two equal rectangular lots are enclosed by fencing the perimeter of a rectangular lot and then putting a fence across its middle. if each lot is to contain 300 square feet, what is the minimum amount of fence (in ft) needed to enclose the lots (include the fence across the middle)?

The artifact was created 11,460 years ago.

Given

that,25% of the carbon-14 found in living trees can be found in a wooden artifact from an ancient tomb and the half-life of carbon-14 is 5730 years Half Time  [tex]t_{1/2}[/tex] = 5730 yearsln 2 / k = 5730k =  5730 / ln 2Let Po = 100P(t) =25 after t yearsP(t) = Po e^ -kt25 = 100 e ^ -(5730t / ln 2)5730t / ln 2 = ln 4

By applying

we get,t = 5730 * log⁴₂t = 11460 years Hence, the artifact was made 11,460 years ago.

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Considering the vertex of the quadratic function at point (6,-2), it is found that:

a) The meaning is that the turning point of the function is at point (6,-2).

b) If the parabola is concave down, then the vertex is a maximum. If the parabola is concave up, then it is a minimum.

c) If the parabola is concave down, then f(2) = f(10) < f(6). If the parabola is concave up, then f(2) = f(10) > f(6).

d) f(2) = f(10).

A quadratic equation is defined by the rule presented as follows:

y = ax² + bx + c.

The vertex can represent either a maximum point or a minimum point, depending on the coefficient a, as follows:

The vertex is also the turning point of the graph of the parabola.

In this problem, the coordinates of the vertex are (6,-2), hence:

When two points are equidistant from the vertex, they have the same numeric value, hence:

f(2) = f(6).

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We will see that the linear equations are:

Parallel line: x = -9

Perpendicular line: y = 3

Here we have the vertical line:

x = -2

A parallel line to this one will also be vertical, of the form:

x = a

And a perpendicular line to this one will be horizontal, of the form:

y = b

We want the parallel line to pass through (-9, 3)

So our line x = a needs to pass through that point, then:

x = -9

Is the parallel line.

And if the perpendicular line y = b needs to pass through that point, then:

y = 3

Is the perpendicular line.

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The value of 150/4 to the nearest tenth is 37.50

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. . In a proper fraction, the numerator is less than the denominator. In improper fraction, the denominator is smaller to the numerator.

The value of 150/4 = 75/2= 37 1/2

1/2 in decimal is 0.5

Therefore 150/4= 37+ 0.5= 37.5

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Answer/Step-by-step explanation:

[tex]-\frac{8}{27} a^{15} = (-\frac{2}{3})^{3} * (a^3)^5 = (-\frac{2}{3} a^{5})^3[/tex]

I hope this helps!

The number of books bought by the school is 92.

Here it is given that the school spend $925 to buy new books for the library.

The cost of each book is $9.95

So we have to find the number of books that can be bought.

By dividing the total money spent by the cost of each book we get the number of books bought.

Let n be the number of books bought.

n × 9.95 = Total money spend on the books

As we know the total money spend on the books is $925.

So we get:

925 = n × 9.95

n = 925/ 9.95

= 92

Therefore the total number of books bought is 92.

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Answer: angle 1 and 4

Step-by-step explanation:

Answer:

190 43/100

Step-by-step explanation:

First, you turn the mixed fractions into improper fractions. 382 3/10 is 3823/10, and 191 87/100 is 19187/100. Then, you need to have a common denominator in order to subtract. This turns 3823/10 into 38230/100. 38230/100 - 9187/100 is 19043/100 since you only subtract the numerators. Finally, you turn it back into a mixed fraction by dividing 19043/100. This equals 190 with a remainder of 43. In conclusion, the answer is 190 43/100. I attached the image where I worked it out to show my thought process a bit more as well. I hope this helped! :D

Answer:

16x² - 18x

Step-by-step explanation:

(25x² + 4 - 30x) - (9x² + 4 - 12x) ← distribute this parenthesis by - 1

= 25x² + 4 - 30x - 9x² - 4 + 12x ← collect like terms

= (25x² - 9x²) + (4 - 4) + (- 30x + 12x)

= 16x² + 0 + (- 18x)

= 16x² - 18x

The range values for the domain of the functions are as follows

x   y

-2  7

0   3

1     1

3    -3

The domain are the input values of the graph the output values are solved using the given functions

The given function 2x-y=3

rearranging gives

y = 3 - 2x

solving for the range values using the domain values: (-2,0,1,3)

= 3 - 2x = 3 - 2 * -2 = 7

= 3 - 2 * 0 = 3

= 3 - 2 * 1 = 1

= 3 - 2 * 3 = -3

The graph is attached

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All the statements about Arithmetic sequence and linear function are correct.

What is Arithmetic sequence and linear function?

When used in mathematics, the term "linear function" describes two different but related ideas: A linear function, also known as a polynomial function of degree zero or one, is a function in calculus and related fields that has a graph that is a straight line.

In an Arithmetic Sequence the difference between one term and the next is a constant. In other words, we just add the same value each time.

Since the  Linear Function has a y-intercept.

Also all the points on a Linear Function connect.

When a line slopes down from left to right, it has a negative slope. This means that a negative change in y is associated with a positive change in x.

That means the Domain of the Linear Function includes negative numbers when the function is decreasing.

Therefore, all the statements are correct.

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For the parallel lines (l//m), the value of x is equal to 25 and the converse used is the alternate exterior angle theorem.

Parallel lines simply refers to two (2) lines that always have the same or equal distance apart and never meet.

The alternate exterior angle theorem states that when two (2) parallel lines are cut through by a transversal, the alternate exterior angles that are formed are congruent or angles of equal measure and magnitude.

By applying the alternate exterior angle theorem to parallel lines (l//m), we have:

4x - 13 = 2x + 37

4x - 2x = 37 + 13

2x = 50

x = 50/2

x = 25

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The mixture of 13% disinfectant solution needs to be made with 8 gallons of 11% solution and 4 gallons of 17% solution respectively.

Let

x + y = 12

0.11x + 0.17y = 0.13 × 12

x + y = 12

0.11x + 0.17y = 1.56

From (1)

x = 12 - y

Substitute into (2)

0.11x + 0.17y = 1.56

0.11(12 - y) + 0.17y = 1.56

1.32 - 0.11y + 0.17y = 1.56

- 0.11y + 0.17y = 1.56 - 1.32

0.06y = 0.24

divide both sides by 0.06

y = 0.24/0.06

y = 4

x + y = 12

x + 4 = 12

x = 12 - 4

x = 8

So therefore, the gallons of 11% solution and

gallons of 17% solution needed are 8 and 4 gallons respectively.

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The nearest whole number to the number 5.2 is 5.

Given number:

= 5.2

we can determine the whole number of any decimals using the properties that is,

if decimal part < .5 its nearest whole number is 0.

example = 0.5 whole number is 0.

if decimal part  >  0.5 its nearest whole number is 1.

In this case,

= 5.2

decimal part  = 0.2 < 0

so the nearest whole number is 5.

Therefore the nearest whole number to the number 5.2 is 5.

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Answer:

a = 9 ; b = 26 ; c = 24

Step-by-step explanation:

(x^2+3x+2x+6)(x+4)

(x^2+5x+6)(x+4)

x^3+5x^2+6x+4x^2+20x+24

x^3+9x^2+26x+24

Yes, a baseball fit in box A.

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m³, cm³, in³, etc.

Volume is simply the amount of space a three-dimensional solid takes up. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Volume is sometimes referred to as capacity. For instance, a cylindrical jar's volume can be used to calculate how much water it can hold.

Given:

The circumference of a regulation baseball is at least 9 inches but no more than 9.25 inches.

So, the maximum value of Circumference

2πr = 9.5

r= 9.5/ 2 x 3.14

r = 1.472 inch

So, Volume of ball = 4/3 πr³

Volume of ball = 4/3 x 3.14 x (1.472)³

Volume of ball = 13.36 inch³ < 64 inch³

Hence, it will fit inside the box.

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The exchange rate if each souvenir costs 200 Jamaican dollars, 38 might be purchased.

The exchange rate refers to the value of one country currency about's currency. It is determined by the foreign currency market, often known as the FOREX market.

Amount needed for vacation = $50 USD = $7,740 JMD

Each souvenir is priced at 200 Jamaican dollars.

One US dollar = 154.8 Jamaican dollars when converted to Jamaican currencies.

50 US dollars = 154.8 × 50

= 7,740 Jamaican dollars

Number of souvenirs you can buy = Amount of money with you for vacation ÷ Cost of each souvenir

= 7,740 Jamaican dollars ÷ 200 Jamaican dollars

= 38.7 souvenirs.

As a result, for 200 Jamaican dollars for each souvenir, about 38 souvenirs may be obtained with 50 US dollars.

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The probability that fewer than 60 out of a random sample of 500 adults will work from home is 0.03

In the given probability case we have;

What is the likelihood that, out of a random sample of 500 persons, fewer than 60 will work from home if 15% of adults in a particular country do so?

Let,

P = 15% = 0.15

n = 500

By considering the binomial distribution case the formula is given by

P( X = x ) = ⁿCₓ * Pˣ * (1 - P)ⁿ⁻ˣ

P( X ≤ 60 ) = ⁿCₓ * Pˣ * (1 - P)ⁿ⁻ˣ

                 = ⁶⁰∑ₓ=₀ (⁵⁰⁰Cₓ) (0.15)ˣ (1 - 0.15)⁵⁰⁰⁻ˣ

                 = 0.031

                 ≅ 0.03

Hence, the probability that fewer than 60 out of a random sample of 500 adults will work from home is 0.03

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[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-16}~,~\stackrel{y_1}{11})\qquad (\stackrel{x_2}{16}~,~\stackrel{y_2}{4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~16 - (-16)~~)^2 + (~~4 - 11~~)^2} \implies d=\sqrt{(16 +16)^2 + (4 -11)^2} \\\\\\ d=\sqrt{( 32 )^2 + ( -7 )^2} \implies d=\sqrt{ 1024 + 49 } \implies d=\sqrt{ 1073 }\implies d\approx 32.76[/tex]

The proportion of bottles that will have more than 18 ounces dispensed into them is 0.0228

Proportion relationship:

Proportion means a relationships between two variables where their ratios are equivalent and it is the way to think about them is that, in a proportional relationship, one variable is always a constant value times the other.

Given,

A company that manufactures and bottles apple juice uses a machine that automatically fills 20-ounce bottles. there is some variation, however, in the amount of liquid dispensed into the bottles. the amount dispensed has been observed to be approximately normally distributed with mean 20 ounces and standard deviation 1 ounce.

Here we need to determine the proportion of bottles that will have more than 18 ounces dispensed into them and round the answer to the four decimal places.

Here we have to use tables to determine the proportion of bottles that will have more than 18 ounces dispensed into them.

Let us consider X denote the amount of juice dispensed.

Then it can be written as,

P (X >18) = P (Z > (20 - 18)/1)

=> P (X >18) = P (Z > 2)

=> 1 - Ф(2)

=> 1 - 0.9772

=> 0.0228

Hence the proportion of the bottles that will have more than 18 ounces dispensed into them is 0.0228.

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The equivalent expressions using only positive exponents are 1/(7x⁵y⁸)⁵ and (5y³/x⁶)⁵

Expression 1

From the question, the expression is given as

(49x¹⁰y¹⁶)⁻⁵/²

Express the radicals as roots

So, we have

(49x¹⁰y¹⁶)⁻⁵/² = √[(49x¹⁰y¹⁶)]⁻⁵

Take the square root of each of the factor in the bracket

This gives

(49x¹⁰y¹⁶)⁻⁵/² = (7x⁵y⁸)⁻⁵

Apply the negative exponent rule of indices

So, we have

(49x¹⁰y¹⁶)⁻⁵/² = 1/(7x⁵y⁸)⁵

Expression 2

From the question, the expression is given as

(125x⁻¹⁸y⁹)⁵/₃

Express the radicals as roots

So, we have

(125x⁻¹⁸y⁹)⁵/₃ = ∛[(125x⁻¹⁸y⁹)]⁵

Take the cube root of each of the factor in the bracket

This gives

(125x⁻¹⁸y⁹)⁵/₃ = (5x⁻⁶y³)⁵

Apply the negative exponent rule of indices

So, we have

(125x⁻¹⁸y⁹)⁵/₃ = (5y³/x⁶)⁵

Hence, the equivalent expression is  (125x⁻¹⁸y⁹)⁵/₃ = (5y³/x⁶)⁵

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Step-by-step explanation:

Randy is 8 years old. His brother is twice as old as Randy. Randy’s sister is three years younger than Randy. Write an expression to represent the age of Randy’s brother.

Randy = R = 8 years

Brother =  B

B = 2R

solving:

B = 2R when R = 8

B = 2(8)

B = 16 years old

Answer: Its 16

Step-by-step explanation:

You need to take randy's age twice so you need to calculate 8x2= 16.

The sum of even numbers between 105 and 351 is 28,044 .

An additive or arithmetic sequence is a sequence of numbers such that the difference between  consecutive terms is constant. For example, the sequence 5, 7, 9, 11, 13, 15 ... is an exponent plus the common difference of 2.

even numbers between 105 and 351

the series will start like

106 , 108 , 110 , .................................. , 346 , 348 , 350

this is a arithmetic progression

a = 106 d  = 2 l = 350

we need to find n

350 = 106 + ( n - 1 ) 2

350 - 106 = (n -1 ) 2

244/2 = n -1

n = 123

now sum = 123/2 ( 106 + 350)

               = 28,044

so the sum of even numbers between 105 and 351 is 28,044 .

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Answer:

x=2

Step-by-step explanation:

add the x onto the other side so it is positive : 7=5+x

then subtract the 5 from both sides so you can isolate the x : 2=x

rewrite the equation: x=2

☆ Hello ☆

The value of x is 2.

[tex] \red{ \sf \underline {\underline{Explantation: }}}[/tex]

¿What are equations?

The equations represent an equality between two mathematical expressions that have at least one variable called unknown.

[tex] \sf \:Solution:[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \begin{gathered}\boldsymbol{\mathsf{7 - x = 5}}\\\boldsymbol{\mathsf{ - x = 5-7}}\\\boldsymbol{\mathsf{ - x = -2}}\ \\ {\mathsf{ x = 2}}\end{gathered}[/tex]

[tex] \bf \:Verification:[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \begin{gathered}\boldsymbol{\mathsf{7 - 2 = 5}}\\\boldsymbol{\mathsf{ 5=5}}\end{gathered}[/tex]

[tex]\green{ \sf \: The \: result \: is} \: \red{\longmapsto} \blue 5[/tex]

The graph of the inequality is attached below.

We are given an inequality. The inequality is linear in nature. An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. The inequality is given below.

y < 2x - 3

We need to graph the inequality. The first step is to find out the corresponding equation of the straight line. The equation is found by replacing the greater-than or less-than sign with the equal-to sign. The equation is given below.

y = 2x - 3

We plot this equation on the graph with a dotted line. Now we shade the area that satisfies the given inequality. The graph is given below.

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Answer:

D

Step-by-step explanation:

Multiply both sides by 3

x − 1 = 9

Add 1 to both sides

x = 10

The system of inequalities that best matches the graph is Option C

Step-by-step explanation:

To find the system of inequalities, we simply need to find the equation of each line.

Thus, let's find the inequality that is represented by each line.

Red Line:

First, let’s determine the slope. To do so, we can use the slope formula:

m = (y₂-y₁) / (x₂-x₁)

We can use any two points that's on the Red Line. Using (3, -2) and (6, -4) and substituting them into the slope formula yields:

m = (-4+2) / (6-3)    = -2/3

Therefore, the slope of the red line is 2.

To write the equation of the red line, we can use the slope-intercept form:

y = mx + c

Notice that our y-intercept of our red line is (0, 3). Therefore, b = 3 and we already determined that m = -2/3:

y = ((-2/3)x) + (-3)

y   = (-2/3)x -3

Now, we need to determine our sign. Notice that the shaded region is below the red line. Therefore, y is less than our equation.

And since our line is shaded, our sign will be less than or equal to. Therefore:

y ≤ (-2/3)x - 3

Blue line:

Again, let’s first find the slope. We can use the two points (3,0) and (0, -3). Hence:

m = (-3-0) / (3-0)  = -3/3  = -1

So, the slope is -1.

We can now use the slope-intercept form. Notice that our y-intercept is (0, 0). Thus, we will substitute -1 for m and 0 for b. This yields:

y = -1x + 0

y = -x

Finally, we will determine our sign. Since the shaded region is above the blue line, our y is lesser than our equation. Therefore, our equation is:

y < -x

Thus, all together, our inequalities are:

y ≤ (-2/3)x - 3

y < -x

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P(The aircraft is discoverd and has no locator) = P(discovered)  x P(no locator/discoved =0.28)

The information is based on the disappearance of the of the light aircraft in the flight in the in a certain country . 70% of the aircraft that disapear while in the flight were discovered . The probability that there is an emergency locator        

in the aircraft given that it is discovered is 60% and the probability that the aircraft that has not discovered have an emergenncy locator is 90%.

a) To determine probiblity it wount be discoverd

Calculation

P(the aircraft is discovered and has a locator) = P(discovered) X P(locator/discovered)

The probability of the flight discovered and has locator is obatained as given below:

P(The aircraft is discoverd and has no locator) = P(discovered)  x P(no locator/discovered)

The probability of the flight not discovered and has a locator is obatained below.

P(The aircraft is not discovered and has a locator) = P(not discovered) x P (locator  | not discorverd)    = 1-0

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