Find the area. Pls help with 12-13

Answer:

90%

Step-by-step explanation:

To find the percent of increase in the height of the tree, we need the change of the height and the original height (40 feet)

The change of height = 76 - 40 = 36 feet

Now, we need to divide the change by the original height to find the percent of increase.

36/40 = 9/10

9/10, which is then 90%.

In linear equation, The price at which the quantity demanded equals the quantity supplied is $ 260."  option (b) is answer.

What in mathematics is a linear equation?

a.  The demand for a product is given by p+3q= 315 or, q = (315 - p)/3 and the supply for this product is given by  p-7q = 65 or, q = (p- 65)/7

The price at which the quantity demanded equals the quantity supplied is given by

              315 - p/3 = p - 65/7

         7( 315 - p ) = 3( p - 65 )

        2405 - 7p = 3p - 195

        2405 + 195 = 3p + 7p

           2600 =  10p

            p = 2600/10 = 260

Thus, the required price is $ 260.

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Depending on the particular isotope, this process can take a variety of times. While for some it will take years and decades, it will just take a microsecond for individuals. Usually, the isotope will decay into a different element or isotope.

Isotopes are two or more different atom types that share the same atomic number and place in the periodic table but have different quantities of neutrons in their nuclei, resulting in various nucleon numbers.

If we start with 180 g of the isotope, after one half-life the quantity will diminish to  180 g/2 = 90 g which exists half the original quantity.

This can be written mathematically as: [tex]$180 g\left(\frac{1}{2}\right)^1$[/tex]

After the second half life: [tex]$\frac{90 g}{2}=45 g=\frac{180 g}{4}=(180 g)\left(\frac{1}{2}\right)^2$[/tex]

After the third half life: [tex]$\frac{45 g}{2}= 22.5 g=\frac{180 g}{8}=(180 g)\left(\frac{1}{2}\right)^3$[/tex]

But now that we are dividing the amount by 2 to a power that grows as the number of half-lives, we can start to notice a pattern.

The original quantity can then be rapidly computed for six half-lives using the formula below:

[tex]$(180 g)\left(\frac{1}{2}\right)^6=(180 g)\left(\frac{1}{64}\right)=\frac{180 g}{64}=2.8 g$$[/tex]

Depending on the particular isotope, this process can take a variety of times. While for some it will take years and decades, it will just take a microsecond for individuals. Usually, the isotope will decay into a different element or isotope.

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The percentage of young adults who send fewer than 218 text messages is 99.87%.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 218

μ = mean = 128

σ = standard deviation = 30

z-score = (218 - 128) / 30

z-score = 90 / 30

z-score = 3

Find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score = 3

probability = 0.9987

To get the percentage, multiply the probability by 100.

percentage = probability x 100

percentage = 0.9987 x 100

percentage = 99.87%

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Answer: 195/4

Step-by-step explanation:

55.557 + 121.4474 + 6.3

we have that

55.557=55.5570

121.4474

6.3=6.3000

so

55.5570

121. 4474

6. 3000

------------------

a. The equation for h is h = 100/x²

b. The function for the volume of the box V, in terms of x is:

v(x) = x²×h

Given, the prism has a square base and a total surface area of 100 cm².

A) let x = the side length of the base and

h = the height of the prism.

equation for h = ?

Volume = b × h

100 cm² = x² × h

h = 100/x²

B) a function for the volume of the box, V, in terms of x.

we know that x is the base and h is the height.

So, volume in terms of x :

v = b×h

v = x² × h

Hence we get the required answers.

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Answer:

d=y-300

Step-by-step explanation:

part 1 of the question is asking us to evaluate expressions to the power of 2. To do that let's remember the following:

Ther is, when a number is elevated to second power it means we have to multiply that number by itself. For example:

In the second part of this question, we are asked to evaluate the square root of a number. Let's remember that the square root is the inverse operation of elevating a number to the second power. That is if we have:

it means:

For example:

The third part of the questions asks us to solve for "x" the following equation:

To do that we take square root on both sides:

Since the square root of a number to the second power is the same number and the square root of 9 is 3, we get:

Given the details above, the sequence of steps below shows that ABCD is a Trapezoid.

A trapezoid, also known as a trapezium, is a closed, flat object with four straight sides and one set of parallel sides. A trapezium's parallel sides are known as the bases, while its non-parallel sides are known as the legs.

Given:

The diagonals of the quadrilateral ABCD intersect at o where AO/BO = CO/DO; which also means that

AO/CO = BO/DO the proof is given as follows:

Create line OE || DC in a way that E lies on BC.

In ΔBDC, based on the Basic Proportionality Theory,

BO/OD = BE/EC ............................1

It is also given that:

AO/CO = BO/DO   ..........................2

Hence, from Equations 1 and 2,

AO/CO = BE/EC

Thus, we can state that on the basis of the Converse of the Basic Proportionality Theorem,

OE || AB

Since AB || OE || DC, it is correct to state that ABCD is a Trapezoid.

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Answer: c

Step-by-step explanation:

Elliptical graphs fail the vertical line test as they have same x and y values at some places. Thus elliptical graph is not a function

Based on your earnings from each of the part-time jobs, your fortnightly earnings would be $1,520

First, find out how much you earn in the first part-time job per week:
= (Number of days per week x Number of hours per day x Pay per hour)

= (3 x 6 x 20)

The find out how much you earn in the second part-time job:

= (Number of days per week x Number of hours per day x Pay per hour)

= (2 x 8 x 25)

In a fortnight (two weeks), your earnings would be:

= (2 weeks x (3 x 6 x 20)) + (2 weeks x (2 x 8 x 25))

= (2 x 360) + (2 x 400)

= 720 + 800

= $1,520

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Fortnightly earnings would be $1,520 based on previous earnings.

Two or more expressions with an Equal sign is called as Equation.

Given that there are two part time jobs.

For first part time

3 days per week I work for 6 hours each day and I earn $20.00 per hour

(3 x 6 x 20)

=360

Second part time

2 days per week, I earn $25.00 per hour, working an 8-hour day.

=2×25×8

=400

Now we need to calculate, the total fortnightly earnings.

= (2 weeks x360) + (2 weeks x 400)

= (2 x 360) + (2 x 400)

= 720 + 800

= $1,520

Hence $1520 is the fortnightly earnings.

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Jane decides to randomly interview 10 freshmen from each of the dorms, these people are her Sample.

What is Sample?

Sampling is the process of choosing a portion of a statistical population to estimate attributes of the entire population in statistics, quality control, and survey methods. Statisticians try to get samples that are typical of the population under consideration.

A little sample or amount of someone or something that is inspected, analyzed, or otherwise investigated to learn more about the rest.

Given: Jane wants to know what percentage of freshmen at her college purchase clothing with college logos. She decides to randomly interview 10 freshmen from each of the dorms.

Therefore, by the above information, these people are her Sample.

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Answer: $31,200 per year

Step-by-step explanation:

The question tells us that they are working 40 hours a week and making 15 dollars an hour. We can find out how much they make a week and then multiply by 52 (number of weeks in a year) to find the amount they make in a year.

Per week:

15 * 40 = $600

Per Year:

600 * 52 = $31,200

Answer:

$31,285.74 per year

Step-by-step explanation:

What we know:

- $15 per hour

- 40 hour weeks

- 52.1429 weeks per year

What we need to find out:

- How much money per year

Step 1: Multiply for how much made per week

We know that we need $15 dollars for 40 hours so we start with multiplying them together to see how much we make a year.

40 x 15 = $600 per week

Step 2: Now multiply the amount of weeks a year by the amount made per week

So now we know that we make $600 per week now we have to multiply the amount of weeks in a year by the money made per week so.

52.1429 x 600 = $31,285.74 per year. So the house keeper makes $31,285.74 per year.

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To solve this problem we change the structure from

1/2 + ? = 7/8

to

7/8 - 1/2 = ?

Now we need to subtract the fractions and find the difference. To do this, make the denominators (the bottom numbers on the fractions) the same.

1/2 = 4/8

then subtracts the numerator

7/8 - 4/8 = 3/8

there is your answer... 3/8

Step-by-step explanation:

open the bracket

y - 1 = 3x - 12

add 1 to both sides

y = 3x - 11

I think that should be it

Okay, here we have this:

Considering the provided information, we are going to write and solve the correspondinf system of equation, so we obtain the following:

According to the information given, we obtain the following system of equations, where we take x as money spent on fruit and y as money spent on green vegetables, so we have:

Now let's solve for x in the second equation:

x+x+5=30

2x+5=30

2x=30-5

2x=25

x=25/2

x=12.5

Now from the value of x that we got, then we will plug it into the first equation to get the value of y:

Then, finally we obtain that she spend $12.5 on fruits and $17.5 on green vegetables.

Work done in stretching spring from 36 cm to 38 cm is 0.333J.

The work needed to stretch a spring is given by the formula mentioned below:

[tex]W_{s}[/tex] = (1/2) K × [tex]x^{2}[/tex]

Here,  k is spring constant and x is the elongation.

So, x = [tex]x_{f} - x_{i}[/tex]

When spring is stretched from 40 cm to 34 cm

x = 40 - 34  = 6cm = 0.06 m

We need to know the spring constant so that we can calculate work.

3 = (1/2) K × [tex](0.06)^{2}[/tex]

K = 1666.67

Now, when spring is stretched from 36 cm to 38 cm

x = 38 - 36 = 2 cm = 0.02 m

[tex]W_{s}[/tex] = (1/2) × (1666.67) × [tex](0.02)^{2}[/tex]

[tex]W_{s}[/tex] = 0.333J

So, 0.333J work is done in stretching spring from 36 cm to 38 cm.

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After combining the like terms of the given expression -4r -2r + 5 the equivalent expression is -6r +5.

As given in the question,

Given expression is equal to :

-4r -2r + 5

Now combine the like terms to get the equivalent expression we have,

Like terms of the given expression -4r -2r + 5 are -4r and -2r

( -4r -2r) +5

= -r (4+2) +5

= -6r +5

Equivalent expression of the given expression -4r -2r + 5  is -6r +5.

Therefore, after combining the like terms of the given expression -4r -2r + 5 the equivalent expression is -6r +5.

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Answer:

D y < 8

Step-by-step explanation:

the range is the interval or set of all valid y (functional result) values.

we can see the y values start at +8, and as the curve is only going down, clearly endlessly, every value smaller than 8 is valid.

8 itself is the be excluded, as there is a hollow point (a filled point would indicate "include").

and therefore we cannot say y <= 8.

we have to use y < 8.

The function that can be used to represent the total amount that will be paid for the room is 100 + 55h.

A function simply means the expression that. an be used to show the relationship between the variables or the data given.

In this case, the interior designer charges $100 to visit a site, plus $55 to design each room.

Let the number of rooms be represented as r.

The function that represents the total amount will be:

= 100 + (55 × h)

= 100 + 55h

This illustrates the concept of functions.

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Step-by-step explanation:

The slope-intercept form of the equation of a line that passes through (5, -4) and has a slope of 3/4 is y = (3/4)x - 31/4.

What is the slope-intercept form?

The slope-intercept form of a line is y=mx + c.

Where, x and y are coordinates. m = slope and c = y intercept.

Given, slope (m) = 3/4

Substituting the values of (x, y) as (5, -4) and m = 3/4, we get:

-4 = (3/4) × 5 + c

⇒ c = -4 - (3/4) × 5 = -4 - 15/4 = -31/4

Now, putting the value of c in the standard equation:

y = (3/4)x - 31/4

⇒ 4y = 3x - 31

⇒ 3x - 4y = 31

Answer is Option C

Step-by-step explanation:

12/4 = x/8

1st: cross multiply

96 = 4x

2nd: divide both sides by 4

96/4 = 4x/4

therefore x = 24

The unit rate of gallon to mile is calculated as: 5/6 gallon per mile.

The unit rate between two variables is simply the ratio of the quantity of one variable to the quantity of the other variable, such that the the denominator of the will be equal to exactly 1.

We are given the variables gallons and miles, where 1/4 of a gallon is to 3/10 mile.

The unit rate between these two variables would be an amount of gallons per mile.

Thus, find the unit rate by dividing 1/4 by 3/10:

1/4 ÷ 3/10

= 1/4 × 10/3

= 10/12

= 5/6

The unit rate is therefore, 5/6 gallon per mile.

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According to the factor theorem, if "a" is any real integer and "f(x)" is a polynomial of degree n larger than or equal to 1, then (x - a) is a factor of f(x) if f(a) = 0.Finding the polynomials' n roots and factoring them are two of their principal applications.

Calculate p(x(*r(x)?

I This theorem comes in very handy when we need to determine the determinant's value in "factors" form.

p(x) =5x

r(x)  = 3x  - 7

p(x)×r(x) =

=5x(3x-7)

5x²  -  7

2×15x²-1

=  30x

p(x)*r(x)  =   30x

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It is known that 1 gallon is 3.78541 litres.

So it follows:

Hence the value of 3.5 gallons is 13.2489 litres.

The measure of Angle A and Angle B are 54° and 122° respectively.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In triangle ABC,

The measure of angle A = (n + 20)°

The measure of angle B = (3n - 10)°

The measure of angle C = n°

Now,

The sum of all the angles of the triangle = 180°

So, we can formulate;

(n + 20)° + (3n - 10)° + n° = 180°

Solve for n as;

n + 20 + 3n - 10 + n = 180

5n + 10 = 180

5n = 180 - 10

5n = 170

Divide by 5, we get;

n = 170/5

n = 34

Thus, The measure of angle A = (n + 20)°

                                               = 34 + 20

                                               = 54°

And, The measure of angle B = (3n - 10)°

                                             = 3 x 34 + 20

                                             = 102 + 20

                                             = 122°

Therefore,

The measure of Angle A and Angle B are 54° and 122° respectively.

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ANSWER

R1, R2, R3, R4, G1, G2, G3, G4. Option B.

Two lines are parallel if they hay the same slope.

The slope, m, of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:

From the graph, line m passes through the points (0, 1) and (3,3), then its slope is:

Equation of a line in slope-intercept form

where m is the slope and (x1, y2) is a point on the line.

The new line has to pass through point P(1, -2). Substituting with this point and m = 2/3 into the general formula: