he amount of​ carbon-14 present in animal bones t years after the​ animal's death is given by ​P(t)equals=Upper P 0 e Superscript negative 0.00012097 tP0e−0.00012097t. How old is an ivory tusk that has lost 26​% of its​ carbon-14?

For this case we have that by definition, the area of a circle is given by:

[tex]A = \pi * r ^ 2[/tex]

Where:

A: It is the radius of the circle

We have as data that the diameter is 10 feet, then the radius is half, that is, 5 feet.

Substituting:

[tex]A = \pi * (5) ^ 2\\A = 25 \pi\\A = 78.5[/tex]

Rounding out we have that the circle area is[tex]79 \ ft ^ 2[/tex]

Answer:

Option A

Answer:

A. 79 ft²

Step-by-step explanation:

Area of a circle is given by the formulae

[tex]A=\pi *r^2[/tex]

where r is the radius of the circle

Given diameter= 10 ft

Radius of a circle is one half the diameter of a circle.

Radius = [tex]r=\frac{10}{2} =5ft[/tex]

Area=[tex]\pi *5^2=3.14*5^2=78.5ft^2\\\\=79ft^2[/tex]

Answer:

Perimeters is 32.44 unit and area is 30 square unit.

Answer:

[tex]P=\frac{11}{40}+\frac{1}{4}-\frac{1}{20}[/tex]

Step-by-step explanation:

Given,

Students of,

Consumer education, n(C) = 22,

French, n(F) = 20,

Both, n(C∩F) = 4,

Total students, n(S) = 80

Thus, the number of students from Consumer Education, French, or both,

n(C∪F) = n(C) + n(F) - n(C∩F)

= 22 + 20 - 4

[tex]\text{Probability}=\frac{\text{Favourable outcomes}}{\text{Total outcomes}}[/tex]

Hence, probability of a student from Consumer Education, French, or both,

[tex]P=\frac{n(C\cup F)}{n(S)}[/tex]

[tex]=\frac{22+20-4}{80}[/tex]

[tex]=\frac{22}{80}+\frac{20}{80}-\frac{4}{80}[/tex]

[tex]=\frac{11}{40}+\frac{1}{4}-\frac{1}{20}[/tex]

LAST option is correct.

The equation of probability, P, that represents a randomly selected student from this class takes Consumer Education, French, or both are: [tex]\rm Probability = \dfrac{1}{4} + \dfrac{11}{40} -\dfrac{ 1}{20}[/tex] .

Given :

In a freshman high school class of 80 students, 22 students take Consumer Education, 20 students take French, and 4 students take both.

Given that students take Consumer Education: n(C) = 22

The students that take French: n(F) = 20

The students that take both: [tex]\rm n(C\cap F) = 4[/tex]

Total Students: n(S) = 80

Students that take Consumer, French, or both:

[tex]\rm n(C\cup F) = n(F) + n(C) - n(C\cap F)[/tex]

[tex]\rm n(C\cup F) = 20 + 22 - 4[/tex]

[tex]\rm Probability = \dfrac{Favourable \;Outcomes}{Total \; Outcomes}[/tex]

[tex]\rm Probability = \dfrac{n(C\cup F)}{n(S)}[/tex]

[tex]\rm Probability = \dfrac{20 + 22 - 4}{80}[/tex]

[tex]\rm Probability = \dfrac{20}{80} + \dfrac{22}{80} -\dfrac{ 4}{80}[/tex]

[tex]\rm Probability = \dfrac{1}{4} + \dfrac{11}{40} -\dfrac{ 1}{20}[/tex]

Therefore, the correct option is D).

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Answer:

2.5 kg

Step-by-step explanation:

Parts of compost = 2 parts

Parts of potting soil = 6 parts

Total parts = 2 parts + 6 parts = 8 parts

from the above, we can see that 2 out of 8 parts of the total mix is compost,

i.e compost makes up [tex]\frac{2}{8}[/tex] of the total mix.

Given: total mix is 10 kg,

the amount of compost is then [tex]\frac{2}{8}[/tex] x 10 kg = 2.5 kg

Answer:Your answer is 2.5

Step-by-step explanation:

Answer:

  175 hot dogs

Step-by-step explanation:

The new price will be $3.85 + 0.55 = $4.40. Since the price has increased by a factor of 4.40/3.85 = 8/7, the number of hot dogs sold, which is inversely proportional, will be ...

  (7/8)·200 = 175 . . . hot dogs sold at the higher price

The vendor can expect to sell approximately 233 hot dogs if the price is increased by 55 cents.

To determine how many hot dogs the vendor can expect to sell if the price is increased by 55 cents, we can use the inverse proportionality relationship between the number of hot dogs sold and the price charged.

First, let's set up a proportion with the initial price and number of hot dogs sold:

$3.85 / 200 = (new price + $0.55) / x

Next, we can cross multiply and solve for x:

x = (200 * ($3.85 + $0.55)) / $3.85

Calculating this expression gives us a value of x ≈ 233.77.

Since the number of hot dogs sold must be a whole number, we round down to the nearest whole number, giving us an estimated value of 233 hot dogs.

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Answer:

5/4

Step-by-step explanation:

The diagonal of a box is found by the formula:

Diagonal = √(length^2 + width^2 + height^2)

Diagonal = √(13^2 + 12^2 + 30^2)

Diagonal = √(169 + 144 + 900)

Diagonal = √1213

Diagonal = 34.828

Rounded to nearest hundredth = 34.83 inches.

Answer:

34.83 in

Step-by-step explanation:

See attached

Answer:

56

Step-by-step explanation:

from observing the graph between x=-3 and x = 1.5, we can see that the highest most point of the graph (i.e the maximum) value occurs at x=-1.6, y = 56

Hence the maximum y-locatoin is 56

Answer:

B) 56

Step-by-step explanation:

Answer:

  y = -1/4

Step-by-step explanation:

  y/5 +3/10 = (y+2)/7

The LCD is 10·7 = 70. Multiplying the equation by 70 gives ...

  14y +21 = 10(y +2)

  14y +21 = 10y +20 . . . . eliminate parentheses

  4y + 21 = 20 . . . . subtract 10y

  4y = -1 . . . . . . . . . subtract 21

  y = -1/4 . . . . . . . . .divide by 4

_____

Check

  (-1/4)/5 +3/10 = (-1/4 +2)/7 . . . . . substitute for y

  -1/20 +6/20 = (7/4)/7 . . . simplify a bit, rewrite 3/10

  5/20 = 1/4 . . . . . . . . . . true

Answer:

Step-by-step explanation:

The equation for the y-axis is x = 0. Your shading is to the left of that, so the inequality will be x ≤ 0.

The blue line has a rise of 3 for a run of 4, so its slope is 3/4. It intercepts the y-axis at y=-5, so the slope-intercept equation for that line is y = 3/4x -5. Since the shading is below that solid line, the inequality is ...

  y ≤ 3/4x -5

ANSWER

The vertex is (1,-3)

EXPLANATION

The given parabola has equation:

[tex] {y}^{2} + 6y + 8x + 1 = 0[/tex]

We group the variables to obtain:

[tex]{y}^{2} + 6y = - 8x - 1 [/tex]

We complete the square to get,

[tex]{y}^{2} + 6y + {3}^{2} = - 8x - 1 + {3}^{2} [/tex]

[tex] {(y+ 3)}^{2} = - 8x +8[/tex]

[tex] {(y+ 3)}^{2} = - 8(x -1)[/tex]

The vertex is of the parabola is (1,-3)

Answer:

(-1,-3)

Step-by-step explanation:

Answer:

  52

Step-by-step explanation:

Put the numbers in the expression and do the arithmetic.

  (-8)² - |-12| = 64 -12 = 52

Answer:

  539

Step-by-step explanation:

The 007C requires the least significant two digits be in the range 35-39. In order for the 10-thousands digit to be zero, the sum of 1000 times the least digit of Genet's number and 2 times the hundreds digit must result in a sum with no thousands. About the only way to do that is to make the least digit 9 and the hundreds digit 5.

Then you have ...

  539 × 1002 = 540078 . . . . . ABC =548

Answer:

x=7

Step-by-step explanation:

Equate the angles 7x-7 and 4x+14 and solve:

7x-7 = 4x+14

7x-4x = 14+7

3x = 21

x = 7

Answer:

x = 7

Step-by-step explanation:

Alternate interior angles are equal. Alternate interior  angles look like these two angles.

7x - 7 = 4x + 14             Add 7 to both sides

7x - 7 + 7 = 4x + 14+7   Combine

7x = 4x + 21                  Subract 4x from both sides

7x-4x = 4x - 4x + 21      Combine

3x = 21                          Divide by 3

3x/3 = 21/3                    Do the division

x = 7  

Answer:

The quotient is: 3x-7

The remainder is: 0

Step-by-step explanation:

We need to divide 9x^2 - 18x - 7 ÷ (3x + 1)

The Division is shown in the figure attached.

The quotient is: 3x-7

The remainder is: 0

Answer:

i think it is 5:17

Step-by-step explanation:

length=50

perimeter=170

the highest factor of 50 and 170 is 10 so the answer will be 5:17

hopefully this made sense

Answer:

3

Step-by-step explanation:

2/3 =2/9  m

2/3 =2m/9                         note: 2/9 m is the same as 2/9 *m/1=2m/9

cross multiply

18=6m

so m=3

[tex]\text{Hey there!}[/tex]

[tex]\text{In order for you to solve for the value of m you have to flip the equation around!}[/tex]

[tex]\text{Here is what I meant}\downarrow[/tex]

[tex]\bf{\frac{2}{9}m=\frac{2}{3}}[/tex]

[tex]\text{Then for your second step, you have to MULTIPLY by\ }\frac{9}{2}\text{\ on your sides}[/tex]

[tex]\text{Here's what I meant}\downarrow[/tex]

[tex]\bf{\frac{9}{2}(\frac{2}{9})m=\frac{9}{2}(\frac{2}{3})}[/tex]

[tex]\text{Cancel out:}\frac{9}{2}(\frac{2}{9}m)\text{\ because it equals to 1}[/tex]

[tex]\text{Keep: \ }\frac{9}{2}(\frac{2}{3})\text{\ because it helps us solve for the value of m}[/tex]

[tex]\text{If you solved the kept one correctly, you have your answer}[/tex]

[tex]\boxed{\boxed{\text{Answer: C. 3}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

[tex]y-12=-\frac{3}{4}(x+4)[/tex]

Step-by-step explanation:

we know that

The equation of the line into slope point form is equal to

[tex]y-y1=m(x-x1)[/tex]

In this problem we have

[tex](x1,y1)=(-4,12)[/tex]

[tex]m=-\frac{3}{4}[/tex]

substitute

[tex]y-12=-\frac{3}{4}(x+4)[/tex]

Answer:

The answer is (D): 2 h 52 min

Step-by-step explanation:

write these equations separately as functions:

A(x)=15+0.02m

B(x)=4.69+0.08m

Since we want to find when they are equal, set them equal to each other:

15+0.02m=4.69+0.08m

simplifying this equation gives

10.31+0.02m=0.08m

subtract 0.02m from both sides

10.31=0.06m

divide both sides by 0.06

m=171.833 etc approximately equals 172 minutes

172 min/60=

2 hours and 52 min

Hope this helps!

Answer:

  2 h 52 min

Step-by-step explanation:

Let m represent the number of minutes that will make the plans have equal cost. Equating the two plan costs, we have ...

  15.00 + 0.02m = 4.69 + 0.08m

  10.31 = 0.06 m . . . . . subtract 4.69+0.02m

  10.31/0.06 = m = 171.8333... ≈ 172 . . . . minutes at equal cost

There are 60 minutes in an hour, so ...

  172 minutes = 120 minutes + 52 minutes = 2 hours + 52 minutes

Plan A will cost the same as Plan B for 2 h 52 min of usage.

For this case we have that the area of the kite is formed by the ara of two triangles with the same base of[tex]9 + 9 = 18[/tex] meters and one with height 9 meters and another with height 6 meters.

So:

[tex]A = \frac {1} {2} b * h + \frac {1} {2} b * h\\A = \frac {1} {2} 18 * 9 + \frac {1} {2} 18 * 6\\A = \frac {1} {2} 162+ \frac {1} {2} 108\\A = 81 + 54\\A = 135 \ m ^ 2[/tex]

ANswer:

Option B

Answer:

135 m^2

Step-by-step explanation:

Gradpoint approved, good luck guys.

[tex]\displaystyle\sum_{n=2}^{91}(3n+8)=\sum_{n=1}^{91}(3n+8)-a_1=(*)\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\a_1=3\cdot1+8=11\\n=91\\a_n=3n+8\\d=a_n-a_{n-1}\\a_2=3\cdot2+8=14\\d=14-11=3\\a_{91}=11+(91-1)\cdot 3=11+90\cdot3=281\\\\S_{91}=\dfrac{11+281}{2}\cdot91=146\cdot91=13286\\\\(*)=13286-11=\boxed{13275}[/tex]

Answer:

-7 > v OR vice-versa [v < -7]

Step-by-step explanation:

Combine like-terms [-5v > 35], then divide by -5.

NOTE: Since you are dividing by a negative, reverse the sign.

Answer:

[tex]{\huge \boxed{V<-7}}[/tex]

Step-by-step explanation:

Add similar into elements. Add the numbers from left to right.

-3v-2v=-5v

Simplify.

-5v>35

Multiply by -1 from both sides of equation.

(-5v)(-1)<35(-1)

Simplify.

35(-1)=-35

5v<-35

Divide by 5 from both sides of equation.

5v/5<-35/5

Simplify, to find the answer.

-35/5=-7

v<-7 is the correct answer.

I hope this helps you, and have a wonderful day!

For this case we have to define trigonometric relations of rectangular triangles that, the cosine of an angle is given by the leg adjacent to the angle on the hypotenuse of the triangle. That is, according to the data of the figure we have:

[tex]Cos (45) = \frac {6} {h}[/tex]

Where:

h: It's the hypotenuse

So:

[tex]\frac {\sqrt {2}} {2} = \frac {6} {h}[/tex]

We cleared h:

[tex]h \sqrt {2} = 6 * 2\\h \sqrt {2} = 12\\h = \frac {12} {\sqrt {2}}[/tex]

We rationalize:

[tex]h = \frac {12 \sqrt {2}} {(\sqrt {2}) ^ 2}\\h = \frac {12 \sqrt {2}} {2}\\h = 6 \sqrt {2}[/tex]

Answer:

Option C

ANSWER

[tex] 6\sqrt{2} \: units[/tex]

EXPLANATION

This is an isosceles right triangle.

The two legs of an isosceles right triangle are equal, hence each of them is 6 units each.

Let h be the hypotenuse, then from the Pythagoras Theorem,

[tex] {h}^{2} = {6}^{2} + {6}^{2} [/tex]

[tex]{h}^{2} = {6}^{2} \times 2[/tex]

Take square root of both sides;

[tex]{h} = \sqrt{ {6}^{2} \times 2 } [/tex]

[tex]{h}= \sqrt{ {6}^{2} } \times \sqrt{2} [/tex]

[tex]{h} = 6\sqrt{2} \: units[/tex]

The correct answer is C

Answer:

Step-by-step explanation:

The area of a triangle is:

A=05*b*h

b= base = x

h = height = x-12

A = (1/2)(x)(x-12)

Answer:

When a number is halfway between two multiples of one thousand, round to "the larger multiple."

For example: If you have 852, the nearest thousand is 1000. So it should be round to 1000.

Answer:

rounded to the larger multiple.

Answer: 2 friends/1 pair

Step-by-step explanation:

Mainly because if you do the math, a pair of friends is 2. Knowing that there is 2 short straws (Which if those are the ones that are chosen you get to go), and 4 long straws. Only 2 friends are going to draw the short straws.

Hope this helped :)

Answer:

15 possible pairs of friends could be chosen in this way.

Step-by-step explanation:

Given : You have 6 friends who want to go to a concert with you, but you only have room in your car for 2 of them. To avoid accusations of favoritism, you have your friends draw straws: There are 4 long and 2 short straws, and the short straws win.

To find : How many possible pairs of friends could be chosen in this way?  

Solution :

Total number of friends = 6

The space in the car is for 2 person.

Since, the order doesn't matter we have to choose 2 people out of 6 so we apply combination.

As There are 4 long and 2 short straws, and the short straws win.

i.e. that 2 friends were chosen.

So, Possible ways to find the pairs of friends is [tex]^6C_2[/tex]

Solving,

[tex]^6C_2=\frac{6!}{2!(6-2)!}[/tex]

[tex]^6C_2=\frac{6\times 5\times 4!}{2\times 1\times 4!}[/tex]

[tex]^6C_2=3\times 5[/tex]

[tex]^6C_2=15[/tex]

Therefore, 15 possible pairs of friends could be chosen in this way.

Andy gets 222 minutes of extra computer time for every math fact he completes. To find out how many extra minutes he got in a specific month, multiply the number of math facts he completed in that month by 222.

To find out how many extra minutes Andy got in February, we need to know how many math facts he completed in February. Let's say he completed x math facts in February. Since Andy gets 222 minutes of extra computer time for every math fact he completes, the total extra minutes he got in February can be calculated by multiplying the number of math facts he completed in February (x) by 222.

So, the total extra minutes Andy got in February is 222x.

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Answer:

1/5; 20%

Step-by-step explanation:

If she is only choosing 2 shirts, and they both have to be white, the probability of choosing those 2 white shirts out of 10 white shirts is 2/10 or, equivalently, 1/5.  In percent form, this is 20%

The probability of a woman randomly choosing two white shirts from a collection of 14 shirts (10 white and 4 red) is approximately 49%, derived through the process of combinations calculation in the field of probability.

The question relates to the field of probability in mathematics. To calculate her probability of selecting two white shirts, we first need to understand the number of total possible outcomes when she is selecting 2 out of the 14 shirts. This is represented by the combination formula C(n, r) = n! / r!(n-r)!, where n is the total number of items to choose from and r is the number of items to choose. Using this combination formula, we find that there are C(14, 2) = 91 total possible combinations of shirts she could end up with.

Next, we need to find the number of combinations that involve her picking 2 white shirts. As there are 10 white shirts, this is represented by C(10, 2) = 45. So, the probability of her taking two white shirts is then the number of desired outcomes divided by the total number of outcomes, or 45 / 91 which simplifies to approximately 0.4945 or 49% when rounded to the nearest whole percent.

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Answer:

tanB=b/a

Step-by-step explanation: