Over what part of the domain is function f increasing ?

The measure of side length EF in the right triangle is 24.

The Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c²  = a² + b²

From the diagram:

Hypotenuse DE = c = 26

Leg DF = a = 10

Leg EF = b = ?

Plug in the values and solve for b:

c²  = a² + b²

26²  = 10² + b²

676  = 100 + b²

b² = 676  - 100

b² = 576

b = +√576 ( we take the positive value since we are dealing with dimensions)

b = 24

Therefore, the length EF is 24.

Option C)24 is the correct answer.

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The percentage rate of change per hour to the nearest hundredth is 3%.

Function to represent decay is A(t)= 150×(\(.97^{t}\)).

Percentage means out of hundred. If we want to calculate percentage the we have to make the fraction out of hundred.

It means that if same thing is distributed among 100 people how much a single person would get.

Now for the given question:

For radioactive decay the mathematical equation is

      A(t) = A(0)\((1-r)^{t}\)

where A(0) is the initial quantity = 150 gm. and r is the rate of decay = 51%

For hourly decay,

     A(24)= A(0)(1-0.51) as 1 day has 24 hour and each day substance decay by 51%.

     A(24)= A(0)×0.49

but,

   A(24)= A(0)\((1-r)^{24}\)

0.49A(0)=A(0)\((1-r)^{24}\)       (we do this to calculate r)

.049= \((1-r)^{24}\)

1-r = \(\sqrt[24]{.49}\)

1-r= 0.97

r = 1- 0.97

r= 0.03

r = 3%

Function for hourly decay,

A(t) = 150 ×\((1-r)^{t}\)

A(t) = 150 ×\((1-0.03)^{t}\)

A(t)= 150×(\(.97^{t}\))

Hence, Hourly rate of decay is 3% and the equation for hourly rate o decay is A(t)=150×\(.97^{t}\).

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Answer: 2x²+4x+6

Step-by-step explanation:

\(\displaystyle\\\frac{2x^3-2x-12}{x-2} =\\\\\frac{2(x^3-x-6)}{x-2}=\\\\ \frac{2(x^2-8+8-x-6)}{x-2} =\\\\\frac{2(x^3-2^3-x+2)}{x-2} =\\\\\frac{2((x^3-2^3)-(x-2))}{x-2}=\\\\\frac{2((x-2)(x^2+2x+2^2)-(x-2))}{x-2} =\\\\\frac{2(x-2)(x^2+2x+4-1)}{x-2}=\\\\2(x^2+2x+3)=\\\\2x^2+4x+6\)

Answer:

- 2.1

Step-by-step explanation:

Given

w - x + y ← substitute given values

= - 14 - (- 10.7) + 1.2

= - 14 + 10.7 + 1.2

= - 2.1

Answer:

Earth, Sun, Sun, Earth

Step-by-step explanation:

The equation of a line that passes through points (2,5) and (4,3) is

y = -x+7.

Finding the equation of a line:

First, we need to find out the slope for the given points.

(X1,Y1) = (2,5)

(X2,Y2) = (4,3)

formula for slope(m) = \(\frac{Y2 - Y1}{X2 - X1}\)

substitute the points in the above formula

\(\frac{3 - 5}{4 - 2}\) = \(\frac{-2}{2}\)

\(\frac{-2}{2}\) = -1

slope for the given points(m) = -1.

m = -1

The equation of a line is y-y1 = m(x-x1), where x and y are variables.

substituting the values in the above equation then :

y-5 = -1(x-2)

y-5 = -x+2

y+x = 2+5

x+y = 7

y = -x+7

Therefore, the equation of the line passing through the points (2,5) and (4,3) is y = -x+7

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Humanity would achieve a life expectancy of 110 years in approximately 60 years.

To calculate the number of years it would take for humanity to achieve a life expectancy of 110 years, we need to determine the number of decades required to reach this goal based on the given rate of increase.

In 2009, the life expectancy was about 80 years. From that point, we need to calculate the difference between the current life expectancy and the target life expectancy of 110 years.

110 years - 80 years = 30 years

Since the rate of increase is 5.3 years every decade, we can divide the difference by the rate to determine the number of decades required:

30 years / 5.3 years per decade ≈ 5.66 decades

Since we can't have a fraction of a decade, we need to round up to the nearest whole number. Therefore, it would take approximately 6 decades for humanity to achieve a life expectancy of 110 years.

To calculate the number of years, we multiply the number of decades by 10:

6 decades * 10 years per decade = 60 years

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Answer:

\(y=-\dfrac{1}{2}x-3\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}\)

Given equation:

\(y=-\dfrac{1}{2}x+1\)

Parallel lines have the same slope.

Therefore, the slope of the line parallel to the given equation is:

\(m=-\dfrac{1}{2}\)

Substitute the found slope and given point (-4, -1) into the point-slope formula:

\(\implies y-(-1)=-\dfrac{1}{2}(x-(-4))\)

\(\implies y+1=-\dfrac{1}{2}(x+4)\)

\(\implies y+1=-\dfrac{1}{2}x-2\)

\(\implies y=-\dfrac{1}{2}x-3\)

Therefore, the equation of the line passing through (-4, -1) and parallel to the given equation is:

\(\boxed{y=-\dfrac{1}{2}x-3}\)

Answer: 3/9 or 1/3

Step-by-step explanation:

3, 6 and 9 are all multiples of 3 equal or below 9.

The equation that shows the relationship between the number of paragliding trips, adventure tours, and his total pay is 55a + 75p = 2725

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

Let a represent the number of adventure tours and p represent the number of paragliding trip, hence:

55a + 75p = 2725

The equation that shows the relationship between the number of paragliding trips, adventure tours, and his total pay is 55a + 75p = 2725

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Answer:

a)the first 3 songs played are by the beatles

Step-by-step explanation:

i think its a

a) The Keynesian cross graphs an economy's planned expenditure function,

\($\mathrm{E}=\mathrm{C}(\mathrm{Y}-\mathrm{T})+\mathrm{I}+\mathrm{G}$\),

and the equilibrium condition that actual expenditure equals planned expenditure.

How do you find the expenditure function?

To derive the expenditure function we can either (i) invert V(·) and solve for M, or (ii) set up the dual of the consumer's choice problem, solve for Hicksian demand functions and substitute them into the objective (i.e., expenditure) function.

The amount by which\($\mathrm{Y}$\)falls is given by the product of the tax multiplier and the increase in taxes

\(: $\Delta \mathrm{Y}=[-\mathrm{MPC} /(1-\mathrm{MPC})] \Delta \mathrm{T}$.\)

c) We can calculate the effect of an equal increase in government expenditure and taxes by adding the two multiplier effects that we used in parts a and b :

\(\Delta \mathrm{Y}=\left[(1 /(1-\mathrm{MPC}))^* \Delta \mathrm{G}\right]-[(\mathrm{MPC} /(1-\mathrm{MPC}))]^* \Delta \mathrm{T}\)

Because government purchases and taxes increase by the same amount, we know that \(\Delta \mathrm{G}=\Delta \mathrm{T}$. Therefore we can rewrite the equation as:$$\Delta \mathrm{Y}=[(1 /(1-\mathrm{MPC}))-(\mathrm{MPC} /(1-\mathrm{MPC}))]^* \Delta \mathrm{G}=\Delta \mathrm{G}\)

This expression tells us that an equal increase in government purchases and taxes increases \($\mathrm{Y}$\) by the amount that \($\mathrm{G}$\) increases. That is, the balanced-budget multiplier is exactly 1 .

Complete question: Consider the Keynesian model with a change in the way that taxes are incorporated: (1) PAE = C + IP + G + NX Definition of Planned Aggregate Expenditure (2) C = C+ mpc (1-1) .y Consumption Function (3) PAE = Y Short-run Equilibrium Condition In this case, taxes paid are proportional to income, i.e. taxes paid are t - Y, where t is the tax rate and 0<t< 1. Disposable income is the part of income after taxes, i.e., (1-t). Y. Solve for the PAE spending line with PAE as a function of Y. What is the slope?

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kshsheveosbwjsvsusvsisvsidvsksns

Step-by-step explanation:

BRAINIST PLSS

The quantity of string he use is 4/15 yd

Fractions are represented as numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing

Given that: He had 4/5 yd of string

Since he uses 1/3 of the string, that means he used 1/3 multiplied by the quantity of the string he has:

1/3 x 4/5 yd = 4/15 yd

Therefore, the amount of string he use is 4/15 yd

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The register contains 8 number of $20 bills and 13 number of $100 bills.

Let 'x' be the of $20 bills.

Let 'y' be of $100 bills.

Total bill = 21

x+y = 21

y = -x+21 ......eq1

Now,

Total price = $1460.

20x + 100y = 1460

Put value of y from eq 1.

20x + 100(-x+21) = 1460

20x-100x+2100=1460

-80x=-640

x=8  (Number of $20 bill)

And,

-8+21=13

y=13 (Number of $100 bills)

Thus, the register contains 8 number of $20 bills and 13 number of $100 bills.

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The complete question is-

A cash register contains $20 bills and $100 bills with a total value of $1460. If there are 21 bills total, then how many of  each does the register contain?

The approximate amount of rotations it would take the monster truck to travel one mile is 1260 rotations.

Now, Based on the tire experiment, it will take fewer rotations for a monster truck with 6ft (which is 72 inches) tires to travel one mile compared to the other 3 tires from before.

This is because larger tires have a greater circumference, which means they are able to cover more distance with each rotation.

Hence, For calculate the approximate amount of rotations it would take the monster truck to travel one mile, we need to use the formula:

Number of rotations = Distance traveled / Circumference of the tire

Since the distance traveled is one mile, which is equal to 5280 feet, we need to convert the tire diameter from feet to inches, and then calculate the circumference:

Hence, We get;

Circumference = π x Diameter Circumference

                        = 3.14 x 72 Circumference

                        = 226.08 inches

Now, we can calculate the number of rotations:

Number of rotations = 5280 feet / (12 inches/foot x 226.08 inches/rotation)

Number of rotations = 5280 / 2712.96

Number of rotations ≈ 1.947 rotations

or ≈ 1260 rotations per mile

Therefore, the approximate amount of rotations it would take the monster truck to travel one mile is 1260 rotations.

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Answer:

2

Step-by-step explanation:

2x2-2=2

Answer:

its m=185t

Step-by-step explanation:

because if you divide

An equation which represent the total meters (m) that Sam runs in t minutes is: B. m = 185t.

Mathematically, a proportional relationship can be represented with the following equation or mathematical expression:

m = kt

Where:

Next, we would determine the constant of proportionality (k) for each candy as follows:

From Jacob's running, we have the following:

Constant of proportionality (k) = t/m

Constant of proportionality (k) = 400/2

Constant of proportionality (k) = 200

Since Sam runs 15 meters less each minute than Jacob does, an equation that represent the total meters (m) that he runs in t minutes is given by:

m = (200 - 15)t

m = 185t

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Answer:

  (b)  3 units

Step-by-step explanation:

You want to know the length of OB' when OB = 3/4 and ∆ABC is dilated about point O by a factor of 4.

The dilation factor multiplies every length.

If OB is 3/4, then OB' is 4(3/4) = 3.

The length of OB' is 3 units.

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1. selection of index number: during the construction of index number it is to be kept in mind that the selection of the index number should be correct accordingly.

2. selection of formula: while the construction of index numbers it is compulsory to select the correct formula for the given question.

3. selection of price: selection of prices should be done accordingly while constructing the index numbers.`

construction of index number is also available in two parts:

1. simple

2. weighted

1. simple: the simple method is classified into simple aggregative and simple relative.

2. weighted: the weighted method is classified into a weighted aggregative and weighted average.

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Answer:

7/6 or 1 1/6

Step-by-step explanation:

2/3 = 4/6

1/2 = 3/6

3/6 + 4/6 = 7/6 = 1 1/6

The angle of the T in the ΔRST is 100° and the value of p is 11.

Define Triangle.

A triangle is a polygon that consists of three sides and three vertices. The fact that the interior angles of a triangle add up to 180 degrees is the most crucial aspect of triangles. This characteristic is known as the angle sum property of a triangle.

i.e., In a give ΔABC, ∠A + ∠B + ∠C = 180°.

Given:

∠R = 37°; ∠S = 43°; ∠T = 10p-10°

Let's take ∠T = x

In ΔRST,

∠R + ∠S + ∠T = 180°

37 + 43 + x =  180°

x = 180 - 80 ⇒ 100

∴ ∠T = 100°

To find the value of p,

 ∠T = 100

10p - 10 = 100

10p = 110 ⇒ 11

∴ p = 11

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Answer:

Triangles in Geometry

Step-by-step explanation:

In this simple economy where the market basket for CPI contains two items, the CPI for year 2 is 102.22%.

The CPI means the Consumer Price Index.

The CPI economically indicates the inflationary trend, using a basket of selected consumer goods and services, and computes their total costs for each period.

The base year's total costs set to 100% are used to compare with the current year's.

Price       1 Bottle of     1 Bar of   2 Bars      Total Cost

              Shampoo       Soap     of Soap    Mkt Basket

                    (a)               (b)             (c)          (a) + (c)

Year 1        $6.50           $1.25     $2.50          $9.00

Year 2      $6.60            $1.30     $2.60         $9.20

CPI for Year 1 (base year) = 100% ($9/$9 x 100)

CPI for Year 2 = 102.22% ($9.20/$9 x 100)

Thus, year 2's Consumer Price Index is 102.22%, compared to year 1's.

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Answer:

102.22

Step-by-step explanation:

Edmentum.

Answer:

Required probability = 2 / 11

Step-by-step explanation:

Sample space of 5 person = 11!

One woman one man arrangement = 2!

Arrangement without woman = 10!

Required probability = [2!][10!] / [11!]

Required probability = 2 / 11

The probability that the parents will be standing next to each​ other is 2/11

Probability is the likelihood or chance that an event will occur.

Given a woman, man and their four children, if their parents will be standing next to each other, that makes it 5 people. The sample space for 5 people is 11!

Pr(parents standing next to each other) =  2!10!/11!

Pr(parents standing next to each other) = 2*10!/11*10!

Pr(parents standing next to each other) = 2/11

Therefore the probability that the parents will be standing next to each​ other is 2/11

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Answer:

A

Step-by-step explanation:

if you dont feel right dont pick my answer

Answer:

d = 5 is a solution to the equation 13 - d = 8

Step-by-step explanation:

We have to solve 13 - d = 8

Now,

13 - d = 8,

We add d on both sides,

13 - d + d = 8 + d

13 = 8 + d

we subtract 8 from both sides,

13 - 8 = 8 - 8 + d

5 = d

d = 5

Hence the answer is 5

Answer:

1/2

Step-by-step explanation:

If a dozen donuts is sell for $3.99, then 5 dozen is sell for 5*$3.99 = $19.95.

1 dozen means 12 donuts, then 5 dozen is equivalent to 5*12 = 60 donuts.

Given that the cost to make 3 donuts is $0.45, then we can use the next proportion to find the cost of 60 donuts:

Solving for x,

5 dozen donuts cost $9.00.

Profit is calculated as follows:

Profit = revenue - cost

In this case, the profit on 5-dozen donuts​ is:

Profit = $19.95 - $9.00

Profit = $10.95