solve the right triangle by completing the table below :) help asap

The inverse of the functions g(x), p(x), and t(x) are expressed as; g⁻¹(x) = 3√(x + 5), p⁻¹(x) = 3√(x/2) - 3, and t⁻¹(x) = (3x/10) - 3. respectively.

A function is said to have an inverse if it is both one-to-one and onto

we replace the functions g(x), p(x), and t(x) with y and make x the subject to arrive at the inverse g⁻¹(x), p⁻¹(x), and t⁻¹(x) as follows;

For g(x)= x³ - 5:

y = x³ - 5

y + 5 = x³ {add 5 both sides}

x = 3√(y + 5) {take cube root}

g⁻¹(x) = 3√(x + 5).

For p(x) = 2(x+3)³:

y = 2(x+3)³

y/2 = (x+3)³ {divide through by 2}

3√(y/2) = x + 3 {take cube root}

x = 3√(y/2) - 3 {subtract 3 from both sides}

p⁻¹(x) = 3√(x/2) - 3.

For t(x) = 10(x-4)/3:

y = 10(x-4)/3

3y = 10(x-4) {cross multiplication}

3y/10 = x + 3 {divide through by 10}

(3y/10) - 3 = x {subtract 3 from both sides}

t⁻¹(x) = (3x/10) - 3.

Therefore, the inverse of the functions g(x), p(x), and t(x) are derived by interchanging the value of x for y and expressed respectively as; g⁻¹(x) = 3√(x + 5), p⁻¹(x) = 3√(x/2) - 3, and t⁻¹(x) = (3x/10) - 3.

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The correct size of the distance matrix for a multivariate data set with 25 subjects and 7 variables is 25 x 25.

Understanding the many objectives and histories of the various types of multivariate analysis, as well as how they connect to one another, is the focus of multivariate statistics.

The distance matrix contains the pairwise distances between all pairs of subjects in the dataset, and therefore has the same number of rows and columns as the number of subjects in the dataset. Since there are 25 subjects in this dataset, the distance matrix will have 25 rows and 25 columns.

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Quadratic equation gives us the fuel efficiencies of the two cars for the given values of fuel consumption and total distance driven.

Let's denote the fuel efficiency of the first car as x miles per gallon, and the fuel efficiency of the second car as y miles per gallon.

We know that the first car consumed a total of a gallons of gas, and the second car consumed b gallons of gas. If we assume that the fuel efficiencies are constant, then the total distance driven by both cars can be calculated using the formula:

distance = fuel consumed / fuel efficiency

So, the total distance driven by both cars is:

(a/x) + (b/y) = total miles

We also know that the sum of their fuel efficiencies was:

x + y = total miles per gallon

We have two equations and two unknowns, so we can solve for x and y. First, we can solve the second equation for x:

x = total miles per gallon - y

Substituting this expression for x into the first equation, we get:

(a / (total miles per gallon - y)) + (b / y) = total miles

Multiplying both sides by y(total miles per gallon - y) to eliminate the denominators, we get:

ay + b(total miles per gallon - y) = total miles * y(total miles per gallon - y)

Expanding the left side and simplifying, we get a quadratic equation in y:

(total miles^2 - a - b) y^2 + (total miles * a) y - ab = 0

Using the quadratic formula, we can solve for y:

y = [(total miles * a) ± sqrt((total miles * a)^2 + 4ab(total miles^2 - a - b))] / 2(total miles^2 - a - b)

We can then use the equation x = total miles per gallon - y to find the value of x. The gives the fuel consumption of both cars.

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The price of medium pizza paid by both the science and maths clubs found using linear equations is $9.50.

What is meant by equation?

A formula known as an equation uses the equals sign (=) to express how two expressions are equal.

Given,

Cost of 5 large pizzas and 2 medium pizzas paid by the science club = $79.00

Cost of  4 large pizzas and 4 medium pizzas paid by the math club = $86.00

Let the cost of medium pizza = x

Cost of large pizza = y

Now using the above equation we can write two linear equations.

2x + 5y = 79

4x + 4y = 86

Solving the above system of linear equations.

We are making the coefficient of the x variable the same.

Multiplying the first equation by 2.

4x + 10y = 158

4x + 4y = 86

Subtracting the equations.

6y = 72

y = 12

Now substituting in any one equation, we get the value of x.

2x + 5 * 12 = 79

2x = 19

x = 9.5

Therefore the price of medium pizza found using linear equations is $9.50.

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Answer:

x=-2(3-2√2), -2(3+2√2)

Considering the definition of pH and pOH, you obtain that:

pH is the Hydrogen Potential. It is a measure of acidity or alkalinity that indicates the amount of hydrogen ions present in a solution or substance.

Mathematically, pH is calculated as the negative base 10 logarithm of the activity of hydrogen ions, that is, the concentration of hydrogen ions:

pH= - log [H⁺]

Similarly, pOH is a measure of hydroxyl ions in a solution and is expressed as the logarithm of the concentration of OH⁻ ions, with the sign changed:

pOH= - log [OH⁻]

The following relationship can be established between pH and pOH:

pOH + pH= 14

In this case, you know that a solution has a pH = 13. So, the pOH can be calculated as:

pOH + 13= 14

pOH= 14 -13

pOH= 1

Then, the concentration of OH⁻ can be calculated as:

1= - log [OH⁻]

[OH⁻]= 10⁻¹

[OH⁻]= 0.1

Finally, a solution with a pH = 13 has 0.1 moles of OH⁻ ions per liter.

On the other side, remembering that pH = 13, the concentration of H⁺ can be calculated as:

13= - log [H⁺]

[H⁺]= 10⁻¹³

[H⁺]= 1×10⁻¹³

So, a solution with a pH = 13 has 1×10⁻¹³ moles of H⁺ ions per liter.

Finally, you have a different solution with an H⁺ concentration of 1.0×10⁻⁴. Replacing in the definition of pH:

pH= - log (1.0×10⁻⁴)

Solving:

pH= 4

Then, a different solution with an H⁺ concentration of 1.0×10⁻⁴ would have a pH= 4.

In summary, you obtain that:

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Answer:

-2a-2

Step-by-step explanation:

We can start solving this expression by combining like terms: Constants, or the number values, and Variables(the letters)

We can combine -6, 4, and 0 to get -2.

We can combine 3a and -5a to get -2a.

-2a + (-2) is the expression we are left with.

We can simplify this to

-2a - 2.

It can't be simplified further, so our answer is

-2a-2.

The two statements  a iff b and (not a) iff (not b) has been explained

The two statements are known as biconditionals, which state that two statements are true if and only if each other.

"a iff b" means that "a" is true if "b" is true, and "a" is false if "b" is false. In other words, "a" and "b" have the same truth value.

"(not a) iff (not b)" means that "not a" is true if and only if "not b" is true, and "not a" is false if and only if "not b" is false.

Therefore, these two statements are equivalent because they express the same idea: "a" and "b" have the same truth value. If "a" is true, then "b" is true, and if "a" is false, then "b" is false. Similarly, if "b" is true, then "a" is true, and if "b" is false, then "a" is false.

These statements are true in cases where both "a" and "b" have the same truth value. If both are true or both are false, then the statements are true. If "a" is true and "b" is false, or vice versa, then the statements are false.

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Answer:

$3.35

Step-by-step explanation:

$50.25 ÷ 15 gallons = $3.35 a gallon

Answer: $44.04

Step-by-step explanation: Add up all the prices 13.75+15.85+11.95 which is 41.55. Now times 41.55 by 6% which is 2.493. Now add the total and the tax. 41.55 + 2.493 = $44.04 as the final total.

The point equidistant from the three sides of a triangle is (c) Incenter .

The Circumcenter of a triangle is defined as a point where perpendicular bisectors of  sides of triangle intersect. It is also equidistant from  3 vertices of triangle .

The Centroid is defined as a point where 3 medians of the triangle intersect.

The Incenter is defined as a point where  angle bisectors of the triangle intersect. It is equidistant from the three sides of the triangle, and is the center of the inscribed circle of the triangle .

The Orthocenter is defined as a point where the 3 altitudes of the triangle intersect.

So , by the definition of the Incenter , the correct option is (c) Incenter .

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The given question is incomplete , the complete question is

The point equidistant from the three sides of a triangle is

(a) Circumcenter

(b) Centroid

(c) Incenter

(d) Orthocenter

Answer:2\1

Step-by-step explanation:24\12 then simplify and get 2\1

Answer:

A ladder leans against the wall of a building. The ladder measures 66 inches and forms an angle of 45 degrees with the ground. How far from the ground, in inches, is the top of the ladder? How far from the wall, in inches, is the base of the ladder?

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

 strawberries to plums  9:1       then total would be 10 parts  of which 1 is plums    so    1 : 10

Answer:

1) 16pi square cm

2) 112pi cubed cm

3) 351.68 cubed cm

Step-by-step explanation:

Question 1: The base of a cylinder is a circle. To find the area of a circle, we can use the formula A = pi(r^2). the radius is 4 centimeters. 4^2 = 16.

The answer to the question is 16pi square cm

Question 2: This question is asking for the volume of the cylinder. To find the volume of the cylinder, we must multiply the area of the base by its height. we know the area of the base is 16pi. 16pi x 7(the height) = 112 pi.

The answer to the question is 112 pi cubed cm

Question 3: If pi were to be 3.14, we just need to substitute pi in the equation for question two with 3.14:

16(3.14) x 7 = 351.68

The answer is 351.68 cubed cm

The addition and subtraction of the fractions by finding the LCD gives:

NUMBER 1: (8y-49) /(y²-49)

NUMBER 2: (x+10) /(2x+8)

NUMBER 3: (7a-2)/10b

NUMBER 4: 1

Least Common Denominator (LCD) refers to the smallest multiple that two or more denominators have in common, and is used in operations involving fractions.

NUMBER 1

y/(y²-49) - 7(y+7) = y/[(y+7)(y-7)] - 7(y+7)

LCD of (y+7)(y-7) and (y+7) is (y+7)(y-7):

                          = [y + 7(y-7)] / [(y+7)(y-7)]

                          = [y + 7y-49)] / [(y+7)(y-7)]

                          = (8y-49) / (y+7)(y-7)

                          = (8y-49) /(y²-49)

NUMBER 2

1/2 + 3/(x + 4) = [1(x+4) + 3*2] /[2(x+4)]

                      = [x+4 + 6] /[2(x+4)]

                      = (x+10) /(2x+8)

NUMBER 3

(a+2)/4b + (a-1)/10b + (a-3)/5b = [5(a+2) + 2(a-1) + 4(a-3)]/20b

                                                 = [5a+10 + 2a-2 + 4a-12]/20b

                                                 = (14a-4)/20b

                                                 = 2(7a-2)/20b

                                                 = (7a-2)/10b

NUMBER 4

x/(x+1) - 1/(x-1) + 2x/(x²-1) = [x(x-1) - 1(x+1) + 2x]/(x²-1)

                                         = [x²-x -x-1 + 2x]/(x²-1)

                                         = (x²-1)/(x²-1)

                                         = 1

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Solving the equation: x - 1/x = 15/13

We will see that the value of x is 28/13

For a number x, we define the reciprocal number as 1/x.

We know that the difference between theses two is 15/13, then we can write:

x - 1/x = 15/13

(x² - x)/x = 15/13

(x² - x) = (15/13)*x

x² - x - (15/13)*x = 0

x² - (1 + 15/13)*x = 0

x² - (28/13)*x = 0

x*(x - 28/13) = 0

x = 0 is not a solution, because 1/x exists, then the solution is x = 28/13.

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Your commission for a month in which your sales people sold $1,250,000 in insurance policies is $62500

We know that in order to determine the percentage, we divide the value by the total value and then multiply the resultant by 100.

The formula for the percentage would be,

percent = (number of parts / total number of possible parts) × 100%

Here, for a particular month your sales people sold $1,250,000 in insurance policies.

As we can see that your commission would be 5% of all sales over $1,000,000

Let us assume that your commission for that month be x dollars.

Since 1,250,000 > 1,000,000

We need to find 5 percent of $1,250,000

i.e., x = 5 percent of $1,250,000

Using percentage formula,

x = 1,250,000 × (5/100)

x = 62500

Therefore, your commission will be 62500 dollars.

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plug in 20 = x for function f(x)

1.2(1.11)^20 = ?

The total volume of compost required for 16 bowls is 67,493.33 cm³

The total weight of compost required for 16 bowls is 155,906.67 gm

The total amount of polythene required for 16 bowls is: 6400π cm²

(i) The volume of compost required per bowl can be calculated as follows:

V = (4/3)πr^3, where r is the radius of the sphere

The radius of each bowl can be calculated as:

r = (d/2) - t, where d is the diameter (21 cm) and t is the thickness (0.5 cm)

So, r = (21/2) - 0.5 = 10 cm

Plugging the value of r into the formula for volume:

V = (4/3)πr^3 = (4/3)π * 10^3 = 4186.67 cm³

The total volume of compost required for 16 bowls is:

16 * 4186.67 = 67,493.33 cm³

The total weight of compost required for 16 bowls is:

67,493.33 cm³ * 2.31 gm/cm³ = 155,906.67 gm

(ii) To find the total amount of polythene required to cover the outer surface of 16 bowls, we first need to calculate the surface area of one bowl.

The surface area of a sphere can be calculated as follows:

A = 4πr^2

Plugging the value of r into the formula for surface area:

A = 4πr^2 = 4π * 10^2 = 400π cm²

The total amount of polythene required for 16 bowls is:

16 * 400π cm² = 6400π cm²

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Answer:

y = 43

Step-by-step explanation:

47° , y and 90° lie on the straight line AB and sum to 180° , that is

47 + y + 90 = 180

y + 137 = 180 ( subtract 137 from both sides )

y = 43

Answer:

Step-by-step explanation:

35tu

(5 and 7 are like terms, and you put the 't' and 'u' in alphabetical order)

Answer:

ut=35

Step-by-step explanation:

5×u×t×7=0

collect like terms

ut=5×7

ut=35

Answer:The error in #1 is that it should read "3x²•(-2x⁴)=3•(-2)•x²⁴=6x⁸". The error in #2 is that it should read "4a²•3a⁵=4•a²•3•a⁵=12a⁷". The error in #3 is that it should read "x⁶•x³=x⁶•x³=x⁹". The error in #4 is that it should read "3⁴•2³=3⁴•2³=24".

Step-by-step explanation:

easy

From The total mass of orange and box, the mass of oranges are 2kg and the mass of empty box is 23kg.

Let's use "o" to represent the mass of one orange and "a" to represent the mass of one apple.

We can set up two equations based on the information given:

Box + Oranges = 25 kg (equation 1)

Box + Apples = 11 kg (equation 2)

Oranges = 3 x Apples (equation 3)

We can substitute equation 3 into equation 1 to eliminate "oranges":

Box + 3a = 25 kg

We can substitute equation 3 into equation 2 to eliminate "oranges" again:

Box + a = 11/3 kg

Now we have two equations with two unknowns. We can solve for "Box" and "a" using either substitution or elimination. For example, we can multiply the second equation by 3 and subtract it from the first equation:

Box + 3a = 25

3(Box + a = 11)

-2Box + 2a = 2

Simplifying, we get:

Box - a = -1

We can add this equation to the second equation to get:

2Box = 11 - 1 = 10

So, Box = 5 kg.

Now we can substitute this value back into equation 2 to find "a":

5 + a = 11/3

a = 2/3 kg

Finally, we can use equation 3 to find the mass of the oranges:

Oranges = 3 x Apples = 3 x (2/3) = 2 kg.

Therefore, the mass of the oranges is 2 kg.

The mass of the empty box is the difference between the total mass of the box and the fruit and the mass of the fruit:

Mass of box = Total mass - Mass of fruit

From equation 1, we know that the total mass of the box and the oranges is 25 kg. From part a, we know that the mass of the oranges is 2 kg. Therefore:

Mass of box = 25 kg - 2 kg = 23 kg.

So, the mass of the empty box is 23 kg.

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____The given question is incomplete, the complete question is given below:

The total mass of a box and some oranges was 25kg . The total mass cii N the same box and some apples was 11kg . The mass of the oranges was 3 times the mass of the apples. (a) Find the mass of the oranges.. (b) Find the mass of the empty box.

Answer:5

Step-by-step explanation:

This is a variation question.

When m is inversely proportional to n,

m ∝ 1/n

Now, there is a constant of 100.

So the formula connecting m and n is

m=k/n where k is the constant

=>m=100/n

Now, n= 20 ( 20 printers)

Thus, m=

100/20=5 minutes.

Hope this helps :)

Answer:

Step-by-step explanation:

your picture is blur. can you repost it?

Answer:

Expected amount = $1.50

Step-by-step explanation:

Let's get a couple of definitions out of the way to understand how to compute the expected value given probabilities

Random Variable is a set of possible values from a random experiment.
We usually denote a random variable using the sets of possible values that the variable can take.

When we toss a fair die, the probability of getting a single number = 1/6 since there are 6 possible outcomes

The probability of getting 2 given numbers say 1 or 2 is twice 1/6 = 2 x 1/6 = 2/3 and so on

The expected value of each outcome is the value attached to each outcome x probability of that outcome

As an example, P(1 or 2) = 2/6 = 1/3

Payout = $3

Expected payout = 3 x 1/3 = $1

The table below summarizes the outcomes, probabilities, payouts and expected payouts

Outcome             Probability              Payout              Expected Payout
                                                                                     (Payout x probability)

X = {1 or 2}            2/6 = 1/3                  $3                     $3 x 1/3 = $1

X = {3}                       1/6                       $5                     $5 x 1/6 = $5/6

X = {4 or 5}           2/6 = 1/3                  $0                      $0 x 1/3 = $0

X = {6}                        1/6                      -2$                     -$2 x 1/6 = -$2/6

The expected payout in the long run is the sum of the individual expected payouts

= $1 + $5/6 + $0 - $2/6    (5/6 - 2/6 = 3/6)

= $1 + $3/6             (3/6 = $0.50)

= $1 + $0.50

= $1.50

The expected value of the game is $2. This means that if you play the game many times, you can expect to win an average of $2 per game in the long run.

It is a branch of mathematics that deals with the occurrence of a random event.

To determine whether you should play the game, we need to calculate the expected value of the game.

The expected value is the sum of the product of each outcome and its probability.

The outcomes and their corresponding probabilities are:

Win $3 with probability 1/3 (if the number is 1 or 2)

Win $5 with probability 1/6 (if the number is 3)

Win $0 with probability 2/6 = 1/3 (if the number is 4 or 5)

Lose $2 with probability 1/6 (if the number is 6)

Using these probabilities and outcomes, we can calculate the expected value as:

Expected value = (3 × 1/3) + (5 × 1/6) + (0 × 1/3) + (-2 × 1/6)

= 1 + 5/6 - 1/6

= 1.666

= 2

Hence, the expected value of the game is $2. This means that if you play the game many times, you can expect to win an average of $2 per game in the long run.

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The equation will be written as [tex]A = 325[1.004]^{12t}[/tex]. The time taken to reach $200 will be 10 years.

Compound interest is defined as the interest levied upon the interest. The formula to calculate the compound interest will be written as:-

[tex]A = P[1+\dfrac{r}{m}]^{rt}[/tex]

Given that Hassan places $325 into a savings account that offers a monthly compound interest rate of 4.7%.

The equation for the compounding on monthly basis,

[tex]A = 325[1+\dfrac{0.047}{12}]^{12t}[/tex]

[tex]A = 325[1.004]^{12t}[/tex]

The time will be calculated as:-

[tex]A = 325[1.004]^{12t}[/tex]

[tex]200 = 325[ 1.004]^{12t}[/tex]

log(0.615) = 12 x t x log(1.004)

12t = 121.77

t = 10 years

Therefore, the equation will appear as  [tex]A = 325[1.004]^{12t}[/tex]. It will take 10 years for the price to reach $200.

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The median should be used to describe a normal or skewed distribution, as it is a better measure of the central tendency than the mean for these types of distributions.

The median is a better measure of the central tendency than the mean when describing a normal or skewed distribution. A normal distribution is a symmetrical distribution of data in which values are evenly spread around the mean. A skewed distribution is when one side of the distribution is longer than the other, with the mean being pulled away from the center. The median is the most appropriate measure of central tendency for both normal and skewed distributions because the mean can be distorted by outliers and extremes in the data. The median is the midpoint in the data and provides a better representation of the middle of the distribution, which can be useful in interpreting the data. Using the median to describe a large distribution or percentage is not as common as it is better to use the mean or mode for these types of distributions.

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