if you need 4/5 of a cup for one pie how many do cups do you need for 9

The population of the country by an exponential function which is used to describe the population of a country in millions t years after the 2003 is, 645.4.

Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.

The population model, which describes the population of a country in millions t years after the 2003 is,

[tex]A=645.4 e^{0.001t}[/tex]

For the year 2003 the value of t will be 0 as no year is passed after 20036. Thus,

[tex]A=645.4 e^{0.001\times0}\\A=645.4 e^{0}\\A=645.4(1)\\A=645.4[/tex]

Thus, the population of the country by an exponential function which is used to describe the population of a country in millions t years after the 2003 is, 645.4.

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Answer:

Substitution

Step-by-step explanation:

In your premises, the state AB = BC is given to be true. In math, substitution is taking one value in an equation and "subbing it out for" one that we know has the same value. This means anywhere we see AB, we can substitute BC and the equation will still be true, because AB = BC.

In the example given, that changes AB + BC = AC to AB + AB = AC.

We substituted the AB with BC, because we know that they are of the same value.

Answer:

3x

Step-by-step explanation:

f(x) = x/3

let , y=f(x)

or y=x/3

inter changing x and y, we get,

x=y/3

or, 3x=y. ( cross multiplication)

therefore f-1(x) 3x

Answer:

Step-by-step explanation:

Answer:

See below ~

Step-by-step explanation:

Q3

Q4

#3

Simiilary

#4

And

Answer:

Step-by-step explanation: Après un an on a 20000(1+t%)+20000

Après 2 ans on a 20000(1+t%)^2+20000(1+t%)^1=44298

On a donc 20000[(1+t%)^2+(1+t%)^1]=44298

En résolvant l’équation de second degré dans R, on obtient : t = 7%

Answer:

yes.

Step-by-step explanation:

300>8/9

300>0.888888889

[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]

      Is 300 greater than 8/9?

[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]

Yes, 300 is greater than [tex]\bold{\dfrac{8}{9}}[/tex].

Remember, proper fractions (fractions with a numerator less than the denominator) are less than 1.

When comparing an integer (like 300) with a fraction (like 8/9), first you need to work out whether or not the fraction is a proper fraction.

Then, you also need to pay attention to the signs, because they may seem trivial, but they are in fact highly significant.

Therefore,

300>8/9 (300 is definitely greater than a number less than 1, right?)

(and the ">" sign means "greater than"

       [tex]\rule{200}{2}[/tex]

The height of the ladder far up the wall to the nearest hundredth is 7.52 foot.

A right angle triangle is formed.

A right angle triangle has one of its angles as 90 degrees. The sides and angles can be found using trigonometric ratios.

The length of the ladder is the hypotenuse side of the triangle formed.

Therefore,

sin 70 = opposite / 8

cross multiply

opposite = 8 sin 70

opposite side = 8 × 0.93969262078

opposite side = 7.51754096629

opposite side = 7.52

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Of the 400 students, 120 students like to drink coffee, 80 students like to drink tea, 160 students like both and 40 students do not like any of these drinks.

Cofee: 70% of 400 = 280 students

Tea: 60% of 400 = 240 students

None: 10% of 400= 40 students

This means that 360 students like coffee, tea or both.

280 + 240 (students who drink either coffe or tea)= 520 - 360 (real number of students who like coffee or tea) = 160 (students who like both coffee and tea.

Moreover, it can be inferred 80 students like tea and 120 studetns like coffee.

Outside the sets 40 students who do not like any of the drinks.

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Answer:

Step-by-step explanation:

First things first, let's explain what a right triangle is. The definition is very simple and might even seem obvious for those who already know it: a right-angled triangle is a triangle where one and only one of the angles is exactly 90°. The other two angles will clearly be smaller than the right angle because the sum of all angles in a triangle is always 180°. In a right angled triangle the sides are defined in a special way. The side opposing the right angle is always the biggest in the triangle and receives the name of "hypotenuse". The other two sides are called catheti. The hypotenuse is opposite the right angle and can be solved by using the Pythagorean theorem. In a right triangle with cathetus a and b and with hypotenuse c, Pythagoras' theorem states that: a² + b² = c².

To solve for c, take the square root of both sides to get c = √(b²+a²). This extension of the Pythagorean theorem can be considered as a "hypotenuse formula".

Steps to solve:

[tex]c=\sqrt{a^{2} +b^{2} } \\c=\sqrt{1.3^{2} +6.1^{2} } \\c=\sqrt{1.69+37.21} \\c=\sqrt{38.9} \\c=6.236986[/tex]

Pedro's total distance moved is 7.5 kilometers

The given parameters are:

The total distance is the sum of the above distances i.e.

Total = 1.2 km + 1.5 km + 2 km + 2.8 km

Evaluate

Total = 7.5 km

Hence, Pedro's total distance moved is 7.5 kilometers

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Answer:

  (E) 90°

Step-by-step explanation:

The diagonals of a parallelogram are equal in length if and only if the parallelogram is a rectangle.

Any angle of a rectangle is 90°.

_____

Adjacent angles of a parallelogram are supplementary. If the diagonals are the same length, the triangles formed by either diagonal are congruent with the triangles formed by the other diagonal. This means adjacent angles are congruent. Congruent supplementary angles are 90°.

Answer:

a. the time spent answering homework

b. time finished and time started

c. subtraction

d. 7:20-6:50 (unsure how this is supposed to be laid out)

e. Carlo spent 30 minutes answering his homework

Answer:

x = 18

Step-by-step explanation:

[tex]\sf x - 3x+9= - 27[/tex]

Let's first combine like terms.

[tex] \sf - 2x+9= - 27[/tex]

Subtract 9 from both sides.

[tex]\sf - 2x= - 27 - 9[/tex]

[tex] \sf - 2x= - 36[/tex]

Divide both sides by −2.

[tex]\sf x=18[/tex]

Answer:

Step-by-step explanation:

A={1,2,3}

n(A)=3

B={5,6}

n(B)=2

Answer:

x = 61°

Step-by-step explanation:

(2x + 3)°+ (x - 6)° = 180°

2x + x + 3 - 6 = 180°

3x - 3 = 180°

3x = 180° + 3

3x = 183°

x = 183°/3

x = 61°

The power of a number says how many times to use the number in a multiplication.

--

For instance 6 to the power of 2

This means

Which is also equal to 36

Answer:

answer = 12

Step-by-step explanation:

Let the smallest number be x

So

X+(x+2)+(x+4)+(x+6)=60

4x+12=60

4x=48

X=12

Answer:

  11 units

Step-by-step explanation:

The height of a trapezoid is the distance between the parallel bases.

__

Here, one base lies on the horizontal line y=5, and the other lies on the horizontal line y = -6. The distance between them is ...

  5 -(-6) = 5 +6 = 11

You can also find this distance by counting the grid squares between the two parallel lines.

The height of the trapezoid is 11 units.

_____

Additional comment

The base lengths are ...

  AB = 2 -(-5) = 7

  CD = 8 -(-7) = 15

The area is 1/2(b1 +b2)h = (1/2)(7 +15)(11) = 121 square units.

Answer:

3xy+5z

Step-by-step explanation:

5(xy+z)-2xy

=5xy+5z-2xy

3xy+5z

The linear inequality is represented by the graph will be, y > 3x + 2. Option B is correct.

Linear inequalities involve at least one linear algebraic expression. A polynomial of degree 1 is compared to another algebraic expression of degree less than or equal to 1.

The line is passes through the following points;

(x₁,y₁) to (x₂,y₂)

(-3,-7) to (0,2)

The equation is found as;

[tex]\rm y-y_1 = \frac{y_2-y_1}{x_2-x_1 } (x-x_1)\\\\\ \rm y-(-7) = \frac{(2-(-7))}{(0-(-3))} (x-(-3))\\\\ y+7 =\frac{9}{3} (x+3)\\\\ y+7 = 3x+9 \\\\ y=3x+2[/tex]

The graph because the shading is above the line and does not include the line.

The linear inequality is represented by the graph will be, y > 3x + 2

Hence, option B is correct.

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Answer:

See below

Step-by-step explanation:

Start with  sin x

  amplitude of 5

      5 sin x

      midline 4

          5 sin (x)  + 4

         period of 4

                   2 pi / 4 = pi/2

                5 sin ( x pi/2 ) + 4

The surface area of the square based pyramid is 61.25 centimetre square

surface area of the pyramid = A + 1 /2 ps

where

A = area of the base

p = perimeter of the base

s = slant height

Therefore,

A = 3.5² = 12.25 cm²

p = 4(3.5) = 14 cm

s = 7 cm

Therefore,

surface area of the pyramid = 12.25 + 1 /2 × 14 × 7

surface area of the pyramid = 61.25 cm²

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Based on the responses, the significance level, and the p-value, we can conclude that the response proportions are not the same for the countries.

The null hypothesis is that the response proportions are the same. The alternate hypothesis is that the response proportions are not the same.

The sample size is large enough for a Chi-Square test to be used because the expected counts are all greater than 5.

Running a Chi-Square analysis shows that the P-value to be 0.000.

The P-Value is less than the significance level of 0.01 so the null hypothesis is rejected. This means that the alternate hypothesis of the response proportions not being the same is true.

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Answer:

C

Step-by-step explanation:

Formula to get the area

A = r^2π

A = 16^2π

A= 804.24 cm^2

As per the given data, the approximate area of the shaded sector is 283 square cm, which is option D.

Area is a measure of the amount of space inside a two-dimensional shape or a flat surface. It is typically measured in square units, such as square meters or square feet.

To find the area of the shaded sector, we need to first find the area of the whole circle, and then multiply it by the fraction of the circle that is shaded.

The area of a circle is given by the formula:

A = [tex]\pi r^2[/tex]

Where r is the radius of the circle. In this case, we are given that the radius of the circle is 18 cm, so we can substitute this value into the formula:

A = [tex]\pi 18^2[/tex]

A = 324π

So, the area of the whole circle is 324π square cm.

The shaded sector has a central angle of 100 degrees, which is a fraction of the total central angle of 360 degrees. So, the fraction of the circle that is shaded is:

100° / 360° = 5/18

Therefore, the area of the shaded sector is:

A = (5/18) * 324π

A = 90π

Using 3.14 as an approximation for π, we get:

A ≈ 90 * 3.14

A ≈ 283

Thus, the approximate area of the shaded sector is 283 square cm, which is option D.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathbf{y - 8(y + 12) + 4}[/tex]

[tex]\huge\textbf{Solving:}[/tex]

[tex]\mathbf{y - 8(y + 12) + 4}[/tex]
[tex]\huge\textbf{DISTRIBUTE -8 WITHIN the}\\\\\\\huge\textbf{PARENTHESES:}[/tex]

[tex]\mathbf{= y - 8(y) - 8(12) + 4}[/tex]

[tex]\mathbf{= y - 8y - 96 + 4}[/tex]

[tex]\huge\textbf{COMBINE the LIKE TERMS:}[/tex]

[tex]\mathbf{= (y - 8y) + (-96 + 4)}[/tex]

[tex]\mathbf{= y - 8y - 96 + 4}[/tex]

[tex]\huge\textbf{Simplify it!}[/tex]

[tex]\mathbf{ = -7y - 92}[/tex]

[tex]\huge\textbf{Answer:}[/tex]

[tex]\huge\boxed{\mathbf{ -7y - 92}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Put in the formula

[tex]\\ \rm\Rrightarrow A=P(1+r)^t[/tex]

[tex]\\ \rm\Rrightarrow 7255=6000(1+0.055)^t[/tex]

[tex]\\ \rm\Rrightarrow 1.20917=(1.055)^t[/tex]

[tex]\\ \rm\Rrightarrow ln1.20917=tln1.055[/tex]

[tex]\\ \rm\Rrightarrow t=\dfrac{ln1.20917}{ln1.055}[/tex]

[tex]\\ \rm\Rrightarrow t=3.5years[/tex]

Answer:

4 years (nearest year) or

3.5 years (nearest tenth) or

3 years, 6 months and 17 days (most accurate)

Step-by-step explanation:

Annual Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+r\right)^{t} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for t:

[tex]\implies \sf 7255=6000(1+0.055)^t[/tex]

[tex]\implies \sf 7255=6000(1.055)^t[/tex]

[tex]\implies \sf \dfrac{7255}{6000}=(1.055)^t[/tex]

Take natural logs of both sides:

[tex]\implies \sf \ln \left(\dfrac{7255}{6000}\right)= \ln (1.055)^t[/tex]

[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]

[tex]\implies \sf \ln \left(\dfrac{7255}{6000}\right)= t\ln (1.055)[/tex]

[tex]\implies \sf t=\dfrac{\ln \left(\dfrac{7255}{6000}\right)}{\ln (1.055)}[/tex]

[tex]\sf \implies t=3.547416819...[/tex]

Therefore, the number of years the principal was invested is:

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