 5 over y

Step-by-step explanation:

Answer:

24 is gonna be the awnser

Answer: I can't see the symbols, but > and ≥ relate the two numbers.

Step-by-step explanation: Let's go through the 4 symbols ≥,  ≤, >, and <. The statements 55 ≤ 35 and 55 < 35 are not true, while 55 ≥ 35 and 55 > 35 are. So, ≥ and > correctly relate the two numbers.

Answer:

  about 1.01 °C per hour

Step-by-step explanation:

We assume the intended temperature function is ...

  t(h) = 18 +4·sin(π/12(h -8))

We are asked for the rate of change when h=9.

__

The rate of change of temperature with respect to time is the derivative of t(h) with respect to h.

  t'(h) = 4(π/12)cos(π/12(h -8)) = π/3·cos(π/12(h -8))

For h = 9 hours after midnight, the rate of change is ...

  t'(9) = π/3·cos(π/12(9 -8)) = π/3·cos(π/12) ≈ (3.14159)(0.965926)/3

  t'(9) ≈ 1.01152

The rate of change of temperature at 9 a.m. is about 1.01 °C/hour.

Answer:

5. $16.8 6.$16.7 7. 4 costumes 8. no because the slope isn't one 9. 28.8

Step-by-step explanation:

For number 5 you would divide the 90 miles by the two gallons of gasoline used which gives you 45. Your car is using one gallon of gas every 45 miles.

If your trip is going to be 270 miles long then you would divide the 270 by 45 to see how many gallons you would use. You would end up using 6 gallons.

Finally you would multiply the 6 by $2.80 to get $16.80

You would spend $16.80

Answer:

120

Step-by-step explanation:

The sum of the angles in a quadrilateral is 360 degrees

2t+t+2t+t = 360

6t = 360

Divide by 6

6t/6 = 360/6

t = 60

Angle Z = 2t

Angle Z = 2*60 = 120

Answer:

\(120 \: \: degrees\)

Second answer is correct.

Step-by-step explanation:

The sum of the angles in a qudrilateral = 360°

\(t + 2t + t + 2t = 360 \\ 6t = 360 \\ \frac{6t}{6} = \frac{360}{6} \\ t = 60\)

angle z

\(2t = 60 \times 2 \\ \: \: \: \: \: \: \: = 120\)

64n³  is the volume of the cube.

What does a math volume mean?

The cube formula is what?

the volume of the cube = s3

the volume of the cube = ( 4n )³  ⇒ 4n × 4n × 4n

                                                   = 64n³

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The possible values of two consecutive even integers, of which the sum of their squares is 1684, are 28 and 30 for positive integers, while for negative integers, they are  -28 and -30.

The difference between two consecutive even integers is 2.

Let the integers be a and (a+2). Then,

a² + (a + 2)² = 1684

a² + a² + 4a + 4 = 1684

2a² + 4a - 1680 = 0

a² + 2a -840 = 0

Hence, we get a quadratic equation.

There are three methods of solving a quadratic equations: by factoring, completing the square, and by using the abc formula.

Use the factoring method:

a² + 2a -840 = (a - 28) (a + 30)

a = 28  and a = -30

Hence, if the integers are positive, they are: 28 and 30.

If the integers are negative, they are -28 and -30.

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The given assertion is false. The option for reason is the principal option:

"  An arrangement of three linear equations in three unknowns can have one solution, an infinite number of solutions, or no solutions."

An arrangement of linear equations is a grouping of at least one linear equation with similar variables.

A linear framework solution is the task of values to variables so that the equations are all concurrently satisfied.

For an arrangement of equations, three types of solutions exist:-

One solution: When the lines (planes) converge at a point.

No Solution: When the lines (planes) are parallel.

Infinitely numerous solutions: When the lines (planes) overlap one another.

Subsequently, the given assertion is false. The option for reason is the principal option:

" The assertion is false. An arrangement of three linear equations in three unknowns can have one solution, an infinite number of solutions, or no solutions."

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refer to the attachment for the complete question:

Answer:

x + 59 = 0    

X= -59

Step-by-step explanation:

Answer:

you could say something like if it got higher say....over the course of my workout I noticed my heart rate got fast,it speeded up, as you can tell by the graph.

Answer:

28%

Step-by-step explanation:

38.40 - 30 = 8.40

x : 100 = 8.40 : 30

x = 8.40 * 100 / 30

x = 840/30

x = 84/3 = 28%

Answer:

The Greatest Common Factor (GCF) of 26 and 78 is 26.

Step-by-step explanation:

The factors of 26 are 1,2,13,26

The factors of 78 are 1,2,3,6,13,26,39,78

So, as we can see, the Greatest Common Factor or Divisor is 26, because it is the greatest number that divides evenly into all of them.

Hope this helps! :)

Answer:

38

Step-by-step explanation:

The first term of the given sequence is 9.

The second term is 13

= 9 + 4 . = 9 + 2 × 2.

The next number is 22.

= 13 + 9 . = 13 + 3 × 3 .

In the same way the next number of the given sequence will be

22 + 4 × 4 .

= 22 + 16 = 38.

The trigonometric ratio sine compares the lengths of the right triangle's two sides. Sin, though commonly abbreviated to sin, is actually pronounced sine.

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Answer:

k can either be

12

or

−

12

.

Step-by-step explanation:

Consider the equation

0=x2+4x+4

. We can solve this by factoring as a perfect square trinomial, so

0=(x+2)2→x=−2 and−2

. Hence, there will be two identical solutions.

The discriminant of the quadratic equation (b2−4ac) can be used to determine the number and the type of solutions. Since a quadratic equations roots are in fact its x intercepts, and a perfect square trinomial will have

2 equal, or 1

distinct solution, the vertex lies on the x axis. We can set the discriminant to 0 and solve:

k2−(4×1×36)=0

k2−144=0

(k+12)(k−12)=0

k=±12

Answer:

x = 3

y = -7

Step-by-step explanation:

y = -4x + 5

y = 3x - 16

Substitute y in the first equation with 3x - 16

3x - 16 = -4x + 5

+4x         +4x

7x - 16 = 5

+16         +16

7x = 21

÷7    ÷7

x = 3

Then, put x = 3 in y = -4x + 5

y = -4(3) + 5

y = -12 + 5

y = -7

Answer:

x = 3; y = -7

Step-by-step explanation:

Both equations are solved for y.

Let's substitute what y is equal to in the first equation, -4x + 5, for y in the second equation.

The original second equation is:

y = 3x - 16

Now we plug in -4x + 5 for y in the second equation.

-4x + 5 = 3x - 16

Subtract 3x from both sides.

-7x + 5 = -16

Subtract 5 from both sides.

-7x = -21

Divide both sides by -7.

-7x/-7 = -21/-7

x = 3

Now that we know the value of x, we use substitution again.

Take the first original equation, y = -4x + 5, and substitute 3 for x. Then solve for y.

Here is the first original equation:

y = -4x + 5

Substitute 3 for x:

y = -4(3) + 5

y = -12 + 5

y = -7

The solution is: x = 3; y = -7

We can check the solution to make sure it is correct.

Take each original equation and plug in the values we found for x and y. Simplify both sides and see if they are equal. If the two sides are equal, the solution is correct.

Check first equation:

y = -4x + 5

-7 = -4(3) + 5

-7 = -12 + 5

-7 = -7

The solution works on the first equation.

Check second equation:

y = 3x - 16

-7 = 3(3) - 16

-7 = 9 - 16

-7 = -7

The solution works in the second equation.

This shows that our solution is correct.

Answer: x = 3; y = -7

Answer:

4'5

Step-by-step explanation: