The approximate **age **of the **bone **is 22920

The** half-life** of an isotope is characterized as the sum of time it takes for there to be half the beginning sum of the radioactive isotope present.

since we know for half time

**N = N₀(1/2) n ** ..........1

where n is the new amount whereas N₀ is the initial amount and n is the number of ** half time **

since the ratio of 14c:12c is 1/16

so the equation 1 gets converted to

N/No =(1/2)n

=>1/16 = (1/2)n

=>(1/2)4 = (1/2)n

=> n= 4

So the age of the bone will be 4* 5730 =22920

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You find a piece of bone that has a 14c/12c ratio that is 1/16 that of the atmospheric 14c/12c ratio. If the half-life of 14C is 57305730 years what is the approximate age of the bone?

[tex] x {6} \div x {15}[/tex]how to solve x to the 6th power divided by x to the 15th power

So, if we apply the power's rule, we notice that if the base is the same, the exponents can be substracted. Like this

So the answer is 1 / x to the 9th power

arcsin (-1)

compute the exact value

–π/2 is the exact value of **arcsine** (-1).

The six main** inverse trigonometric **functions include **arcsin**. It is the** sine function's inverse trigonometric function**. The mathematical symbol for arcsin, commonly known as** inverse sine**, is arcsin x or sin-1x (read as sine inverse x). Sin-1x is not the same as (sin x)-1; that is, sin-1x is not the **reciprocal function **of sin x. This is an important distinction to make. We may use the six inverse trigonometric functions **arccos, arcsin, arctan, arcsec, arccsc, and arccot **to calculate angles. Arcsin x calculates the angle that **corresponds** to the** right-angled triangle's perpendicular **to **hypotenuse ratio.** We shall examine the idea of** arcsin** in this article and determine its formula. We'll also talk about the** domain **and** range**.

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(5x²+23x+16) + (x+4)

÷

**Answer:**

5x2 + 24x + 20

**Step-by-step explanation:**

A rectangle has an area of 40 square units. The length is

6 units greater than the width.

Mark this and return

What are the dimensions of the rectangle?

O 8 by 5

O 10 by 4

O11 by 9

O 13 by 7

Save and Exit

Next

Submit

The **dimensions** of the **rectangle **will be equal to 10 by 4.

A **rectangle** may be defined as the closed figure having **four sides** with the interior angles equal to 90°. it has two dimensions the length and the width. The** area** of a rectangle may be defined as the **product** of its length and width. According to the question the area of the rectangle is given as 40 square units. Let us assume the **length** as 'l' units and **width** as 'b' units. It is given that length is 6 units greater than the width that is l = (b + 6).

Now, the **area of the rectangle** = l×b

40 = (b + 6)×b

40 = b² + 6b

=> b² + 6b - 40 = 0

=> b = [-6 ± √(36 + 160)]/2

=> b = (-6 ± 14)/2

=>b = 4 units, since width cannot be **negative**.

Now, length = b + 6 = 10 units.

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A right pyramid has a surface area of 258 cm2. A right cone has a base radius of 4 cm. The cone and pyramid have equal surface areas. What is the height of the cone to the nearest tenth of a centimetre?

The **height of the cone** to the nearest tenth of a centimeter is** 17.40 cm.**

From the given information provided in the question, we can solve this problem by following a few steps.

The surface area of a right pyramid is** 258 cm²** according to the question.

The surface area of the cone is equal to the surface area of the right pyramid. Therefore the surface area of the cone is also **258 cm².**

The surface area of a cone is denoted as** ( πrh + πr² )**.

Where h is denoted as the **height **and, r is denoted as the **radius of the cone** which is **4 cm.**

Hence the surface area of the cone is,

**SA = (π× 4× h+ π× 4² ) cm²**

Now, we can generate an equation, as **both represent **the value of the **surface area** of the cone.

(π× 4× h+ π× 4² ) = 258

Or, (12.56h + 39.44) = 258 [ **The value of π is 3.14 **]

Or, 12.56h = 258 - 39.44 [ subtracting 39.44 from both sides ]

Or, 12.56h = 218.56

Or, h = 218.56/12.56 [ dividing both sides by 12.56]

Or, h = 17.40

Now, we can conclude that the** **height of the cone is **17.40 cm.**

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can someone please help me answer this im really confused. Thank you so much if you help!!

**Answer:**

y=2X - 6

**Step-by-step explanation:**

find the slope using the 2 points

m = 8-2/7-3 = 2

substitute 4,2 in the equation y=mx+b and solve for b.

2 = 2x4+b

b=-6

y = 2x - 6

**Answer:**

Slope intercept formula: y = 2x -6

Point Slope formula y = 2x-6

**Step-by-step explanation:**

1) Find the slope

2) Choose a point and plug it into the equation y = mx+b

3) Solve for b

4) Plug-in new slope (m) and new y-intercept (b) into equation y = mx+b

**Solving:**

4 = x1

2 = y1

7 = x2

8 = y2

to find slope with slope formula:

m = y2-y1/x2-x1 = 8-2/7-4 = 6/3 = 2

now plug in,

y = 2x+b

to find b, take any one of the pair

(i will choose (4,2) )

2 = 2(4) + b

now solve for b,

2 = 8+b

b = -6

**Slope intercept formula: y = 2x -6**

for point slope: y-y1 = m(x-x1)

as we know our slope is 2 and points are (0,-6) where 0 is x1 and -6 is y1

now we plug in,

y-(-6) = 2(x-0)

y+6 = 2x

**Point Slope formula y = 2x-6**

**Hope this helps! Please like!!**

:)

b/c=a solve for c b nb

**Answer: **

**b = ca**

**c = ba**

**Step-by-step explanation:**

the product x squared and y increased by 4

X*y+2 that's the answer lol

Your equation is written like this

(X^2) * (y + 4)

(Assuming you said the product of x squared and y increased by 4)

(X^2) * (y + 4)

(Assuming you said the product of x squared and y increased by 4)

Nathan eats the same amount of lunch meat everyday. If Nathan eats 2 pounds of lunch meat in 8 days, he eats pound(s) of lunch meat per day

Using **fraction**, He consumes **1/4 pound** of **lunch meat **each day.

A fraction, expresses a** piece of a whole,** a fraction, such as one-half, eight-fifths, or three-quarters, specifies the number of **components **of a respective size.

Given,

He consumes **2 pounds **of beef in** 8 days.**

We need to determine how much meat he consumes each day.

To ascertain:

He consumes** 2/4 of a pound **of beef in a day.

**= 1/4**

He thus consumes **1/4 pound **or less of lunch meat every day.

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3. A tomato sauce company currently sells tomato sauce in a

cylindrical can that has a radius of 5 cm and a height of 12 cm.

They have plans to use larger cans to sell tomato sauce in bulk.

The new cylindrical cans are to be similar to the original cans

and have a height of 60 cm.

If the original can holds 1487 cm³ of tomato sauce,

how much tomato sauce will the new can hold?

√x cm³

V=

** Tomato sauce will the new can hold is ** 743[tex]cm^{3[/tex]

**let take us take,**

**V = Sh **

[tex]S_{1} =S_{2}[/tex]** **

** **[tex]h_{1[/tex] = 12 cm

[tex]h_{2}[/tex] = 60 cm

[tex]\frac{V_{1} }{V_{2} } = \frac{h_{1} }{h_{2} }[/tex]

[tex]\frac{1487}{v_2} } = \frac{12}{60}[/tex]

= 743[tex]cm^{3[/tex]

What is Height? **Height** means the vertical **distance**, either between the top and bottom of something or between the bottom and the thing above it. height refers to being tall or short as measured **vertically**.

Height is a way of measuring someone or something from the bottom to the top or from the **head** to the **feet**. In other words, height indicates how tall someone or something is. We can compare how tall we will be when we grow up. We often compare the** average height** of men and women in different countries.

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Kelly drove 238 miles on 6 1/6 gallons of gasoline. Calculate how many miles per gallon she gets in her vehicle.

**Kelly** gets 38.59 miles per **gallon** of **gasoline**

**Miles** drove by Kelly = 238 miles

Gasoline used by the car = 6 1/6 gallons

**Gasoline** used in the car in improper fraction = 37/6 gallons

Average fuel economy: Average fuel economy of a car gives the distance covered by the car in one gallon of gasoline. This is an important factor to consider while buying or using a car as it is a major source of expenditure for the car.

To calculate miles per **gallon** we use the following formula:

Miles per gallon = Miles driven/ Gasoline used in the car

= 238/(37/6)

= 238*6/37

= 38.59

Miles per gallon = 38.59

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If you earn $7.50 per hour at your job how much will you earn if you work 25 hours?

**Answer:**

$187.5

**Step-by-step explanation:**

.

Answer:

187.50

Step-by-step explanation:

7.5(25)=187.50

hope this helped

have a good day^^

I need help with this can someone please help?

HG is the answer.

hope this helps

The first one is **GH Segment.**

Both shapes are similar. The figure on the right is a scaled version of the figure on the left. The **VU** edge in the left figure corresponds to the **GH** edge in the right figure.

The second one is %[tex]150[/tex].

As can be seen, the **VU** edge is [tex]2[/tex] units long while the **GH** edge is [tex]3[/tex] units long. By proportioning these edges and multiplying by [tex]100[/tex], we find the scaling factor. It is [tex]\frac{3}{2}[/tex].

26 = -12u - 9 + 7u solve for u and simplify as much as possible

**Answer:**

u = -7

**Step-by-step explanation:**

26 = -12u - 9 + 7u

combine u terms on right side:

26 = -5u - 9

add 9 to both sides:

26 + 9 = -5u - 9 + 9

35 = -5u

divide both sides by -5:

35/-5 = -5u/-5

**u = -7**

7.

In the given image, the measure of 2x is

Only enter the number.

P

N

142°

90°

X

* REQUIRED

M

U

**Answer:**

Angle LMN = 180 - 142

= 38° (sum of angles on a straight line=180)

x = 180 - 90 - 38

= 52° (sum of angles in triangle=180)

Dominoes region seven manager projects a net income of $725,000 the net income typically represents 30% of total annual sales based on his projections what will be the annual sales￼

We were informed that the net income will be $725,000, since that value represents 30% of the total annual sales we can apply a rule of three to solve the problem. We do that by making 30% represent $725,000 in the same proportion that 100% represents the total anual sales, x. We have:

[tex]\frac{30}{100}\text{ }\frac{\text{ \%}}{\text{ \%}}=\frac{725000}{x}[/tex]We can cross multiply to find the value of "x".

[tex]\begin{gathered} 30\cdot x=100\cdot725000 \\ x=\frac{72500000}{30} \\ x=2416666.667 \end{gathered}[/tex]The total annual sale on this year will be approximately $2,416,666.667.

The function -2x^2-8x+42 represents the approximate height of an object (x seconds) after it is thrown off the top of a building. How many seconds does it take for the object to hit the ground?

The function is given to be:

[tex]-2x^2-8x+42[/tex]The object hits the ground when the function is equal to zero:

[tex]-2x^2-8x+42=0[/tex]Solving the equation by factorization, we have:

[tex]\begin{gathered} 2(-x^2-4x+21)=0 \\ -x^2-4x+21=0 \\ -x^2-7x+3x+21=0 \\ -x(x+7)+3(x+7)=0 \\ \therefore \\ (-x+3)(x+7)=0 \\ Hence \\ x=3,x=-7 \end{gathered}[/tex]Since the time cannot be negative, then the time will be 3 seconds.

**Therefore, it will take ****3 seconds**** for the object to hit the ground.**

Please help!! It’s geometry and I just need the answer quick

**Answer:**

4.5

**Step-by-step explanation:**

The half-life of a certain medication is 2 hours, and a patient takes a single 400-milligram dose of the medication.

After 6 hours, there will be X milligrams of medication left in the patient's body.

After 7 hours, there will be X milligrams of medication left in the patient's body. Round your answer to the nearest hundredth.

After 8 hours, there will be X milligrams of medication left in the patient's body.

The number of **milligrams** of medication medication left after 6 hours is; 50 milligrams.

The number of **milligrams** of medication medication left after 7 hours is; 35.36 milligrams.

The number of **milligrams** of medication medication left after 8 hours is; 25 milligrams.

It follows from the task content that the amount of medications left in the patient's body be determined in each case.

Recall the formula for the amount of substance remaining for half life situations is as follows;

A = N (1/2)^(t/half-life)

Since **half life** = 2 hours and **N** = 400 milligrams;

Hence;

At t = 6hrs; A = 400(1/2)^(6/2) = 400(1/2)³ = 50millograms.At t = 7hrs; A = 400(1/2)^(7/2) = 400(1/2)^(3.5) = 35.36 millograms.At t = 8hrs; A = 400(1/2)^(8/2) = 400(1/2)⁴ = 25 millograms.Read more on **half-life**;

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PLEASE HELP NOW!!! THX :))

You are baking doughnuts for your class. There are 8 total students in your class and you have baked 11 doughnuts. Write and solve an equation to find the additional number x of doughnuts you need to bake in order to have 4 doughnuts for each student. Write your equation so that the units on each side of the equation are doughnuts per student.

**Answer: 4x + 11 = 4(8) **

**Step-by-step explanation:**

Idil is deciding between two different movie streaming sites to subscribe to. Plan A costs $18 per month plus $1 per movie watched. Plan B costs $8 per month plus $3 per movie watched. Let AA represent the monthly cost of Plan A if Idil watches x per month, and let B represent the monthly cost of Plan B if Idil watches x movies per month. Write an equation for each situation, in terms of x, and determine which plan would be cheaper if Idil plans on watching 6 movies each month.

The** cheaper plan** here would be** plan A. **The equation that is written in terms of the plans on movies is 0 < x < 5

For the plan A, we would have the function to be given as

A = 1x + 18

This is due to thge fact that this plan is said to cost $18 per month plus $1 per movie watched.

For plan B the function would have to be:

B = 3x + 8

The equation that we would have here would be

1x + 18 < 3x + 8

= x - 3x < 8 - 18

= -2x < -10

x < 5

Hence we would have the **equation** as 0 < x < 5

Cheaper plan

1x6 + 18 = 24

3x 6+ 8 = 18 + 8 = 26

Plan A id **cheaper**

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1. A trapezoid is pictured on the right. Its bottom base a is not changing while its top base b is increasing at the rate of 3 inches per second while its height h is decreasing at the rate of 0.5 inches per second. How fast is the area of the trapezoid changing, measured in square inches per second, at this moment?

A) -2.5

B) -.75

C) 1

D) 2

(Please explain)

Answer:

the answer is A...

Step-by-step explanation:

Calculate Area (A):

The area formula for a square is denoted below:

A = s2

Taking the square root of both sides, we get:

s = √A

s = √3

s = 1.7320508075689

i don't know non of this and i need help pls

By using the fact that ∠4 and ∠5 add up to 180° and ∠5 = ∠7, we conclude that the **measures **of the **angles **are:

∠5 = ∠7 = 56°.

How to find the measures of the angles?For angles formed by the interception between lines meet the following property.

If the angles are one next to the other, the measures add up to 180°.

If not, then the two angles have the** same measure.**

This means that:

∠5 = ∠7

∠8 = ∠6

And so on.

If the two horizontal** lines are parallel**, then:

∠5 = ∠1

And we know that:

∠4 + ∠1 = 180°

124° + ∠1 = 180°

∠1 = 180° - 124° = 56°

Then we get that:

∠5 = ∠7 = 56°.

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ASAP!!

4/3x + 2/3x = 1/3x +5

Solve the equation for X and include all steps to get Branliest.

**Answer: x=3**

**Step-by-step explanation:** Multiply both sides of the equation by 3 to get 4x+2x=x+15. Combine like terms. (underlined) 6x=x+15. Move variable to left side and change its sign. 6x-x=15. Combine like terms again. 5x=15. Divide both sides of the equation by 5 to get** ****x=3.**

PLEASE HELP WHAT IS THE ANSWER

Triangle DAC is isosceles.

The correct option; **Angle BAD** is congruent to angle BCA, is requited to show ΔDBA ≅ ΔCBA by **side-angle-side** congruence theorem.

If all 3 corresponding sides are equal as well as all 3 corresponding angles seem to be equal in measure, two triangles are said to be congruent.

These triangles could be moved, rotated, flipped, and turned to look exactly the same. They coincide if they are repositioned. ' is the symbol of congruence.**side-angle-side** congruence theorem: By **SAS rule**, two triangles are said to be congruent if any two sides and the angle would include between the sides with one triangle are equivalent to a corresponding two sides and also the angle would include here between sides of the second triangle.

For the given** triangles**;

ΔDBA and ΔCBA

Side AC = Side AD

Side AB = Side AB (common)

Thus, to make both triangles congruent the angles falling in between these two triangles must be equal.

Thus, **Angle BAD** is congruent to angle BCA,

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Express as a trinomial. (x-9)(x+6)

The expression of (x-9)(x+6) as a** trinomial **is x² -3x - 54

A **trinomial** is an algebraic expression that has three non-zero terms.

In a simpler terms, the definition of a** trinomial **is a math equation that has three terms which are connected by plus or minus notations.

Therefore, let's express (x-9)(x+6) as a **trinomial**.

Hence,

(x-9) (x+6) = x² + 6x - 9x - 54

Finally,

x² + 6x - 9x - 54 = x² -3x - 54

Therefore, the** trinomial **form of (x-9)(x+6) is x² -3x - 54

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keisha's basketball team must decide on a new uniform. the seventh-graders will pick the color of the shorts (black or gold) and the eighth-graders will pick the color of the jersey (black, white, or gold), but the two groups of players will not confer together. if, for both garments, each possible color is equally likely to be chosen, what is the probability that the shorts will be a different color than the jersey? express your answer as a common fraction.

The **probability **that the shorts of the basketball team will be of a different color than the jersey is **2/3**.

Probability can be found using the following formula;

probability = number of favorable outcomes or events ÷ total number of outcomes or events

In order to calculate the probability that the **shorts **will be of a different color than the **jersey**, we first determine the total number of combinations that are possible;

1- Black-Black

2- Black-White

3- Black-Gold

4- Gold-Black

5- Gold-White

6- Gold-Gold

Hence there are a total of 6 possible combinations of shorts and jerseys out of which 2 are the same and 4 are different.

Therefore the probability that the shorts will be of a different color can be calculated as follows;

probability = number of favorable outcomes or events ÷ total number of outcomes or events

probability = 4 ÷ 6

probability = 2/3

Hence, 2/3 is the probability that the shorts will be of a different color than the jersey.

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The PTA prepared 10 gallons of punch to serve at their first meeting. If each serving is eight ounces, how many people can be served?

Based on **mathematical operations**, the **number** of people that 10 gallons of punch can serve is 192 persons.

The number of people can be determined using **mathematical operations** of **multiplication** based on converting the gallons to ounces and **division**.

The number of gallons of punch to serve at the first meeting = 10 gallons

The quantity of punch per serving = 8 ounces

1 gallon = 153.722 ounces

10 gallons = 1537.22 ounces

The persons that can be served 8 ounces from the 10 gallons = 192 (1,537.22/8).

Thus, **mathematically**, from the 10 gallons of punch, the PTA can serve 192 persons.

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WILL MARK BRAINIEST Rewrite the radical expression as an expression with a rational exponent. 3 square root x 7

a x21

b x4

c x7/3

d x 3/7

The answer is x7/3 because i did that lesson

Penny is going to make a donation to our local animal shelter. The price of each item she will donate is shown.

so far she has 30 cans of cat food 34 cans of dog food and 18 bags of cat she wants the value of her donation to be more than $380 how many bags of dog food does Penny need to donate to meet her goal?

**Answer:**

Second Choice: **8.73b + 171.48 > 381**

**Step-by-step explanation:**

This is a tricky question because the first two choices both represent an inequality that satisfy the conditions

First, let's eliminate obvious wrong choices.

If b represents the number of bags of dog food and one bag costs $8.73, there should be term 8.73b somewhere in the inequality since 8.73b represents the total $ cost of b bags of dog food.

This means we can eliminate the last two choices

Let's deal with the knowns and compute the dollar amounts of each of the products being donated

30 cans of cat food at $0.57 per can = 0.57 x 30 = $17.10

34 cans of dog food at $0.84 per can = 0.84 x 34 = $28.56

18 bags of cat food at $$6.99 per bag = 6.99 x 18 = $125.82

The sum of these is $171.48

She is also donating b bags of dog food at $8.73 per bag = 8.73 x b = $8.73b

So the total cost of the donation =

8,73b + 171.48 which has to exceed 381

So the inequality is **8.73b + 171.48 > 381**

Which is the choice you have selected and I believe it is correct

Now, the tricky part comes because if you subtract 171.84 from both sides of the inequality we get

8.73b > 318 - 171.48

Both inequalities are equivalent but we would not write an inequality of the type where the RHS is a mathematical expression. We would instead simplify the right hand side and write it as

8.73b > 209.52 (381-171.48 = 209.52)

I believe the way the question is worded is the LHS should be the $sum of all the donations and the RHS the minimum value.

So the best choice is choice 2: **8.73b + 171.48 > 381**

i hope that helps.

The demand for cattle and an increase in railroad construction across the u. S. Contributed most directly to .
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what are the ratio and decimals for sin a ,cos a,tan a
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A dog running of constant speed of 3m/s increases it's speed to 7m/s upon seeing a lion. if the mass of the dog is 20kg, the work it does in achieving the new speed is.......
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