Solve for p.
2 /
P - 6 = -4

p=

The composition of function is g ( x ) f ( x ) = 5x⁴ - 40x

Given data ,

Let the first function be g ( x ) = x³ - 8

Let the second function be h ( x ) = 5x

So, the composition of functions , g(x) x h(x) would be:

(x³ - 8) (5x)

We can distribute the multiplication to get:

5x ( x³ ) - 5x ( 8 )

On simplifying , we get

A = 5x⁴ - 40x

Hence , the result of the operation g(x) x h(x) is 5x⁴ - 40x

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The chance that the hospital will run out of sleeping pills on any given day is 0.5000 (or 0.5000 with four decimal places).

To calculate the chance that the hospital will run out of sleeping pills on any given day, we can use the normal distribution and Z-score.

First, let's calculate the Z-score using the formula:

Z = (X - μ) / σ

Where:

X = consumption rate per day (1,155 pills)

μ = average consumption rate per day (1,155 pills)

σ = standard deviation (81 pills)

Z = (1,155 - 1,155) / 81

Z = 0

Now, we need to find the probability associated with this Z-score. However, since the demand for sleeping pills can be considered continuous and not discrete, we need to calculate the area under the curve from negative infinity up to the Z-score. This represents the probability of not running out of sleeping pills.

We discover that the region to the left of a Z-score of 0 is 0.5000 using a basic normal distribution table or statistical software.

To find the probability of running out of sleeping pills, we subtract this probability from 1:

Probability of running out of sleeping pills = 1 - 0.5000

Probability of running out of sleeping pills = 0.5000

Therefore, on any given day, the hospital has a 0.5000 (or 0.5000 with four decimal places) chance of running out of sleeping tablets.

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a (9, π/4) in polar coordinates corresponds to (x, y) = (9√2/2, 9√2/2) in rectangular coordinates. b (7, π/2) in polar coordinates corresponds to (x, y) = (0, 7) in rectangular coordinates. c (6, 0) in polar coordinates corresponds to (x, y) = (6, 0) in rectangular coordinates.

To convert from polar to rectangular coordinates, we can use the following formulas:

x = r * cos(θ)

y = r * sin(θ)

Let's apply these formulas to each given set of polar coordinates:

(a) (9, π/4):

Using the formulas, we have:

x = 9 * cos(π/4) = 9 * (√2/2) = 9√2/2

y = 9 * sin(π/4) = 9 * (√2/2) = 9√2/2

Therefore, the rectangular coordinates are (x, y) = (9√2/2, 9√2/2).

(b) (7, π/2):

Using the formulas, we have:

x = 7 * cos(π/2) = 7 * 0 = 0

y = 7 * sin(π/2) = 7 * 1 = 7

Therefore, the rectangular coordinates are (x, y) = (0, 7).

(c) (6, 0):

Using the formulas, we have:

x = 6 * cos(0) = 6 * 1 = 6

y = 6 * sin(0) = 6 * 0 = 0

Therefore, the rectangular coordinates are (x, y) = (6, 0).

In summary:

(a) (9, π/4) in polar coordinates corresponds to (x, y) = (9√2/2, 9√2/2) in rectangular coordinates.

(b) (7, π/2) in polar coordinates corresponds to (x, y) = (0, 7) in rectangular coordinates.

(c) (6, 0) in polar coordinates corresponds to (x, y) = (6, 0) in rectangular coordinates.

It is important to note that converting from polar to rectangular coordinates allows us to express points in the Cartesian coordinate system, where x represents the horizontal position and y represents the vertical position. By using the formulas x = r * cos(θ) and y = r * sin(θ), we can determine the corresponding rectangular coordinates based on the given polar coordinates.

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The roots of the characteristic polynomial are the values that satisfy the polynomial.

What is a characteristic polynomial ?

In linear algebra, a polynomial that has the eigenvalues as roots and is invariant under matrix similarity is referred to as a characteristic polynomial of a square matrix. The equation created by equating the characteristic polynomial to zero is known as the characteristic equation.

Now the root of the characteristic polynomial are the values which satisfy the polynomial. it means that when this values are substituted in the equation we get the answer as 0.

Hence, The roots of the characteristic polynomial are the values that satisfy the polynomial.

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At the end of the current year, Kwame's suspended passive activity loss with respect to Activities A and B is $40,000.

To determine the amount of Kwame's suspended passive activity loss at the end of the current year, we need to calculate the excess of the passive activity losses over the at-risk amounts for each activity.

For Activity A, the income generated is $60,000, which is greater than the at-risk amount of $10,000. Therefore, there is no suspended passive activity loss for Activity A.

For Activity B, the loss incurred is $100,000, which exceeds the at-risk amount of $100,000. Thus, the excess loss of $100,000 minus the at-risk amount of $100,000 results in a suspended passive activity loss of $0 for Activity B.

Since only Activity B has a suspended passive activity loss, the total suspended passive activity loss for Kwame at the end of the current year is $0.

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The missing parts for both triangles to be congruent are:

1. AE ≅ BD.

2. ∠CAB ≅ FED.

3. ∠BA ≅ DA.

Two triangles can be proven to be congruent by the following criteria:

Therefore, the following are the missing parts in the pair of triangles:

1. The missing parts that weren't shown for both triangles to be congruent by SAS is: AE ≅ BD.

2.  The missing parts that weren't shown for both triangles to be congruent by ASA is: ∠CAB ≅ FED.

3. The missing parts that weren't shown for both triangles to be congruent by SSS is: ∠BA ≅ DA.

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By mathematical induction, we can conclude that the sum of any four consecutive integers has the form 4k+2 for some integer k.

To prove that the sum of any four consecutive integers has the form 4k+2 for some integer k, we can use mathematical induction.

Let's start with the base case: four consecutive integers starting from 1 are 1, 2, 3, and 4. Their sum is 10, which can be written as 4(2)+2. So the statement holds true for the base case.

Now let's assume that the statement is true for some arbitrary set of four consecutive integers a, a+1, a+2, and a+3. We want to show that it also holds true for the next set of four consecutive integers: a+1, a+2, a+3, and a+4.

The sum of these four consecutive integers is (a+1) + (a+2) + (a+3) + (a+4) = 4a + 10. We can rewrite this as 4(a+2) + 2, which is in the form 4k+2, where k is equal to (a+2).

Therefore, we can conclude that the sum of any four consecutive integers has the form 4k+2 for some integer k.

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After answering the presented question, we can conclude that equation Therefore, the answer is: 8 adults and 12 children went to the movies.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

system of equations -

\(x + y = 20 \\9x + 6y = 144 \\x = 20 - y\\9(20 - y) + 6y = 144\\180 - 3y = 144\\-3y = -36\\y = 12\\x + 12 = 20\\x = 8\\\)

So there were 8 adults who went to the movies.

Therefore, the answer is: 8 adults and 12 children went to the movies.

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 \(\bold{Hello!}\\\bold{Your~Answer~Is~Below!}\)

______________________________

 \(\bold{Solution~Steps:}\)

1.) Input \(a=4\), \(b=3\), and \(c=9\) into the equation.

2.) Calculate 4 to the power of 2.

3.) Multiply 2 and 3.

4.) Multiply 6 and 9.

5.) Subtract 54 from 16.

6.) Fraction \(\frac{-38}{7}\) can be rewritten as a decimal by dividing:

______________________________

 \(\bold{Answer:}\)

______________________________

 \(\bold{Hope~this~helps,}\\\bold{And~best~of~luck!}\\\\\bold{~~~~~~~-TotallyNotTrillex}\)

Answer:

$15

Step-by-step explanation:

22+25=47

47-32=15

So Aiden has $15.

Answer:

You are using CAH which is adjacent/hypotenuse

Step-by-step explanation:

1.7101007166283435 is your answer

Answer:

1.710

Step-by-step explanation:

It got deleted before, idk why, but you are using CAH, so adjacent over hypotenuse. You would have to multiply cos(70) by 5 to get the answer.

Answer:

20

Step-by-step explanation:

The lower quartile Q₁ is the value at the left side of the box, that is

Q₁ = 20

Step-by-step explanation:

8k - 12 = 3

8k = 3 +12

8k = 15

k = 15/8

k = 1.875

Answer:

8k-12=3

8k=3+12 [we equate the negative 12 from LHS and take it to RHS and its value becomes positive there fore 3 +12 is possible]

8k=15

k=15/8[algebraic rule of there is no sign between number and variable there is ment to be multiplication and when the multiply is taken to next sign it becomes division and becomes a denominator]

k=1.875

Answer:

\(\orange{ \rule{40pt}{555555pt}}\)

It will take the town 21 years 4 months to reach 4600 in population

a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

initial population = 3000

population increase every year = 2.5% of 3000

which is 2.5/100 x 3000 = 75

let the time taken to reach 4600 be d

increment for d number of years = 75d

Total population after d years is 75d + 3000

so 75d + 3000 = 4600

75d = 4600  - 3000

75d = 1600

d = 1600/75

d = 21.33 years which is 21 years 4 months

In conclusion 21 years 4 months is the time taken for the ton tto get tto 4600

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Answer:

1/5 or 0.2

Step-by-step explanation:

1/4 x 4/5 =

=1x4/4x5
=4/20 -OR- 1/5 -OR- 0.2

Answer:

See Explanation

Step-by-step explanation:

\(

\because \sin\bigg(\frac{\pi}{2} + x\bigg)= \cos x\\

\&\: \sin (\pi - x) = \sin x\\\\

Now,

\frac{\sin\bigg(\frac{\pi}{2} + x\bigg)}{\sin (\pi - x)} = \cot x\\\\

LHS

= \frac{\sin\bigg(\frac{\pi}{2} + x\bigg)}{\sin (\pi - x)} \\\\

=\frac{\cos x}{sinx} \\\\

= \cot x\\\\

= RHS\\\\

Hence\: Proved

\)

The two irrational numbers that sum up to 2 are (√5 - 2) and (4 - √5)

Irrational numbers are numbers that cannot be expressed or written as a quotient of integers.

Example of irrational numbers are; √5 , √7, √3, etc

Irrational numbers that can add up to 2

(√5 - 2) + (4 - √5)

expand the bracket

√5-2 + 4-√5

collect like terms

√5 - √5 -2 + 4

-2 + 4

2

Hence, the two irrational numbers that sum up to 2 are (√5 - 2) and (4 - √5)

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Now

\(\\ \rm\longmapsto Speed=\dfrac{Distance}{Time}\)

\(\\ \rm\longmapsto Time=\dfrac{Distance}{Speed}\)

\(\\ \rm\longmapsto Time=\dfrac{150\times 10^6}{3\times 10^5}\)

\(\\ \rm\longmapsto Time=50\times 10^1\)

\(\\ \rm\longmapsto Time=500s\)

\(\\ \rm\longmapsto Time=8.33min\)

Answer:  25 silver coins need to be added in the purse.

Let the number of silver coins be x. Given, the ratio of gold coins to silver coins in the purse is 2:5 and there are 10 gold coins in the purse. Therefore, we can write:

2/5 = 10/x

x = 25

Thus, there are 25 silver coins in the purse.

To make the ratio of gold coins to silver coins change to 3:4, we need to add (3/2) * 10 = 15 gold coins and (4/5) * 25 = 20 silver coins.

Therefore, the smallest number of coins that needs to be added so that the ratio of gold coins to silver coins changes to 3:4 is 20.

Explanation:

The given ratio of gold coins to silver coins in the purse is 2:5 and the number of gold coins is given to be 10. We need to find the smallest number of coins that needs to be added so that the ratio of gold coins to silver coins changes to 3:4.Let the number of silver coins be x. We can write:2/5 = 10/xCross-multiplying, we get:2x = 50x = 25Thus, there are 25 silver coins in the purse.

Now, we need to add some coins to make the ratio of gold coins to silver coins 3:4. Let the number of gold coins to be added be y. Then, the new ratio becomes:(10+y)/(25+z) = 3/4where z is the number of silver coins to be added. Cross-multiplying, we get:40 + 3y = 30 + 4zSimplifying, we get:z = (3/4)y + (5/2)We need to find the smallest value of y and z. We know that y and z are integers. So, we can take y = 2.5, which is not an integer. So, we take y = 3. Then, we get:z = (3/4)(3) + (5/2) = (9/4) + (10/4) = 19/4Since z is an integer, we take z = 5.

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Answer:

Step-by-step explanation:

a-b=2

\(\frac{27^{\frac{1}{3} b} }{9^{\frac{1}{2}a } } \\=\frac{(3^{3}) ^{\frac{1}{3} b} }{(3^{2} )^{\frac{1}{2} a} } \\=\frac{3^b}{3^a} \\=3^{b-a} \\=3^{-(-b+a)} \\=3^{-2}\\=\frac{1}{3^2} \\=\frac{1}{9}\)

Answer:

Yo, check this out, S=a×a=a², the formula to find the area of a square.

Step-by-step explanation:

S=49 yd²

S=a×a=a²

a²=49===> √a²=√49 yd²===> |a|=7 yd===> a=7, –7

but be aware that we ain't got no squares with a negative length, so the answer is

7 yd

Research that provides data which can be expressed with numbers is called quantitative research.

Quantitative research is a type of research that focuses on gathering and analyzing numerical data. It involves collecting information or data that can be measured and quantified, such as numerical values, statistics, or counts. This research method aims to objectively study and understand phenomena by using mathematical and statistical techniques to analyze the data.

Quantitative research typically involves the use of structured surveys, experiments, observations, or existing data sources to gather information. Researchers often employ statistical methods to analyze the data and draw conclusions or make predictions based on the numerical findings.

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Answer:

√113

10.6301458127

10.63 (2 d.p)

Step-by-step explanation:

The distance formula is:

√[(x₂ - x₁)² + (y₂ - y₁)²]

x₂ = (-1)

x₁ = 6

y₂ = 8

y₁ = 16

Substitute those values into the equation:

√[(-1 - 6)² + (8 - 16)²]

Perform the arithmetic (the subtractions inside the brackets:

√[(-7)² + (-8)²]

Square the values:

√[49 + 64]

Add them

√[113]

Calculate the square root of the value:

√[113] = 10.6301458127

Whether you want the answer in one of these forms, it's up to you/your teacher:

√113

10.6301458127

10.63 (2 d.p)

Answer:

It’s 17.6

Step-by-step explanation:

By using multiplication and division, it can be calculated that-

The multiple according to the number 3 = 162

The submultiple according to the number 7 = 7

What is multiplication and division?

Repeated addition is called multiplication. Multiplication is used to find the product of two or more numbers.

Division is the process in which a value of single unit can be calculated from the value of multiple unit.

The number to be divided is called dividend. The  number by which dividend is divided is the divisor. The result obtained is called quotient and the remaining part is the remainder.

This is a problem of multiplication and division.

One segment measures 161 cm

So, to find the multiple according to the number 3, we have to divide 161 by 3

161 \(\div\) 3 = 53.67

Nearest integer of 53.67 is 54

The multiple according to the number 3 = 54 \(\times\) 3 = 162

To find the submultiple according to the number 7, we have to divide 161 by 7

161 \(\div\) 7 = 23

Nearest integer of 23 is 23

The submultiple according to the number 7 = 161 \(\div\) 23 = 7

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Answer:yes they are considered real numbers

Step-by-step explanation:

Right now, the ratio of nonfiction to fiction is 9:18.  If this is reduced, it is a ratio of 1:2, so there needs to be twice as many fiction books as nonfiction.

If we add 6 fiction books, we have 24 fiction books.  We can now set up this equation:

\(1/2=x/24\)

Now we cross multiply

2x=24

We can solve for x by dividing both sides by two, so:

x = 12.  There will be 12 nonfiction books.