An archeologist has found a fossil in which 35% of its carbon-14 remains. Hold old is the fossil?

Answer:

50%

Step-by-step explanation:

The total number of marbles is 7 + 3 + 2 + 8 = 20

Blue or red means that the total on any one draw is 7 + 3 = 10

You would expect to draw blue or red 1/2 the time.

Out of 150 throws, you would get 1/2 * 150 which is 75 but that is not what you are asked.

% = (1/2 ) * 100  = 50% of the time

Answer:

TRUE

Step-by-step explanation:

The well known trigonometry identity states that cot^2(x) + 1 = csc^2(x), rearrangin the equation we have that cot^2(x) - csc^2(x) = -1, which is exactly the expression in the statement. Therefore, the expression is TRUE.

Answer:

A. 22.5° AND D. 22°30’

Step-by-step explanation:

First of all, it's the correct answer on ap*x

To convert π/8 to degrees, replace π with 180°.

π/8 = 180°/8 = 22.5° (A)

Convert 22.5° to degrees minutes seconds

22.5° = 22°30’ (D)

To convert an angle from radians to degrees, multiply by 180/π. The angle measuring π/8 radians is equal to 22.5°.

To convert an angle from radians to degrees, we use the conversion factor 180/π. So, an angle of π/8 radians is equal to:

Therefore, the angle measuring π/8 radians is equal to 22.5°.

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Answer:its 12

Step-by-step explanation:

The number can each term of the equation be multiplied by to eliminate the fractions before solving is 12, the correct option is D.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that;

Equation 6 – x + = x + 5

Now,

the least common multiple of 2 and 3, which are the denominators of the fractions in the equation. Multiplying each term by 12 will clear the fractions and result in an equivalent equation without fractions. For example: 12(6 - x + ) = 12(x + 5) 2 3 Simplifying, we get: 72 - 12x + 4 = 12x + 60. This is an equation without fractions that can be solved for x.

Therefore, by the given equation the answer will be 12.

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Here it is: 0.156

That is the decimal representation of 156/1000

.156.

If they are “thousandths” then you know there is 3 decimal places.

Hope this helps!

Answer:

B. Domain: -5/2

Range: 1/2

Step-by-step explanation:

If you plug -5/2 for x, it becomes no solution due to the zero in the denominator.

If you plug 1/2 for y and let your calculator do its thing, it becomes no solution.

Because these values cannot be solved for in the equation, they are excluded from the domain and range.

Edit: I got it correct on the Unit Review on edge.

The domain and range values that are excluded from the function given as  f ( x ) = ( x + 3 ) / ( 2x + 5 ) are x = -5/2 and y = 0

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

The function f(x) = (x + 3)/(2x + 5) has certain values that are excluded from its domain and range.

The function f(x) is defined for all real numbers except for the values of x that make the denominator (2x + 5) equal to zero.

Therefore, the values of x that are excluded from the domain of f(x) are those that satisfy the equation 2x + 5 = 0.

2x + 5 = 0

2x = -5

x = -5/2

The range of f(x) is all real numbers except for zero (0), because it is never equal to zero.

Hence , the values excluded from the domain of f(x) are x = -5/2 and the values excluded from the range of f(x) are y = 0

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Answer:

C

Step-by-step explanation:

The easiest way to determine this is to realize that time is the independent variable (n) and temperature is the dependent variable (a).

From the table, we can plug in the two points (n) into n of each equation and see if that equals the temperature values (a).

A little thinking would get us to plug the numbers in C first.

[tex]a(n)=46-(n-1)*4\\46-(5-1)*4=30[/tex]

Works!!

Now, second number:

[tex]a(n)=46-(n-1)*4\\46-(6-1)*4=26[/tex]

Works!!

Hence, C is the correct answer.

Answer:

[tex]a(n)=46-(n-1) \times 4[/tex]

Step-by-step explanation:

It's important to know that the graph is showing a linear function, which means its equation cannot be exponential. So, choices A and B are not correct here.

To find the correct equation, we could find the slope first with the following formula and the two given points

[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }\\ m=\frac{26-30}{6-5}=4[/tex]

Now, we use the point-slope formula to find the equation

[tex]y-y_{1} =m(x-x_{1} )\\y-30=4(x-5)\\y=4x-20+30\\y=4x+10[/tex]

Notice that choice C has the same coefficient of 4, which is the slope of the line. Therefore, that's the right answer.

Let's prove it for [tex]n=6[/tex]

[tex]a(n)=46-(n-1) \times 4\\a(6)=46-(6-1) \times 4=46-20=26[/tex]

As the table shows.

Therefore, choice C is correct.

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

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

We have the points (1, 5) and (1, -3).

Substitute:

[tex]m=\dfrav{-3-5}{1-1}=\dfrac{-8}{0}\ \bold{!}[/tex]

Dividing by zero is not possible.

The slope does not exist.

Conclusion: this is a vertical line with the equation x = a

From the points

(1, 5) → x = 1, y = 5

(1, -3) → x = 1, y = -3

we have the equation x = 1.

Answer:

R(p) = -4p^2 + 300p when p=20.

R(p) = -4(20)^2 + 300(20)

R(p) = -1600 + 6000

R(p) = 4400

The mass when p=20 years is 4400.

Answer:

AC ≈ 10.5 cm (1 dec. place )

Step-by-step explanation:

Given

tan55° = [tex]\frac{15}{b}[/tex]

Multiply both sides by b

b × tan55° = 15 ( divide both sides by tan55° )

AC = b = [tex]\frac{15}{tan55}[/tex] ≈ 10.5 cm

That's too easy...

[tex]y=x+4\\x=y-4[/tex]

Answer:

total cost = 150 + 25n

Step-by-step explanation:

total cost = flat fee + cost per person* number of people

total cost = 150 + 25n

Answer:

Step-by-step explanation:

a - number of lawn that Tim needs to mow

310 < 120 + 30a

190 < 30a

6.333 < a

a > 6.333

Tim needs to mow at least 7 lawns to earn more than $310

Answer:

28 i think.

Step-by-step explanation:

Answer:

The actual distance between the two cities is 28 kilometers

Step-by-step explanation:

A map has a scale of 3.5 inches = 20 kilometers

Distance between two cities on the map = 4.9 inches

We can use the unitary method in this question to get the actual distance between two cities

∵ 3.5 inches on the map = 20 kilometers

∴ 1 inch distance on the map = [tex]\frac{20}{3.5}[/tex] kilometers

∴ 4.9 inches on the map = [tex]\frac{20}{3.5}\times 4.9[/tex]

                                         = 28 kilometers

Therefore, the actual distance between the two cities is 28 kilometers.

Answer:

A 30

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles

100 = 70+x

Subtract 70 from each side

100-70 = 70-70 +x

30 =x

A. and C. are fractions. this is because they are only proportions of a whole unless they are a mixed number. but in this case, these numbers do not go over 1 (a whole).

Answer: Option A and Option C

[tex]\frac{3}{7}[/tex] and [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

The numbers in the form of fraction have the following form:

[tex]\frac{b}{c}[/tex]

Where b is known as numerator and c is known as denominator.

To know which of the numbers shown has a fraction form, identify all those with the form [tex]\frac{b}{c}[/tex]

Then you can see that the answer is option A and option C

[tex]\frac{3}{7}[/tex] and [tex]\frac{1}{2}[/tex]

Answer:

54 is x

Step-by-step explanation:

Sounds like you describing vertical angles. Vertical angles are congruent so that means 2x+2=3x-52

2=1x-52. Subtracted 2x on both sides

54=1x. Added 52 on both sides

54=x. Since 1 times x is x

Answer:

1/6

Step-by-step explanation:

[tex]\frac{1}{3}x=\frac{1}{18}\\3(\frac{1}{3}x=\frac{1}{18} )\\[/tex]

[tex]x=3/18\\x=1/6[/tex]

Answer: 120 different ways. It is a permutation.

Step-by-step explanation:

Because 1st, 2nd, and 3rd are different positions and the order of placing matters, this is a permutation. (In Combinations, the order doesn’t matter, like in choosing people to be on a team without any positions). The calculation is 6x5x4 because there are 6 competitors who could get first, 5 who could get second (the 6th already has first place), and 4 who could get 3rd ( the other two already have 1st and 2nd place).

The number of ways to award the medals in 120 different ways.

When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.

Given

Because 1st, 2nd, and 3rd are different positions and the order of placing matters, this is a permutation. (In Combinations, the order doesn’t matter, like in choosing people to be on a team without any positions). The calculation is 6x5x4 because there are 6 competitors who could get first, 5 who could get second (the 6th already has a first place), and 4 who could get 3rd ( the other two already have 1st and 2nd place).

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Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point on a line

We have the equation:

[tex]y-3=-\dfrac{2}{3}(x+6)\\\\y-3=-\dfrac{2}{3}(x-(-6))[/tex]

the coordinates of the point is (-6, 3).

Only on the first graph the line passes through the point (-6, 3).

Answer:

A

Step-by-step explanation:

The simplified expression is [tex]\(\frac{a^9}{8}\)[/tex].

To simplify the expression [tex]\((a^3/2)^3\)[/tex], follow these steps:

1. Apply the power of a power rule, which states that [tex]\((x^m)^n = x^{m \times n}\)[/tex]. In this case, [tex]\(x = a^3/2\)[/tex], [tex]\(m = 1\)[/tex], and [tex]\(n = 3\)[/tex].

2. Distribute the exponent over the numerator and the denominator:

[tex]\((a^3/2)^3 = (a^3)^3 / (2)^3\)[/tex].

3. Apply the power of a power rule to [tex]\((a^3)^3\)[/tex]:

 [tex]\((a^3)^3 = a^{3 \times 3} = a^9\)[/tex].

4. Apply the power of a power rule to [tex]\(2^3\)[/tex]:

 [tex]\(2^3 = 8\)[/tex].

5. Combine the results to get the simplified expression:

 [tex]\(\frac{a^9}{8}\)[/tex].

Therefore, the expression [tex]\((a^3/2)^3\)[/tex] simplifies to [tex]\(\frac{a^9}{8}\)[/tex].

Answer:

(2, 2), (3, 1), (4, 2)

Step-by-step explanation:

y ≥-1/3 x + 2

y < 2x + 3

(2, 2), (3, 1), (4, 2)

(2, 2), (3, –1), (4, 1)

(2, 2), (1, –2), (0, 2)

(2, 2), (1, 2), (2, 0)

I will assume which we determining which set of points is a solution

(2,2) is in all the sets, so we ignore it

Looking at the graph, we do not have negative solutions for y when x >0 so (3,-1) cannot be a solution and (1,-2) cannot be a solution

(2, 2), (3, 1), (4, 2)

(2, 2), (3, –1), (4, 1)   x

(2, 2), (1, –2), (0, 2)   x

(2, 2), (1, 2), (2, 0)

Again looking at the graph (2,0) is not a solution

(2, 2), (3, 1), (4, 2)

(2, 2), (3, –1), (4, 1)   x

(2, 2), (1, –2), (0, 2)   x

(2, 2), (1, 2), (2, 0)  x

Answer:

(2, 2), (3, 1), (4, 2)

Step-by-step explanation:

So I simplify the expression and it is..

8x^3  +  14x^2  +  5x  −  15

____

I hope this helps, as always. I wish you the best of luck and have a nice day, friend..

Answer:

8,000-24x

Step-by-step explanation:

there's 24 months in 2 years. If it's value decreased from 8,000 at a constant rate over a 2 year period, the equation would be 8,000-24x

Answer:

B. [tex]8,000-24x[/tex].

Step-by-step explanation:

We have been given that Desmond wants to sell his car that he paid $8,000 for 2 years ago. The car depreciated, or decreased in value, at a constant rate each month over a 2-year period.

Since the value of car depreciates at a constant rate each month, so the value of car depreciated in 2 years would be [tex]2\times 12=24[/tex].

There are 24 months in two years, so value of car depreciated in 2 years would be 24x.

The initial value of car is $8,000, so value of car after 2 years would be [tex]8,000-24x[/tex].

Therefore, option B is the correct choice.

Step-by-step answer:

Step 1:

find out the amount and direction of the vertical translation.

+3 means translating 3 units up, and -6 means translating 6 units down.

Step 2:

to each of the coordinate pairs, add the value of the translation to the y-coordinate (i.e. the second number of the pair).

For example, if the translation is +3, and if one of the vertices is (4,1), then the image of the vertex is (4,1+3) = (4,4).

Repeat for the rest of the vertices.

Step 3:

Check by graphing both image and preimage to see if the shapes are identical.  If not, look for a mistake in the translation process.

To translate a figure vertically, add the translation value to the y-coordinates of each vertex. For a translation of 'k' units, the new vertices will be (x, y + k). This keeps the shape the same and only changes its position vertically.

To find the coordinates of the image vertices when a figure is translated vertically,

you need to follow these simple steps:

This method ensures that the shape of the figure remains unchanged and it is only shifted up or down vertically.

Answer:

15.79%

Step-by-step explanation:

do 95-80 which is 15

then do 15/95 as a fraction then multiply that number by 100 to get 15 15/19 then turn that into a decimal and you get 15.79%

Jillian's percent error in estimating the time it would take her to run 7 miles is 15.79%.

Jillian's percent error in her run can be calculated by taking the absolute value of the difference between her estimated time and actual time, divided by the estimated time, and then multiplied by 100 to get the percentage. Here is the calculation step-by-step:

Therefore, Jillian's percent error in her estimation is 15.79%.

Answer: 6x + 4

6x represents 6 times the quantity x.

+ 4 represents plus 4.

Put 6x and + 4 together to get 6x + 4.

Answer:

[tex]-2\dfrac{1}{4}\div\left(-\dfrac{2}{3}\right)=\dfrac{27}{8}=3\dfrac{3}{8}}[/tex]

Step-by-step explanation:

[tex]-2\dfrac{1}{4}\div\left(-\dfrac{2}{3}\right)\qquad\text{the quotient of two negative numbers is positive}\\\\=2\dfrac{1}{4}\div\dfrac{2}{3}\qquad\text{convert the mixed number to the improper fraction}\\\\=\dfrac{2\cdot4+1}{4}\div\dfrac{2}{3}=\dfrac{9}{4}\div\dfrac{2}{3}\\\\\text{dividing by a fraction is the same as multiplying by its reciprocal.}\\\\=\dfrac{9}{4}\cdot\dfrac{3}{2}=\dfrac{9\cdot3}{4\cdot2}=\dfrac{27}{8}\qquad\text{convert to the mixed number}\\\\=3\dfrac{3}{8}[/tex]

Answer:

A. 10i and -10i

Step-by-step explanation:

We are given our equation as

[tex]x^2+101=1\\[/tex]

Let us subtract 101 from both hand sides

[tex]x^2+101-101=1-101\\[/tex]

[tex]x^2=-100[/tex]

Now taking square roots on both hand sides

[tex]\sqrt{x^{2}}} = \sqrt{-100}[/tex]

[tex]x=\sqrt{100} * \sqrt{-1}[/tex]

[tex]x=10 * (+i) \\x=10*(-i)\\[/tex]

[tex]x=+10i \\x=-10i\\[/tex]

Answer:

Option D [tex]x^{2} -x-6=0[/tex]

Step-by-step explanation:

Verify each quadratic equation

case A) we have

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

This quadratic equation has a leading coefficient of 1

Substitute the value of x=3 and x=-2 in the equation

For x=3

[tex](3)^{2} +(3)+6=0[/tex]

[tex]18=0[/tex] ----> is not true

therefore

x=3 is not a solution of the quadratic equation

case B) we have

[tex]x^{2} -x-5=0[/tex]

This quadratic equation has a leading coefficient of 1

Substitute the value of x=3 and x=-2 in the equation

For x=3

[tex](3)^{2} -(3)-5=0[/tex]

[tex]1=0[/tex] ----> is not true

therefore

x=3 is not a solution of the quadratic equation

case C) we have

[tex]x^{2} +x+5=0[/tex]

This quadratic equation has a leading coefficient of 1

Substitute the value of x=3 and x=-2 in the equation

For x=3

[tex](3)^{2} +(3)+5=0[/tex]

[tex]17=0[/tex] ----> is not true

therefore

x=3 is not a solution of the quadratic equation

case D) we have

[tex]x^{2} -x-6=0[/tex]

This quadratic equation has a leading coefficient of 1

Substitute the value of x=3 and x=-2 in the equation

For x=3

[tex](3)^{2} -(3)-6=0[/tex]

[tex]0=0[/tex] ----> is true

therefore

x=3 is a solution of the quadratic equation

For x=-2

[tex](-2)^{2} -(-2)-6=0[/tex]

[tex]4+2-6=0[/tex]

[tex]0=0[/tex] ----> is true

therefore

x=-2 is a solution of the quadratic equation