What would be the inverse of the equation

y=log(1/4)x^5

On solving the linear equation in two variables, the duration of Plan A workout is 1.5 hours and the duration of Plan B workout is 2 hours.

According to the question, the total hours of Plan A workouts on Friday and Saturday are (8 + 2) = 10,

and the total hours of Plan B workouts are (3 + 5) = 8.

If the duration of Plan A workout is "x" hours, then the duration of Plan B workout is "y" hours.

According to the question, the total hours spent in Plan A workouts is 10, and the total hours spent in Plan B workouts is 8. So, we can write two equations as:

8x + 3y = 1510x + 5y = 8By

solving these equations, we get:

x = 1.5y = 2

Therefore, the duration of Plan A workout is 1.5 hours, and the duration of Plan B workout is 2 hours.

Therefore, the answer is: Duration of Plan A workout is 1.5 hours and that of Plan B workout is 2 hours

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Answer:

f^4 g^8

Step-by-step explanation:

(F^1g^2)^4

Js multiply the exponent by  the one outside so 1x4=4

n 2x4=8

so the answer would be f^4 g^8

The probability of Bob and Joan's fourth child having sickle cell disease, given that their first three children are healthy, is 6.25%.

When Bob and Joan have children, each child has a 25% chance of inheriting two copies of the sickle cell gene and thus developing the disease, a 50% chance of inheriting one copy of the sickle cell gene and being a carrier like their parents, and a 25% chance of inheriting two copies of the normal gene and not carrying the disease.

To understand this probability calculation mathematically, we can use the laws of probability. We can define the probability of the fourth child inheriting the sickle cell gene as P(s), and the probability of the fourth child inheriting the normal gene as P(n).

Since Bob and Joan are each heterozygous carriers for the sickle cell gene, we know that P(s) = 0.25 (25%), and P(n) = 0.75 (75%). We can use the multiplication rule of probability to calculate the probability of their fourth child inheriting two copies of the sickle cell gene, which is:

P(sickle cell disease) = P(s) x P(s) = 0.25 x 0.25 = 0.0625 or 6.25%

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Complete Question:

Bob and Joan know from a blood test that they are each heterozygous (carriers) for the autosomal recessive gene that causes sickle cell disease. If their first three children are healthy, what is the probability that their fourth child will have the disease?

The length of BD is 25.06 mm

The six trigonometric functions of an angle in a right-angled triangle are related by a set of fundamental identities in trigonometry known as the Circle identities.

Given that,

AC = 22 mm and OE = 6 mm

So, AE = AC/2

Then AC = 11 mm

Therefore, OA is a radius then,

By Pythagoras theorem,

OA² = AE² + OE²

AO² = 11² + 6² = 121+36

AO² = 157

AO = √157 = 12.53 ( radius )

Then , BD = 2 * radius = 2 * 12.53 = 25.06 mm

Therefore, the length of BD is 25.06 mm

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Thus, the area of the rectangular face of the phone is found to be:

Area = 200 sq. in.

Due to the diversity of shapes seen in geometry, geometry is also referred to as the study of shapes.

Dimensions of the face of rectangular face of phone:

Length = 20 inches

width =  10 inches

Area = length x width

Area = 20 x 10

Area = 200 sq. in.

Thus, the area of the rectangular face of the phone is found to be:

Area = 200 sq. in.

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Complete question:

The top face of a phone is a rectangle measuring 20 inches by 10 inches. find the area of the face of the phone.

The time at which the population reaches 4,000 is t ≈ 2.51 hours after 12 pm or approximately 2:30 pm. A) The growth constant can be found using the formula for exponential growth:

$-N = N_0 e^{kt}$

where N₀ is the initial population, N is the final population, t is the time elapsed, and k is the growth constant.

Using the given information, we can set up two equations:

500 = N₀e^(0k)

1500 = N₀e^(2k)

Dividing the second equation by the first, we get:

3 = e^(2k)

Taking the natural logarithm of both sides, we get:

ln(3) = 2k

Therefore, the growth constant k is (ln(3))/2, approximately 0.549.

The population as a function of time can now be expressed as:

N(t) = 500e^(0.549t)

B) To find the population at 5 pm, we need to substitute t = 5 into the equation we found in part A:

N(5) = 500e^(0.549*5) ≈ 4,206

Therefore, the population at 5 pm is approximately 4,206 bacteria.

C) To find the time the population reaches 4,000, we need to solve the equation N(t) = 4,000 for t:

4,000 = 500e^(0.549t)

Dividing both sides by 500, we get:

8 = e^(0.549t)

Taking the natural logarithm of both sides, we get:

ln(8) = 0.549t

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Therefore , the solution of the given problem of angles comes out to be the regular polygon has a 230 centimeter circumference.

The largest and smallest walls of a skew are determined by the point at which the lines that make up its ends meet. At a junction, it's possible that two routes will cross. Another result of two objects interacting is an angle. They most closely resemble dihedral shapes. Two line beams can be arranged in a variety of ways between their extremities to form a two-dimensional curve.

Here,

All of the edges and angles make up a regular polygon. If a regular polygon's exterior angle is 18 degrees, then the internal angle is:

180 minus the external angle is the interior angle.

180 degrees minus 18 degrees is the interior angle.

Angle inside equals 162 degrees

Sum of internal angles is equal to (n - 2)°, or 180°.

=> (n - 2) × 180 = n × 162

When we simplify and solve for n, we obtain:

=> 180n - 360 = 162n

=> 18n = 360

=> n = 20

The regular polygon in the example has 20 edges.

Given that the length of each side is 11.5 centimeters, the polygon's circumference is as follows:

Circumference is equal to the sum of the lengths of all the edges.

=> Circumference = 20.1 centimeters.

=> 230 centimeters is the circumference.

Consequently, the regular polygon has a 230 centimeter circumference.

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During the sale, the stereo system was sold for 30% less than its original price of $710, so the discount amount was:

0.30 x $710 = $213

Therefore, the sale price of the stereo system was:

$710 - $213 = $497

After the sale, the discounted price of $497 was marked up by 30%. The markup amount is:

0.30 x $497 = $149.10

So the final price of the stereo system after the markup is:

$497 + $149.10 = $646.10

Therefore, the price of the stereo system after the markup is $646.10.

Answer:

a diagonal?

Step-by-step explanation:

Therefore, the area of the trapezoid is 84cm².

A trapezoid (also known as a trapezium) is a four-sided geometric shape with two parallel sides and two non-parallel sides that meet at two endpoints. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs. The distance between the two bases is the height of the trapezoid. The formula for finding the area of a trapezoid is (base1 + base2) x height / 2. The formula for finding the perimeter of a trapezoid is the sum of the lengths of all four sides.

To find the area of a trapezoid, you can use the formula:

[tex]A = (B1 + B2) * h / 2[/tex]

where A is the area of the trapezoid, B1 and B2 are the lengths of the parallel sides (also called bases), and h is the height (the perpendicular distance between the bases).

Using the values, you provided:

[tex]B1 = 8cm\\B2 = 16cm\\h = 7cm[/tex]

Plugging these values into the formula, we get:

[tex]A = (8cm + 16cm) * 7cm / 2[/tex]

[tex]A = 24cm * 7cm / 2[/tex]

[tex]A = 168/2cm^{2}[/tex]

[tex]A = 84cm^{2}[/tex]

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the value of f(5) is 10, which is option (b) ,  the value of f(-2) is -12, which is option (d).  To find the value of f(5) using synthetic substitution, we first set up the synthetic division table as follows:

5 | 3  -9  -20

   |||___

   |   |   |

We write the coefficients of the polynomial in the top row of the table and the root (in this case, 5) outside the division symbol. We then bring down the first coefficient (3) and multiply it by the root to get 15, which we write below the second coefficient (-9). We add 15 and -9 to get 6, which we then multiply by the root to get 30, which we write below the third coefficient (-20). We add 30 and -20 to get 10, which is the remainder. Therefore, the value of f(5) is 10, which is option (b).

6) To find f(-2) using synthetic substitution, we set up the synthetic division table as follows:

-2 | 1   0   8   24

  |_|||

  |    |   |   |

We write the coefficients of the polynomial in the top row of the table and the root (in this case, -2) outside the division symbol. We then bring down the first coefficient (1) and multiply it by the root to get -2, which we write below the second coefficient (0). We add -2 and 0 to get -2, which we then multiply by the root to get 4, which we write below the third coefficient (8). We add 4 and 8 to get 12, which we then multiply by the root to get -24, which we write below the fourth coefficient (24). We add 12 and -24 to get -12, which is the remainder. Therefore, the value of f(-2) is -12, which is option (d).

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The lengths of the altitude "a", the line segment "b", and the diagonal "c" of the regular hexagon are: a = 3, b = 3√3, c = 6√3.

Since the hexagon is regular, all six sides are congruent to each other, and all six angles are congruent to each other. Let's call the length of each side "s".

To find the length of the altitude "a", we can draw a perpendicular bisector from the center of the hexagon to one of the sides. This bisector will bisect the side into two segments of length "s/2", and it will also form a right triangle with "a" as the altitude and "s/2" as one of the legs. Using the Pythagorean theorem, we can solve for "a":

[tex]a^2 + b^2 = 6^2\\a^2 = 6^2 - b^2[/tex]

To find the length of "b", we can draw one of the radii from the center of the hexagon to a vertex. This radius will bisect the angle at the vertex and also bisect the opposite side. This will form two right triangles, each with one leg of length "s/2" and one acute angle of 30 degrees. Using trigonometry, we can solve for "b":

cos(30) = b/6

√3/2 = b/6

b = 3√3

Sin 30 = a/6

1/2 = a/6

a = 3

c = b + b =  3√3 +  3√3 = 6√3

Therefore, the lengths of the altitude "a", the line segment "b", and the diagonal "c" of the regular hexagon are:

a = 3

b = 3√3

c = 6√3

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The value of a is obtained as 7, for the given expression, obtained using the scientific notations.

Numbers that are either too little or too huge to put in conventional decimal form can be expressed using scientific notation. Scientific notation is often known as standard index form simply scientific form among experts.

This notation is frequently used in the work of engineers, mathematicians, and scientists to make it considerably simpler to write large numbers. By using the "SCI" display option on the calculator, you can utilise scientific notation when using one.

The given number is:

63,000,000,000

Write the number in its scientific notation:

6.3 x 10¹⁰

Comparable number is 6.3 x 10³ which is 10ᵃ times larger than the 6.3 x 10¹⁰.

Dividing:

=  6.3 x 10¹⁰ / 6.3 x 10³

= 10⁷

Now, 10⁷ = 10ᵃ

As the base is same , thus the value of a = 7.

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Answer:

50.3

Step-by-step explanation:

Area of circle: pi*r ^2

the problem tells us that r =4 and that pi = 3.142

so,

its (4^2) * 3.142 or 50.3 (rounded)

~ lmk if u got Qs

Answer:

Step-by-step explanation:

Answer: 34 tins

If there were 35 tins then this would be rounded up to 40 tins. So 34 is the highest number that will be rounded to 30.

The largest possible amount of tins in the box is 34.

Although the term "rounding" is a general one, we typically use the terms "round up" or "round down" to indicate whether the number has gone up or down after being rounded. The supplied number is said to be rounded up when the rounded number is increased, and it is said to be rounded down when the rounded number is dropped.

We have,

A box contains 30 tins of beans (to the nearest 10).

Now, we know to round off we need to focus that whether the number is greater than 5 or less than 5.

If greater than 5 than round of to next number otherwise round off to previous number.

Here, the largest number of tins can be 34 because greater than 34 leads to round off 40.

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The equation of the straight line is y = -2x - 4, the value of x₁ is -1 and the value of y₁ is -2.

To find the equation of a straight line given its slope and one point, we use the point-slope form of the equation:

−y − y₁​ = m(x−x₁ )

where m is the slope of the line, and (x₁, y₁) is the given point.

In this case, m = -2 and the point is (-1, -2). So we have:

x₁ = -1

y₁ = -2

m = -2

Substituting these values into the point-slope form, we get:

y−(−2)=−2(x−(−1))

Simplifying and rearranging terms, we get the equation of the line:

y + 2 = -2x - 2

y = -2x - 4

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The range stays 48°.

To determine how the range changes when a value of 80.4° is added, we need to follow these steps:
Identify the minimum and maximum values in the original data set.
Calculate the original range by subtracting the minimum value from the maximum value.
Add the new value (80.4°) to the data set.
Identify the new minimum and maximum values.
Calculate the new range.
Compare the original and new ranges.

The minimum value is 57°, and the maximum value is 105°.
The original range is 105° - 57° = 48°.
Add the new value: [58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57, 80.4].
The new minimum value is still 57°, and the new maximum value remains 105°.
The new range is still 105° - 57° = 48°.
Since the original range and the new range are both 48°, the range does not change.
The range stays 48°.

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Use differentials to estimate the amount of metal in a closed cylindrical can with diameter 10 cm and height 15 cm if the metal is 0.1 cm thick.Therefore, the estimated amount of metal in the can is 0.001416.

To estimate the amount of metal in a closed cylindrical can with diameter 10 cm and height 15 cm if the metal is 0.1 cm thick, we can use differentials.

First, let's calculate the volume of the can. The volume of a cylinder is calculated by the formula

[tex]V = πr^{2} h,[/tex]

where r is the radius of the cylinder, and h is its height.

In this case, the radius is 5 cm and the height is 15 cm, so the volume of the can is

[tex]V = π x (5 cm)^{2}  x 15 cm = 707.1 cm^{3}[/tex]

Next, we need to calculate the volume of the metal. The volume of a rectangular prism is

V = l x w x h,

where l is the length, w is the width, and h is the height. In this case, the length and width are both 10 cm, and the height is 0.1 cm, so the volume of the metal is

[tex]V = 10 cm x 10 cm x 0.1 cm = 1 cm^{3}[/tex]

Finally, we can calculate the amount of metal in the can by dividing the volume of the metal by the volume of the can:

[tex]1 cm^{3} / 707.1 cm^{3}  = 0.001416.[/tex]

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Answer: 11 1/3 gallons of lemonade

Answer:

A

Step-by-step explanation:

He shouldn't of added the "^1" to c because its changed the value to c^5 in the final step when it should really be c^4

Answer:

D

Step-by-step explanation:

The sin is equal to the opposite of the chord

Answer:

x = 2

x = 1/2

Step-by-step explanation:

To solve the given equation (x-2)(2x-1) = 0, we need to find the values of 'x' that make the left-hand side of the equation equal to zero. For this, we need to use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.

Using the zero product property, we can set each factor equal to zero and solve for 'x'.

First factor: x - 2 = 0

Adding 2 to both sides, we get:

x = 2

Second factor: 2x - 1 = 0

Adding 1 to both sides, we get:

2x = 1

Dividing by 2 on both sides, we get:

x = 1/2

Therefore, the solutions to the given equation (x-2)(2x-1) = 0 are x = 2 and x = 1/2.

We can verify our solutions by plugging them back into the original equation and checking if the left-hand side equals zero.

When x = 2, we have:

(x-2)(2x-1) = (2-2)(2(2)-1) = 0, which is true.

When x = 1/2, we have:

(x-2)(2x-1) = (1/2-2)(2(1/2)-1) = (-3/2)(0) = 0, which is also true.

Therefore, our solutions are correct.

FYI, you could've also multiplied the polynomials to get a quadratic equation, though this is terribly inefficient for this case.

Answer:

In short, to solve the equation (x-2)(2x-1) = 0, we use the zero product property by setting each factor equal to zero and solving for x. The solutions are x = 2 and x = 1/2.

Step-by-step explanation:

The equation (x-2)(2x-1) = 0 can be solved by finding the values of x that make the left-hand side of the equation equal to zero.

To do this, we can use the zero product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero.

Therefore, we set each factor equal to zero and solve for x:

x-2 = 0 or 2x-1 = 0

Solving each equation for x, we get:

x = 2 or x = 1/2

So the solutions to the equation (x-2)(2x-1) = 0 are x = 2 and x = 1/2.

The brief storytelling of their scoring in the game based on the function is given below:

In a thrilling football game, the Carolina Panthers, Charlotte's professional football team, played with fierce determination to score points as the game progressed. Their performance could be tracked through a function that related the time passed in minutes to the number of points scored by the team.

At the 0-minute mark, the game started with both teams at 0 points. The Panthers quickly picked up the pace, and by the 10-minute mark, they managed to score a touchdown followed by a successful extra point attempt, bringing their score to 10 points.

As the clock continued ticking, the Panthers scored a field goal by the 20-minute mark, adding another 3 points to their total, raising the score to 13 points. Ten minutes later, at the 30-minute mark, they secured another field goal, further increasing their lead to 16 points.

The 40-minute mark proved to be a turning point for the Panthers, as they managed to score a touchdown with an extra point, and followed up by another field goal. These successful attempts added 10 points to their score, bringing the total to 23 points.

As the game approached its final stages, the Panthers displayed their best performance yet. By the 50-minute mark, they had scored two touchdowns, each with a successful extra point attempt, adding a whopping 14 points to their score, taking it to 36 points.

However, as the game reached its final 10 minutes, the Panthers were unable to capitalize on any further scoring opportunities. The score remained at 36 points by the end of the 60-minute game.

In summary, throughout the game, the Panthers scored a total of 4 touchdowns with extra points and 4 field goals, amassing a final score of 36 points. Their relentless effort and strategic play led them to a strong performance in the match.

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Answer:

f = 2

Step-by-step explanation:

10 = 6 + 2f

subtract 6 from both sides

4 = 2f

divide both sides by 2

2 = f

We have that, the probability of hitting the coin toss at least 6 out of 7 times is approximately 0.0625. Which corresponds to option d. 0.0625.

1. Determine the probability of success and failure.

Since the coin is fair, the probability of success (flipping it correctly) is 0.5, and the probability of failure (flipping it incorrectly) is also 0.5.

2. Calculate the probability of flipping the coin correctly exactly 6 times.

Using the binomial probability formula

[tex]P(X = 6) = C(7, 6) * (0.5)^6 * (0.5)^1\\P(X = 6) = 7 * (0.5)^6 * (0.5)^1\\P(X = 6) \approx 0.0547\\[/tex]

3. Calculate the probability of performing the toss correctly all 7 times.

Using the binomial probability formula.

[tex]P(X = 7) = C(7, 7) * (0.5)^7 * (0.5)^0\\P(X = 7) = 1 * (0.5)^7 * 1\\P(X = 7) \approx 0.0078\\[/tex]

4. Calculate the probability of calling the flip correctly at least 6 times.

[tex]P(X \geq  6) = P(X = 6) + P(X = 7)\\P(X \geq  6) \approx 0.0547 + 0.0078\\P(X \geq  6) \approx 0.0625\\[/tex]

Thus, the probability of hitting the coin toss at least 6 out of 7 times is approximately 0.0625, which corresponds to option d. 0.0625.

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Answer:

Mean of given observations = Sum of given observations Total number of observations

∴11=x+(x+2)+(x+4)+(x+6)+(x+8)÷5

⇒55=5x+20

5x=55-20

5x=35

x=35/5

x=7

Hence, the value of x is 7.

The correct answer is that the average age of all the students at City College could not be exactly 22, but it could be close to it. Since the average age of a sample of 190 students at City College is 22, it can be concluded that the average age of all the students at City College could not be exactly 22 because the sample is only a part of the population.

The population is always larger than the sample. Therefore, it cannot be concluded that the average age of all the students at City College must be more than 22 or must be less than 22.In addition, the standard deviation of the sample is needed to determine the exact range of ages for the population.

It is possible that the population has a higher or lower average age than the sample, but without the standard deviation, it is impossible to say for sure.In conclusion, the given statement that the average age of all the students at City College must be more than 22 or must be less than 22, since the population is always larger than the sample, is not accurate. It could not be exactly 22 but could be close to it, depending on the standard deviation of the sample.

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Tina will need 32 cups of water to make the iced tea.

Answer:

x = 138°

Step-by-step explanation:

The measure of the angle formed by two tangents drawn from outside point of circle is half the difference of intercepted arcs.

           Near arc = 42°

           Far arc    = 360 - 42 = 318°

            [tex]\boxed{\bf x = \dfrac{1}{2}(Far \ arc - near \ arc)}[/tex]

                 [tex]= \dfrac{1}{2}*(318-42)\\\\= \dfrac{1}{2}*276\\\\= 138^\circ[/tex]