Ancient paintings were found on cave walls in South America. The Carbon-14 in the paintings was measured and was found to be 19% of the original weight. How old were the paintings?

A. 3,839
B. 9,239
C. 13,839
D. 19,239

Answer:

False

Step-by-step explanation:

If two spheres have the same center but different radii, they are NOT called concentric spheres. They would be called congruent circles if they have the same center but different radii.

Answer:

false

Step-by-step explanation:

Answer:

1 plant

Step-by-step explanation:

The T.Rex dinosaur eats ten twelffths of a plant and later eats two twelfths of a plant. In total, the T.Rex dinosaur ate:

[tex]\frac{10}{12} + \frac{2}{12} =\frac{12}{12}=1[/tex]

Therefore, the dinsaur in total ate one entire plant.

It's better to solve the problem by using fractions instead of decimals. If we had used decimals the response would be the following:

[tex]0.833333+0.166666=0.999999[/tex] which can be rounded to 1.

Answer:

A(2,2)

Step-by-step explanation:

Let the vertex A has coordinates [tex](x_A,y_A)[/tex]

Vectors AB and AB' are perpendicular, then

[tex]\overrightarrow {AB}=(2-x_A,6-y_A)\\ \\\overrightarrow {AB'}=(-2-x_A,2-y_A)\\ \\\overrightarrow {AB}\perp\overrightarrow {AB'}\Rightarrow \overrightarrow {AB}\cdot \overrightarrow {AB'}=0\Rightarrow (2-x_A)(-2-x_A)+(6-y_A)(2-y_A)=0[/tex]

Vectors AC and AC' are perpendicular, then

[tex]\overrightarrow {AC}=(4-x_A,3-y_A)\\ \\\overrightarrow {AC'}=(1-x_A,4-y_A)\\ \\\overrightarrow {AC}\perp\overrightarrow {AC'}\Rightarrow \overrightarrow {AC}\cdot \overrightarrow {AC'}=0\Rightarrow (4-x_A)(1-x_A)+(3-y_A)(4-y_A)=0[/tex]

Now, solve the system of two equations:

[tex]\left\{\begin{array}{l}(2-x_A)(-2-x_A)+(6-y_A)(2-y_A)=0\\ \\(4-x_A)(1-x_A)+(3-y_A)(4-y_A)=0\end{array}\right.\\ \\\left\{\begin{array}{l}-4-2x_A+2x_A+x_A^2+12-6y_A-2y_A+y^2_A=0\\ \\4-4x_A-x_A+x_A^2+12-3y_A-4y_A+y_A^2=0\end{array}\right.\\ \\\left\{\begin{array}{l}x_A^2+y_A^2-8y_A+8=0\\ \\x_A^2+y_A^2-5x_A-7y_A+16=0\end{array}\right.[/tex]

Subtract these two equations:

[tex]5x_A-y_A-8=0\Rightarrow y_A=5x_A-8[/tex]

Substitute it into the first equation:

[tex]x_A^2+(5x_A-8)^2-8(5x_A-8)+8=0\\ \\x_A^2+25x_A^2-80x_A+64-40x_A+64+8=0\\ \\26x_A^2-120x_A+136=0\\ \\13x_A^2-60x_A+68=0\\ \\D=(-60)^2-4\cdot 13\cdot 68=3600-3536=64\\ \\x_{A_{1,2}}=\dfrac{60\pm8}{2\cdot 13}=\dfrac{34}{13},2[/tex]

Then

[tex]y_{A_{1,2}}=5\cdot \dfrac{34}{13}-8 \text{ or } 5\cdot 2-8\\ \\=\dfrac{66}{13}\text{ or } 2[/tex]

Rotation by 90° counterclockwise about A(2,2) gives image points B' and C' (see attached diagram)

Answer:

b. 5/7

Step-by-step explanation:

The line goes through the points (0, 0) and (7, 5).  Let's use those points in the slope formula:

[tex]m=\frac{5-0}{7-0}=\frac{5}{7}[/tex]

The slope of that line is 5/7

The slope of the given line is 5/7

In the given graph, the line passes through the center (0, 0) and (7, 5)

So the slope will be   [tex]\frac{5-0}{7-0} = \frac{5}{7}[/tex]

So option B is correct

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Answer:

The number is 15.

Step-by-step explanation:

If you look closely, the sum of any two adjacent boxes in the bottom row gives the number in the top row. For example, the sum of the first two boxes 27 and 18 gives the number 45.

27+18 = 45

Similarly,

21+x = 36 (Third and fourth boxes in bottom row)

Solving, we get x=15.

We can confirm this by checking with the last two boxes.

x+13 = 28

x=15

So, the answer is 15.

Please mark Brainliest if this helps!

Explanation:

A fraction of an hour costs the same as an hour.

  actual time ⇒ time charged ⇒ cost of parking

  5 min ⇒ 1 hour ⇒ $3

  1 hour ⇒ 1 hour ⇒ $3

  1 hour 50 min ⇒ 2 hours ⇒ $6

  2 hours ⇒ 2 hours ⇒ $6

  2 hours 1 min ⇒ 3 hours ⇒ $9

  3 1/2 hours ⇒ 4 hours ⇒ $12

Answer:

86 because 180 subtract 94 is 86

Answer:

The correct answer is option D. 94 °

Step-by-step explanation:

From the figure we get,

l║ m ║ o and  n║ p

To find the measure of <16

It is given that, m<1 = 94°

m<1 + m<4 = 180  [ Same side exterior angles of parallel lines are supplementary]

m<4 = 180 - m<1 = 180 - 94 = 86°

Similarly, m<4 + m<16 = 180

m<16 = 180 - m<4 = 180 -  86 = 94°

The correct answer is option D. 94 °

Answer:

Step-by-step explanation:

If we let a, b, c represent the numbers of type-1, type-2, and type-3 cabinets produced in the first week, respectively, we can write three equations in these unknowns:

It can be convenient to let a machine solver find the solution to this set of equations. Most graphing calculators can handle it, along with several web sites.

__

Solving by hand, we can subtract the second equation from twice the first. This gives ...

  2(a +b +c) -(a +2b -c) - 2(110) -(10)

  a +3c = 210 . . . . simplify

Subtracting this from 3 times the third equation gives ...

  3(3a +c) -(a +3c) = 3(110) -(210)

  8a = 120 . . . . . simplify

  a = 15 . . . . . . . divide by 8

Using this in the third equation of the original set, we have ...

  3·15 +c = 110

  c = 65 . . . . . . subtract 45

Then, in the first equation, we get ...

  15 + b + 65 = 110

  b = 30 . . . . . . . subtract 80

The solution is (type-1, type-2, type-3) = (15, 30, 65) for the first week.

The problem provides a set of linear equations. Solving this system by substitution or elimination method will give the number of cabinets of each type produced each week. The equations are formed based on the conditions provided in the problem.

From the information provided, we can use a system of equations to solve this. Let's denote the number of type-1 cabinets made in the first week as x , the number of type-2 cabinets as y, and the number of type-3 cabinets as z. The first condition in the problem gives us the equation x + 2y = z + 10. The total number of cabinets produced in each week is 110, so we get the equation x + y + z = 110 for the first week. From the second week's conditions, we know that no type-2 cabinets were made (y=0), the number of type-3 cabinets was the same (z=z) and the number of type-1 cabinets was three times as much as the first week (x=3x), this means 3x + 0 + z = 110.. Solving this system of equations will provide the number of cabinets produced for each type.

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Final answer:

Chung has a ratio of 6 trucks to 5 cars (6:5), and Brian has a ratio of 4 trucks to 5 cars (4:5). Chung has a higher ratio of trucks to cars compared to Brian.

Explanation:

To compare the ratios of trucks to cars for Chung and Brian, we simply write down the number of trucks and cars each has and form a ratio for each. For Chung, the ratio of trucks to cars is 6 trucks to 5 cars, which can be written as 6:5 or ⅓. For Brian, the ratio of trucks to cars is 4 trucks to 5 cars, or 4:5 or ⅔.

Now, by comparing these two ratios, we see that Chung has a higher ratio of trucks to cars (6:5) compared to Brian (4:5), which means Chung has more trucks relative to cars in his toy box than Brian does.

To compare Chung's and Brian's ratios of trucks to cars, we have to calculate each ratio and then compare them.
**Chung's Ratio:**
Chung has 6 trucks and 5 cars. The ratio of trucks to cars for Chung is the number of trucks divided by the number of cars.
Chung's trucks to cars ratio = Number of trucks / Number of cars
                            = 6 / 5                    
**Brian's Ratio:**
Brian has 4 trucks and 5 cars. The ratio of trucks to cars for Brian is the number of trucks divided by the number of cars.
Brian's trucks to cars ratio = Number of trucks / Number of cars
                            = 4 / 5
Both ratios are to be compared now.
**Comparing Ratios:**
Chung's ratio is 6/5, which is 1.2 when converted into a decimal.
Brian's ratio is 4/5, which is 0.8 when converted into a decimal.
Since 1.2 (Chung's ratio) is greater than 0.8 (Brian's ratio), we can conclude that Chung has a higher ratio of trucks to cars compared to Brian.
Therefore, the correct comparison of their ratios is: "Chung has a higher ratio of trucks to cars than Brian."

Answer:

  110

Step-by-step explanation:

z is apparently 10 times x.

10 times 11 is 110.

Answer:

  y = 2/3x + 5/3

Step-by-step explanation:

The slope of the line is ...

  slope = (change in y)/(change in x) = (3-1)/(2-(-1)) = 2/3

Then the point-slope form of the desired line can be written ...

  y = m(x -h) +k . . . . . slope m through point (h, k)

  y = 2/3(x +1) +1 . . . . slope 2/3 through point (-1, 1)

  y = 2/3x + 5/3 . . . . . . simplify to slope-intercept form

The equation that describes a line through points (-1, 1) and (2, 3) in slope-intercept form is y = 2/3x + 5/3, determined by calculating the slope and y-intercept.

The question asks to find the equation in slope-intercept form that describes a line through (-1, 1) and (2, 3). In order to do this, we need to find the slope and y-intercept of the line.

The slope of the line (m) can be determined by using the formula m = [tex](y_2 - y_1) / (x_2 - x_1)[/tex]. Inserting the given points into this formula gives: m = (3 - 1) / (2 - (-1)) = 2 / 3 = 2/3.

To find the y-intercept (b), we can use the point-slope form of the equation and solve for 'b', y = mx + b, insert the slope we found and one of the given points, let's utilise (-1, 1): 1 = 2/3*(-1) + b, which simplifies to b = 5/3.

So, the equation of the straight line in slope-intercept form is y = 2/3x + 5/3.

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Answer:

Step-by-step explanation:

They are all true

the answer is a

a square should have 4 lines or sides the same length any longer or shorter would make it a rectangle

Answer:

B 6.3

Step-by-step explanation:

r = 8

l = 2*3.14*r

l = 50.24

s=l/360*45

s≈6.3

For this case we have that by definition, the arc length is given by:

[tex]Al = 2 \pi * r *\frac {a} {360}[/tex]

Where:

r: It's the radio

a: It is the angle of the sector

Then, according to the data we have:

[tex]Al = 2 \pi * 8 * \frac {45} {360}\\Al = 2 * 3.14 * 8 * \frac {45} {360}\\Al = 50.24 * \frac {45} {360}\\Al = 6.28[/tex]

Rounding we have 6.3in

Answer:

Option B

Answer: First option is correct.

Step-by-step explanation:

Since we have given that

4.05, 1.35, 0.45, 0.15, ...

Since it is a geometric sequence.

So, here, a = 4.05

r = [tex]\dfrac{a_2}{a_1}=\dfrac{1.35}{4.05}=0.33[/tex]

So, we know the formula for nth term in geometric sequence.

[tex]a_n=ar^{n-1}\\\\a_n=4.05(0.3)^{n-1}[/tex]

Hence, First option is correct.

Answer:

an=4.05^(1/3)n−1

Step-by-step explanation:

Answer:

Option C.) Geometric, common ratio = 3

Step-by-step explanation:

we know that

In a Geometric Sequence each term is found by multiplying the previous term by a constant

The constant is called the common ratio

In this problem we have

For x=1, f(1)=3

For x=2, f(2)=9

For x=3, f(3)=27

For x=4, f(4)=81

so

f(2)/f(1)=9/3=3 -----> f(2)=3*f(1)

f(3)/f(2)=27/9=3 -----> f(3)=3*f(2)

f(4)/f(3)=81/27=3 -----> f(4)=3*f(3)

f(n+1)/f(n)=3 -----> f(n+1)=3*f(n)

therefore

This is a Geometric sequence and the common ratio is equal to 3

The sequence is a geometric sequence with a common ratio of 3.

The sequence given is a geometric sequence. A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In this case, the common ratio can be found by dividing a term in the sequence by its preceding term. For example, if we divide the second term (9) by the first term (3), we get 3. The same goes for the rest of the terms in the sequence. Therefore, the correct answer is Option C: Geometric, common ratio = 3.

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Answer: 0.8025

Step-by-step explanation:

Given : The number of defective calculators : 17

The number of calculators are not defective : 37

Total calculators : 37+17=54

The probability of the calculators are defective : [tex]\dfrac{17}{54}=\dfrac{1}{3}[/tex]

Binomial distribution formula :-

[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex], where P(x) is the probability of success in x trials, n is total trials and p is the probability of success for one trial.

The probability that at least one of the calculators is defective is given by :-

[tex]P(x\geq1)=1-P(0)\\\=1-(^4C_0(\dfrac{1}{3})^0(1-\dfrac{1}{3})^4)\\\\=1-(\dfrac{2}{3})^4=0.80246913\approx0.8025[/tex]

Answer:

b. Statistic

Step-by-step explanation:

b. Statistic because the value is a numerical measurement describing a characteristic of a sample.

Answer:

Option b

Step-by-step explanation:

Given that a sample of employees is selected and it is found that 55 % own a vehicle.

Before we answer the questions let us understand the difference between a parameter and a statistic.

Parameters are numbers that summarizes the data of a population.  But statistics are numbers that summarizes the data of a sample.

Sample is a subset of population i.e. a small portion of the whole population is sample.

Here 55% is the proportion of the sample of employees.  Since this is a number summarizing the data about a sample this is called statistic.

b. Statistic because the value is a numerical measurement describing a characteristic of a sample.

Answer:

The slope is 2

Step-by-step explanation:

The slope of a line passing through two points is given by:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

which is the difference between the y-coordinates of two points divided by the difference between x-coordinates of two points

We are given:

Difference between x-coordinates = 3

Difference between y-coordinates = 6

So,

[tex]m = \frac{6}{3}\\=2[/tex]

The slope of the line that passes through these points is 2 ..

Answer:

765.

Step-by-step explanation:

Sum of n terms = a1 (r^n - 1) / (r - 1) where a1 = the first term and r = the common ratio.

Here r = 6/3 = 2 and  a1 = 3.

Sum of 8 terms = 3 * ( 2^8 - 1) / 2 -1)

= 3 * 255

= 765 (answer).

Hey! I just answered this on plato. the answer is that it includes negative factors, which makes not all solutions viable.

Answer:

Look at the attachment

Step-by-step explanation:

First we need to find out the equations that will represent each inequality:

For the bacteria:

This is an exponential growth equation, the formula is simple:

y≤[tex]n*(1+r)^{x}[/tex]  where n is the starting point of the sample, r is the rate and x is the variable dependent on time so:

y≤[tex]100*(1+0.062)^{x}[/tex]

y≤[tex]100*(1.062)^{x}[/tex]

For the container:

This is a line equation, following the formula:

y<mx+b where m is the slope or growing rate (100 more per hour), and b is the starting point (300 bacteria)

y< 100x+300

The graph will be like is showed in the attachment, and the solution is the intersecting area to the right of both functions, since they are trying to find out if the inhibitor works, the rate of growth will be equal or smaller than 6.2% thus closing in to 100 bacterias as a constant in time if it works.

Answer:

2 complex conjugates

Step-by-step explanation:

The discriminate is the part of the quadratic formula that is under the radical sign.  If the discriminate is negative, that means that the solutions, both of them, are complex conjugates, aka imaginary solutions.

For this case we have that by definition, the discriminant of an equation is given by:

[tex]D = b ^ 2-4 (a) (c)[/tex]

We have the following cases:

[tex]D> 0:[/tex] Two different real roots

[tex]D = 0:[/tex]Two equal real roots

[tex]D <0:[/tex] Two different complex roots

In this case we have to:

[tex]D = -6[/tex], [tex]-6 <0[/tex] , Then we have two different complex roots.

Answer:

OPTION B

Answer:

x = (C-By)/A

Step-by-step explanation:

Ax + By = C

Subtract By from each side

Ax + By-By = C-By

Ax = C -By

Divide each side by A

Ax/A = (C-By)/A

x = (C-By)/A

[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{3})~\hspace{10em} slope = m\implies -4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-3=-4[x-(-4)]\implies y-3=-4(x+4)[/tex]

[tex]\bf y-3=-4x-16\implies y=-4x-13\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Answer: The answer would be 333

Step-by-step explanation: Hope this was helpful

To make at least $5,000, Anna must sell a minimum of 200 at-the-door tickets priced at $25 each. This is the minimum required, but the venue's capacity allows for selling up to 400 tickets to potentially exceed the fundraising goal.

The question asks us to calculate the minimum number of at-the-door tickets Anna needs to sell to meet the fundraiser target of at least $5,000, given the constraints of the venue capacity and the ticket prices. This can be solved by first identifying the total amount needed to be raised and then calculating the number of at-the-door tickets needed if no pre-sale tickets are sold.

Since at-the-door tickets sell for $25 each, we divide the total amount Anna wants to raise ($5,000) by the price of each at-the-door ticket:

$5,000 ÷ $25 = 200 tickets

This means Anna will have to sell at least 200 at-the-door tickets to raise $5,000. However, the venue limits the capacity to 400 people, and it is not specified how many pre-sale tickets are sold. To ensure reaching the target, assuming no pre-sale tickets are sold, Anna should aim to sell all 400 tickets at the door. Selling any fewer at the door would require pre-sale tickets to make up the difference to reach the $5,000 target.

Therefore, the minimum number of at-the-door tickets Anna needs to sell to reach the $5,000 goal is 200, although to fully utilize the venue's capacity and potentially exceed the target, she can sell up to 400 tickets at the door.

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Answer:

  [tex]8a^6b^{-1}[/tex]

Step-by-step explanation:

This is math that involves the properties of exponents. For this problem, three rules are used:

[tex](ab)^c=a^cb^c\\\\(a^b)^c=a^{bc}\\\\a^{-b}=\dfrac{1}{a^b}[/tex]

So, your expression can be written as ...

[tex]\dfrac{(2a^2)^3}{b}=\dfrac{2^3(a^2)^3}{b^1}=8a^6b^{-1}[/tex]

The mathematics involved is about exponential notation and algebraic expressions. The expression (2a^2)^3/b simplifies to 8a^6b^-1.

The math involved here is known as exponential notation and algebraic expressions. In the given expression (2a^2)^3/b, the power rule of exponents can be applied, where to simplify the power of a power, we multiply the exponents. Therefore, (2a^2)^3 becomes 2^3 * (a^2)^3 which equals 8a^6. The expression then becomes 8a^6/b. This can be rewritten as 8a^6b^-1 (since anything divided by b can be written as multiplied by b^-1) adhering to the ca^pb^q format. So, the equivalent form of the given expression is 8a^6b^-1.

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Answer:

The probability that you will choose a consonant and then a vowel is 0.21....

Step-by-step explanation:

Total no of tiles = 28 + 12 = 40

First you should choose a consonant = 12/40

Second you should choose a vowel = 28/40

So the probability you choose a consonant and then a vowel:

= 12/40 * 28/40

=336/1600

=0.21

So the probability that you will choose a consonant and then a vowel is 0.21....

Answer:

4.

Step-by-step explanation:

The smallest number of hot dogs packages and hot dog buns that has the same amount of is the least common multiple between 6 and 8.

6 = 3*2

8 = [tex]2^{3}[/tex]

So, the least common multiple is the product of each multiple with the biggest exponent, that is [tex]2^{3}*3=24[/tex]. Then, Xanthia has to buy 4 hot dog packages to have 24 hotdogs and 24 hotdog buns.

To solve this problem, we first find the least common multiple (LCM) of 6 and 8. 6=2*3 and 8=2^3, so their LCM is 2^3*3=24. Therefore, Xanthia can buy 24÷6=4 hot dog packages and 24÷8=3 hot dog bun packages to have an equal number of hot dogs and hot dog buns. So you have an answer of 4.

Please give me brainliest, I'm trying to get to a higher rank... You don't have to tho, I respect that someone else deserves it sometimes.

Answer:

  A. 25°

Step-by-step explanation:

The angles on either side of the bisector are congruent, so ...

  (3x -5)° = (x +15)°

  2x = 20 . . . . . . . . . . . . divide by °; add 5-x

  x = 10 . . . . . . . . . . . . . .divide by 2

Substitute this result into the expression for the angle measure:

m∠BAC = (3·10 -5)° = 25°

Answer: 30

Step-by-step explanation:

Let x be the number of Beetles.

Then , the number of Acuras = [tex]\dfrac{1}{2}x[/tex]

Also, The number of Camrys is 80% of the number of Acuras and Beetles together.

Thus , the number of Camrys =[tex]0.8(x+\dfrac{1}{2}x)[/tex]

Now, the total number of cars in parking lot will be :-

[tex]x+\dfrac{1}{2}x+0.8(x+\dfrac{1}{2}x)=81\\\\\Rightarrow\ \dfrac{3x}{2}+0.8(\dfrac{3x}{2})=81\\\\\Rightarrow\ \dfrac{3x+2.4x}{2}=81\\\\\Rightarrow\ 5.4x=2\times81\\\\\Rightarrow\ x=\dfrac{162}{5.4}=30[/tex]

Hence, there are 30 Beetles.

Answer:

30 of the cars

Step-by-step explanation:

I just did the question on Alcumus.

Hope this helped! :)

The pattern in the sequence 9, 3, 1, 1/3 involves each number being a third of the previous number. Following this rule, the next number after 1/3, obtained by dividing by 3, is 1/9.

To determine the next number in the sequence 9, 3, 1, 1/3, we need to identify the pattern or rule that is being followed. Observing the sequence, each subsequent number appears to be a third of the previous number. The first number is 9, and dividing by 3 gives us 3. Dividing the second number, 3, by 3 gives us 1.

Similarly, dividing the third number, 1, by 3 gives us 1/3. Following this logic, to find the next number in the sequence, we divide 1/3 by 3.

Using the arithmetic of division with fractions, we have (1/3) ÷ 3 = (1/3) ÷ (3/1) = 1/9. Therefore, the next number in the sequence is 1/9. We can assume that the rule being applied in this sequence is to divide each number by 3 to find the next number, which aligns with the mathematical pattern identification techniques commonly used.

The next number in the sequence is 1/9.

To find the next number in the sequence 9, 3, 1, 1/3, we need to identify the pattern. This sequence is a geometric sequence where each term is obtained by multiplying the previous term by a common ratio.

Step-by-step:

To find the next term, we continue this pattern:
1/3× (1/3) = 1/9