For the function f(x) = 2 (x − 1), find ƒ−¹(x).

Answer: 250

Step-by-step explanation: because i got it right

Hence, it will take about 43.28 minutes for the population to reach 12,000 and  there are approximately 7742.85 people in the world after 105 minutes.

A exponential is an exponents or power in mathematics that must be increased from a given denominator to get a certain value. In other words, just as division is the opposite of multiplication,

the logarithm is the greater operating of exponentiation. The base 10-logarithm (written as log) or the beta coefficient (written as ln), which has a baseline of e, the mathematical constant roughly equal to 2.71828, are the two most widely used logarithms.

In many mathematical fields in science, engineering, and technology, logarithms are employed to facilitate calculations and express extremely big or extremely small values.

given

a) The culture's initial size is:

P(0) = [tex]500/e^{15415*15}[/tex]

≈ 98.90

b) We can easily enter t = 105 into the exponential growth model to determine the population after 105 minutes:

P(105)=98.9*[tex]e^{15415*105}[/tex]

≈ 7742.85

Hence, there are approximately 7742.85 people in the world after 105 minutes.

d) To determine the population's peak, we set P(t) = 12000 and solve for t as follows:

1200=98.9*[tex]e^{0.15415t(0.15415t)}[/tex]

By taking the natural logarithm and dividing both sides by 98.90, we arrive at:

ln(12000/98.90) = 0.15415t

To solve for t, we obtain:

t ≈ 43.28

Hence, it will take about 43.28 minutes for the population to reach 12,000 and  there are approximately 7742.85 people in the world after 105 minutes.

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Answer:

x = 29

Step-by-step explanation:

The whole circle is 360°.

Theorem regarding angles inside a circle says that the angle is one half of the arc it encompasses. So m∠S = 0.5 * arc PQR. Also m∠Q = 0.5 * arc PSR.

Think about this, arc PQS + arc RQS = 360°. We have a formula for each of these arc measurements in terms of x.

The arc that corresponds to ∠R is some part of the circle, and the arc that corresponds to ∠P is the other part of the circle.

(5x + 20) + (7x - 8) = 360

12x + 12 = 360

12x = 348

x = 29

Answer:

Step-by-step explanation:

Diameter = 7 cm, Radius = 1/2 diameter = 3,5 cm

Step-by-step explanation:

Radius is the line or length from the center of the circle to the side, and is half the diameter. Diameter is a line from one side of the circle to the other, passing through the center point, and is 2 times the radius. With this information we can see the diameter is 7cm and the radius would be half of that, with 3.5cm being the radius.

If Gopal, Krishna and Govind are partners sharing profits and losses in the ratio of 5 4 3. The gaining ratio will be: (a) 5:3.

Since Krishna is retiring, her share of profit will now be divided between Gopal and Govind in the same ratio as their existing profit-sharing ratio.

The total amount paid to Krishna is 1,20,000. Out of this, Gopal has paid 80,000 and Govind has paid 40,000.

So, the share of profit purchased by Gopal is:

5/12 x 120,000 = 50,000

And the share of profit purchased by Govind is:

3/12 x 120,000 = 30,000

Now, the total profit sharing ratio of the remaining partners (Gopal and Govind) will be:

5:3 + 3:3 = 8:3

Therefore, the gaining ratio will be:

Gopal = 50,000 / (50,000 + 30,000) = 5/8

Govind = 30,000 / (50,000 + 30,000) = 3/8

So, the gaining ratio of Gopal and Govind will be 5:3, which is option (a).

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Answer:

-79

Step-by-step explanation:

-7(x+6) + 12                       x = 7

-7( 7 + 6) + 12

-7(13) + 12

-91 + 12

-79

So, the answer is -79

The surface area of the rectangular prism with dimensions of 12 ft, 14 ft, and 20 ft is 1376 square feet.

What is surface area?

The area is the space occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.

To find the surface area of a rectangular prism with dimensions of 12 ft, 14 ft, and 20 ft, we need to calculate the area of each face and then add them together.

First, let's calculate the area of the top and bottom faces, which are both rectangles with dimensions of 12 ft by 20 ft:

Area of top and bottom faces = 2 x (12 ft x 20 ft) = 480 square feet

Next, let's calculate the area of the front and back faces, which are both rectangles with dimensions of 12 ft by 14 ft:

Area of front and back faces = 2 x (12 ft x 14 ft) = 336 square feet

Finally, let's calculate the area of the left and right faces, which are both rectangles with dimensions of 14 ft by 20 ft:

Area of left and right faces = 2 x (14 ft x 20 ft) = 560 square feet

To find the total surface area, we add up the area of all six faces:

Total surface area = Area of top and bottom faces + Area of front and back faces + Area of left and right faces

Total surface area = 480 sq ft + 336 sq ft + 560 sq ft = 1376 sq ft

Therefore, the surface area of the rectangular prism with dimensions of 12 ft, 14 ft, and 20 ft is 1376 square feet.

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Answer:

-12

Step-by-step explanation:

g(x)=3x,h(x)= x²-4

(g•h)(0)=g(h(0))

=g(0²-4)

=g(-4)

=3×(-4)

=-12

The measures of the angles are:

m ∠GAL = 90°

m ∠LAO = 71°

m ∠CAO = 109°

m ∠KAC = 71°

From the question, we are to determine the measure of the angles

m ∠GAL = 90° (Right angle)

m ∠LAO

m ∠LAO + m ∠GAL + 19° = 180° (Sum of angles on a straight line)

m ∠LAO + 90° + 19° = 180°

m ∠LAO = 180° - 90° - 19°

m ∠LAO = 90° - 19°

m ∠LAO = 71°

m ∠CAO

m ∠CAO = m ∠KAL (Vertically opposite angles)

m ∠KAL = m ∠GAL + 19°

m ∠KAL = 90° + 19°

m ∠KAL = 109°

Therefore,

m ∠CAO = 109°

m ∠KAC = m ∠LAO (Vertically opposite angles)

m ∠LAO = 71°

Therefore,

m ∠KAC = 71°

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or Part A, we can use the formula for confidence intervals:

CI = p ± Zsqrt((pq)/n)

where p is the proportion of almonds found in the sample (13/100 = 0.13), q is 1-p, Z is the z-value for a 99% confidence level (2.576), and n is the sample size (100). Plugging in these values, we get:

CI = 0.13 ± 2.576sqrt((0.130.87)/100)

which simplifies to:

CI = (0.045, 0.215)

Therefore, we are 99% confident that the true proportion of almonds in the population of planters mixed nuts is between 0.045 and 0.215.

For Part B, we can use the Central Limit Theorem to assume normality if the sample size is large enough. Since n = 100 is greater than or equal to 30, we can assume normality.

For Part C, we can use the formula n = (Z^2 p q) / E^2 to calculate the sample size needed. Here, Z is the z-value for a 99% confidence level (2.576), p is the estimated proportion of almonds (0.13), q is 1-p, and E is the maximum error of the estimate in decimal form (0.05). Plugging in these values, we get:

n = (2.576^2 0.13 0.87) / 0.05^2

which simplifies to approximately 276. Therefore, a sample size of at least 276 planters mixed nuts would be needed to estimate the true proportion of almonds with 99% confidence and an error of 0.05

Answer:

  $7734.82

Step-by-step explanation:

You want to know the amount that will result in $20,000 after 20 years when 4.75% interest is compounded continuously.

The formula for account value is ...

  A = P·e^(rt)

We want to find P when A=20,000, r=0.0475, and t=20.

  20000 = P·e^(0.0475·20)

  P = 20000·e^(-0.0475·20) ≈ 7734.82

You would have to deposit $7734.82 in the account to have $20,000 in 20 years.

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Answer:

We can use the definition of tangent to find the value of \tan\theta. Tangent is defined as the ratio of the opposite side to the adjacent side in a right triangle.

To find the value of \tan\theta, we need to first find the values of the adjacent and opposite sides of the triangle. We know that the terminal side of angle \theta passes through the point (-8,9) in the Cartesian plane. This means that the coordinates of the endpoint of the terminal side are (-8,9).

We can now draw a right triangle with the hypotenuse as the terminal side of angle \theta, and the adjacent and opposite sides as the x and y coordinates of the endpoint of the terminal side. We can use the Pythagorean theorem to find the length of the hypotenuse.

The length of the adjacent side is -8 (since it is to the left of the origin) and the length of the opposite side is 9 (since it is above the origin). Therefore, we have:

adjacent = -8

opposite = 9

hypotenuse = \sqrt{(-8)^2 + 9^2} = \sqrt{64 + 81} = \sqrt{145}

Now we can use the definition of tangent to find the value of \tan\theta:

\tan\theta = \frac{opposite}{adjacent} = \frac{9}{-8} = -\frac{9}{8}

Therefore, the exact value of \tan\theta is -\frac{9}{8} in simplest radical form.

The value of x that satisfies the equation log(2x) = 2 is 50, which is obtained by applying the definition of logarithms and simplifying the resulting equation.

The given equation is log(2x) = 2. To solve this equation for x, we first use the definition of logarithms, which states that log(base a)(b) = c is equivalent to [tex]a^c = b[/tex]. In this case, the base of the logarithm is not specified, so we assume it is base 10.

To solve for x in the equation log(2x) = 2, we first need to use the definition of logarithms, which states that log(base a)(b) = c is equivalent to [tex]a^c = b[/tex].

In this case, we have:

log(2x) = 2

Using the definition of logarithms, we can rewrite this as:

[tex]10^2 = 2x[/tex]

Simplifying, we get:

100 = 2x

Dividing both sides by 2, we get:

50 = x

Therefore, the value of x that satisfies the equation log(2x) = 2 is 50.

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Answer:

1.6

Step-by-step explanation:

it is this one trust me

Answer:

f(g(x))=3x+8

g(f(x))=3x-2

Step-by-step explanation:

f(x)=3x-7, g(x)=x+5

f(g(x))=f(x+5)

=3(x+5)-7

=3x+15-7

=3x+8

g(f(x))=g(3x-7)

=3x-7+5

=3x-2

The measure of minor arc UT is equal to the measure of angle UWT, which is half the central angle ZWT. The measure of sector UST is equal to the measure of central angle ZST, which is 2*34 - 112 = -44 degrees. The measure of major arc UT is 360 - 17 = 343 degrees and the measure of segment UST is 343 - 316 = 27 degrees.

A circle is a geometric shape that consists of all the points in a plane that are equidistant from a given point called the center. It is a perfectly round shape and has a constant diameter, which is the distance between any two points on the circle passing through the center.

Given information:

Circle Z

VZ = ZW (equal chords)

SV = 21

m = 112

To find:

UT

WT

ST

Measure of minor arc UT

Measure of sector UST

Since VZ = ZW, we can conclude that SZ is the perpendicular bisector of VW. Therefore, SV = SW = 21.

a) Using the theorem of the perpendicular bisector, we can say that UT = WT = (1/2)VW. Since VZ = ZW, we have VW = VZ + ZW = 2VZ. Therefore, UT = WT = (1/2)2VZ = VZ = 2.

b) Similarly, WT = VZ = 2.

c) Since SV = SW, we can say that ST = SW - TW = 21 - WT = 21 - 2 = 19.

d) The measure of minor arc UT is equal to the measure of angle UWT, which is half the measure of the central angle ZWT. Since VZ = ZW, the central angle ZVW is an isosceles triangle, and the measure of angle ZVW is (180 - 112)/2 = 34 degrees. Therefore, the measure of minor arc UT is 1/2 * 34 = 17 degrees.

e) The measure of sector UST is equal to the measure of central angle ZST. Since VZ = ZW, the central angle ZVW is an isosceles triangle, and the measure of angle ZVW is (180 - 112)/2 = 34 degrees. Therefore, the measure of central angle ZST is 2*34 - 112 = -44 degrees (measured counterclockwise from ZV). However, since angles are usually measured in the range 0 to 360 degrees, we can add 360 to -44 to get 316 degrees. Therefore, the measure of sector UST is 316 degrees.

f) We have already found the measures of minor arc UT and sector UST. Therefore, we can say that the measure of major arc UT is 360 - 17 = 343 degrees, and the measure of segment UST is 343 - 316 = 27 degrees.

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Since the dividend per share is computed as Quarterly Dividend Payment / Shares, $1.52 is the yearly dividend for each share of Merck.

One of the four crucial steps in the division process is the dividend. It is necessary to divide the entire into several equal sections. For instance, if the result of the division of 10 by 2 is 5, then 10 is the dividend, which is split into two equal pieces, and 2 is the divisor. The result of the division is 5, the quotient, and the remainder is 0.

Given: The following steps can be taken in order to obtain the dividend per share for the quarterly payment:

Dividend per share is determined using the formula Quarter Dividend Payment / Shares.

The dividend equals $0.38 per share when $1,140 is divided by 3,000 shares.

To calculate the annual dividend per share, multiply the dividend paid every three months per share times the number of quarters in a year:

The annual dividend per share is equal to the quarter dividend per company multiplied by the total number of quarters in a year.

The annual dividend per share is calculated as $0.38 multiplied by four quarters, or $1.52 per share.

Since the calculation for the dividend per share is Periodic Dividend Payment / Shares, the annual dividend for each share of Merck is $1.52.

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The rate of inflation used to make this calculation is 4%

The equation

y = 100(0.96)^x

represents the purchasing power of $100 after x years of inflation. In this equation, 0.96 is the inflation rate.

This means that the purchasing power of $100 decreases by 4% each year due to inflation.

To understand this better, let's take an example. Suppose you have $100 today and the inflation rate is 4%. This means that the purchasing power of $100 will be reduced by 4% after one year. So, after one year, the value of $100 will be $96. If the inflation rate remains the same, after two years, the value of

$100 will be $92.16 ($96 * 0.96)  and so on.

It is important to note that inflation rates can vary over time and across countries, and can have a significant impact on the economy and the purchasing power of consumers. Understanding inflation and its effects is crucial for making informed financial decisions.

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GF preserves the identity and addition operations, and hence GF: V→U is an isomorphism.

First, we will show that GF is linear. Let u, v be vectors in V and c be a scalar in K. Then we have:

[tex]GF(cu + v) = G(F(cu + v)) = G(cF(u) + F(v)) = G(cF(u)) + G(F(v))= cG(F(u)) + G(F(v)) = c(GF(u)) + GF(v)[/tex]

Thus, GF is linear.

Next, we will show that GF is bijective. Since F and G are isomorphisms, they are both invertible. Let[tex]F^-1[/tex]and [tex]G^-1[/tex] denote their respective inverses. Then for any u in U, we have:

[tex](GF)^-1(u) = F^-1(G^-1(u))[/tex]

This shows that GF is invertible, and hence bijective.

Finally, we will show that GF preserves the identity and addition operations. Let v1, v2 be vectors in V. Then we have:

[tex]GF(v1 + v2) = G(F(v1 + v2)) = G(F(v1) + F(v2)) = G(F(v1)) + G(F(v2))= GF(v1) + GF(v2)[/tex]

Also, since F and G are isomorphisms, they preserve the identity operations:

[tex]GF(0v) = G(F(0v)) = G(0w) = 0u\\GF(v) = G(F(v)) = G(0w) = 0u if v=0v[/tex]

Thus, GF preserves the identity and addition operations, and hence GF: V→U is an isomorphism.

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The blend of minimum cost with an octane rating of at least 90 is 11.11% type A gasoline and 55.56% type B gasoline, with a cost per liter of $0.6917.

What is the blend of minimum cost with an octane rating of at least 90?

Let x be the fraction of type A gasoline and y be the fraction of type B gasoline in the blend.

Since we want the blend to have an octane rating of at least 90, we can set up the following equation:

80x + 92y ≥ 90(x + y)

Simplifying this equation,

10x ≥ 2y

y ≤ 5x

We also want to minimize the cost of the blend, which can be expressed as 0.83x + 0.98y

Now we can use the inequalities we've established to find the minimum cost.

We know that y ≤ 5x

So we can substitute y = 5x into the cost equation 0.83x + 0.98(5x)

Simplifying and we get,

5.85x

This is the cost per liter of the blend, so we want to minimize this expression. To do so, we can use calculus and take the derivative with respect to x,

d/dx (5.85x) = 5.85

Setting this equal to zero to find the minimum value of the expression, we get:

5.85 = 0

This is not possible, so we know that the minimum value occurs at the boundary of the feasible region. That is, either x = 0 or y = 5x.

If x = 0, then the cost per liter is simply 0.98y, which we want to minimize subject to the constraint that 92y ≥ 90y, or y ≥ 45. We also have the constraint that y ≤ 1 (since we can't have more than 100% type B gasoline in the blend). So the minimum cost occurs when y = 1, and the cost per liter is 0.98.

If y = 5x, then the cost per liter is 0.83x + 4.9x = 5.73x. We want to minimize this subject to the constraints that 80x + 460x ≥ 90(1 + 4x), or x ≥ 0.0278, and that x ≤ 1. We can also use the inequality y ≤ 1 to get,

5x ≤ 1

x ≤ 0.2

So the feasible range for x is 0.0278 ≤ x ≤ 0.2. We can now calculate the cost of the blend for each value of x in this range and choose the minimum. This is a straightforward calculation, and we find that the minimum cost occurs when x = 0.1111 and y = 0.5556, and the cost per liter is $0.6917.

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Answer:

Step-by-step explanation:

Let's denote the time that Adrian traveled on the bike at 13 mph by "t" and the time that he walked at 3 mph by "9 - t" (since the total trip took 9 hours).

Since we know that the total distance traveled was 87 miles, we can write the equation:

distance traveled on bike + distance traveled walking = 87

Using the formula distance = rate x time, we can express the distance traveled on the bike and walking in terms of time:

13t + 3(9 - t) = 87

Simplifying this equation:

13t + 27 - 3t = 87

10t = 60

t = 6

Therefore, Adrian traveled on the bike for 6 hours (at 13 mph) and walked for 3 hours (at 3 mph).

Therefore, A grain silo has a cylindrical shape the answer is: 12,689 ft³ (cubic feet).

Percentage is a way of expressing a proportion or a part of a whole as a fraction of 100. It is represented by the symbol % (per cent), which means "per hundred". For example, if you say that 50% of a group of 100 people like chocolate, it means that 50 out of 100 people or 0.5 (50/100) of the total group like chocolate. Percentages are commonly used in many fields, including finance, business, mathematics, and statistics.

The formula for the volume of a cylinder is:

V = π[tex]r^{2}[/tex]h

where V is the volume, r is the radius, and h is the height.

Substituting the given values, we get:

[tex]V = 3.14 *9^2 *49[/tex]

[tex]V = 12,689.46[/tex]

Rounding to the nearest whole number, the volume of the silo is approximately 12,689 cubic feet.

Therefore, the answer is:

12,689 ft³ (cubic feet)

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Answer:

Try restarting your computer or using a different web browser

Step-by-step explanation:

Blank #1: 6
Blank #2: 2

Answer:

1.P(9,then 3) = (1/10)*(1/10)=1/100

Step-by-step explanation:

hope it helps and no explanation

the company can pack 224 basketballs into each truck.

To calculate the number of basketballs that can be packed into the truck

Number of basketballs = Volume of truck / Volume of each basketball package

first calculate the volume of the truck

The volume of the truck is:

Volume = Length x Width x Height

Volume = 10.5 ft x 8 ft x 9 ft

Volume = 756 cubic feet

The volume of each basketball package  is:

Volume = Side x Side x Side

Volume = 1.5 ft x 1.5 ft x 1.5 ft

Volume = 3.375 cubic feet

Now, we can calculate the number of basketballs :

Number of basketballs = Volume of truck / Volume of each basketball package

Number of basketballs = 756 cubic feet / 3.375 cubic feet

Number of basketballs = 224

Therefore, the company can pack 224 basketballs into each truck.

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Since Olivia's fruit salad contains more apples than Amadou's, it will have a more apple-like flavour based on percent laws.

We must compute the percent of apples in each fruit salad in order to determine which salad will taste most apple-like.

Nine cups of melon plus ten cups of apples equals 19 cups of fruit in Amadou's fruit salad. Therefore, the fruit salad Amadou made contains:

10 cups of apples divided by 19 cups of fruit equals 100% of the percentage of apples in Amadou's fruit salad, or 52.63%.

2 cups of melon and 3 cups of apples total 5 cups of fruit for Olivia's fruit salad. So, there are: in Olivia's fruit salad.

3 cups of apples divided by 5 cups of fruit equals 100% of the percentage of apples in Olivia's fruit salad, which comes out to 60%.

When we compare the percentage of apples in the two fruit salads, we can observe that Olivia's salad contains more apples than Amadou's. Olivia's fruit salad will therefore taste more apple-like.

In conclusion, we can figure out which fruit salad will taste more appley by figuring out the percentage of apples in each salad. As there are more apples in Olivia's fruit salad than in Amadou's, it will taste more apple-like.

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Answer:

103.34 degrees

Step-by-step explanation:

The sum of angles in a triangle always equals 180 degrees. In other words, 40+(2x-30)+(x+20) = 180. Next, add the figures in both brackets so it becomes (2x-30+x+20), and then group like terms. (2x+x-30-20) which is 3x -50, because -30-20 is -50. The whole equation becomes 40+3x-50 = 180.

Group like terms again, so it becomes 30-50+3x = 180 which is -20+3x=180. Group like terms again but move the -20 to the side of the 180, and since it crosses the equal to sign, the - becomes + so it's 3x=180+20, resulting in 3x=200. Now to make x stand alone, we divide both sides by 3. 3x/3 is x and 200/3 is 66.6 recurring or 66.67. Now we know that x = 66.67, we substitute it in the formula for the angle at B. It becomes (2 times 66.67-30) which is 133.34 - 30, which becomes 103.34 as the answer. If told to round, it becomes 103 degrees.

Answer:

3

Step-by-step explanation:

If blue, then 60%. 2/5 are red and 1/3 are blue. Two redfish and three bluefish are present. if the aquarium has 1 fewer redfish than bluefish. 60% of the fish are blue. There are 5 out of 3 blue fish in the aquarium.

y(y + 5) = 750, y² – 5y = 750, y(y – 5) + 750 = 0 are the equations that can be used to solve for y, the length of the room.

It is used to measure the size of two-dimensional shapes, such as circles, rectangles, and triangles, and is also used to measure the surface area of three-dimensional shapes, such as cubes, pyramids, and cylinders.

Option 1: y(y + 5) = 750

This equation can be used to solve for y, the length of the room. The area of a rectangular room is equal to the product of its length and width. Therefore, the equation for the area of the room can be expressed as Area = Length x Width.

Substituting y for Length and y+5 for Width, yields Area = y(y+5). Rearranging this equation to solve for y, yields y(y+5) = 750.

Option 2: y² – 5y = 750

This equation can be used to solve for y, the length of the room. This equation can be derived by substituting y for Length and y+5 for Width in the equation Area = Length x Width.

Rearranging this equation yields Area = y² – 5y. Substituting this equation with the given area of 750, yields y² – 5y = 750.

Option 3: y(y – 5) + 750 = 0

This equation can also be used to solve for y, the length of the room. This equation can be derived by substituting y for Length and y+5 for Width in the equation Area = Length x Width.

Rearranging this equation yields Area = y(y – 5).

To find the length of the room, the given area of 750 must be added to both sides of the equation. This yields y(y – 5) + 750 = 0.

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