Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)

By answering the supplied question, we may infer that the response is percentage Thus, pizza was chosen as the celebratory food by 75% of the pupils in Karen's class.

A ratio or value stated as a percentage of 100 is referred to as a percentage in mathematics. The abbreviations "pct.," "pct," and "pc" are also sporadically used. Nonetheless, the percentage symbol "%" is frequently used to denote it. The percentage amount is dimensionally empty. When the denominator is 100, percentages are essentially fractions. To show that a number is a percentage, a percent symbol (%) should be used next to it. For instance, you receive a 75% grade if you correctly answer 75 out of 25 questions (75/100) on a test. For percentage calculations, multiply the outcome by 100 after dividing the amount by the total. The percentage is calculated by multiplying (value/total) by 100%.

We must divide the number of students who chose pizza (15) by the total number of students (20) and multiply the result by 100 to determine the percentage of students who chose pizza:

(15/20) x 100 = 75%

Thus, pizza was chosen as the celebratory food by 75% of the pupils in Karen's class.

To know more about percentage visit:

https://brainly.com/question/28269290

#SPJ1

The solution for c in the equation is 35/3

From the question, we have the following parameters that can be used in our computation:

\(c = 5\frac{5}{6} \times 2 \)

Express the equation properly

So, we have the following representation

c = 5 5/6 * 2

Convert the fraction to improper​ fraction

So, we have the following representation

c = 35/6 * 2

Evaluate the products

c = 35/3

Hence, the solution is 35/3

Read more about equations at

https://brainly.com/question/18831322

#SPJ1

The zeros of the polynomial p(x)=x²+16 are x = 4i and x = -4i. The zeros of the polynomial can be found using the Quadratic Formula: x = (-b ± √(b²-4ac))/(2a), where a, b, and c are the coefficients of the polynomial. In this case, a = 1, b = 0, and c = 16.

Plugging in these values into the Quadratic Formula, we get:

x = (-0 ± √(0²-4(1)(16)))/(2(1))

Simplifying the expression, we get:

x = (0 ± √(-64))/(2)

Since the square root of a negative number is a nonreal number, we can write this as:

x = (0 ± 8i)/(2)

Simplifying further, we get:

x = 0 ± 4i

So the zeros of the polynomial are x = 4i and x = -4i, both of which are nonreal numbers.

Know more about Quadratic Formula here:

https://brainly.com/question/22364785

#SPJ11

The graph of this equation will be a straight line with a slope of 1/2 and a y-intercept of -5/6.

To solve the given linear equation, we can use the method of isolating the variable on one side of the equation. Here are the steps to solve the equation:

Step 1: Start with the given equation: -3x + 6y = -5

Step 2: Isolate the variable on one side of the equation. We can do this by adding 3x to both sides of the equation:

-3x + 6y + 3x = -5 + 3x

Simplifying the equation gives us:

6y = 3x - 5

Step 3: Now, we can isolate the y variable by dividing both sides of the equation by 6:

(6y)/6 = (3x - 5)/6

Simplifying the equation gives us:

y = (3/6)x - (5/6)

Step 4: Simplify the fractions by reducing them:

y = (1/2)x - (5/6)

This is the final solution of the given linear equation. The graph of this equation will be a straight line with a slope of 1/2 and a y-intercept of -5/6.

To know more about linear equations, refer here:

https://brainly.com/question/29739212#

#SPJ11

Answer:

4x+3y

Step-by-step explanation:

Combining like terms, we get:

5x - x + 4y - y = 4x + 3y

Therefore, 5x+4y-x-y simplifies to 4x+3y.

The approximate solution using the three-point formula with step size h = 1/2 is y(t) = 0 for all t.

The boundary value problem given is y′′ − y = 0 with boundary conditions y(0) = 0 and y(2) = e2 − e−2.

(a) To find the exact solution y(t), we can use the characteristic equation r^2 - 1 = 0. This gives us r = 1 and r = -1. The general solution is therefore y(t) = c1e^t + c2e^-t.

Using the boundary conditions, we can find the constants c1 and c2.

For y(0) = 0, we have 0 = c1 + c2, which gives us c2 = -c1.

For y(2) = e2 − e−2, we have e2 − e−2 = c1e^2 + c2e^-2. Substituting c2 = -c1, we get e2 − e−2 = c1e^2 - c1e^-2.

Solving for c1, we get c1 = (e2 − e−2)/(e^2 - e^-2) = 1/2. Therefore, c2 = -1/2.

The exact solution is y(t) = (1/2)e^t - (1/2)e^-t.

(b) To use the three-point formula with step size h = 1/2, we can set up a table with tn and yn values.

tn | yn
---|---
0  | 0
1/2| y1
1  | y2
3/2| y3
2  | e2 - e-2

The three-point formula is yn+1 = yn-1 + 2h(y′n). We can use this formula to find the values of y1, y2, and y3.

For y1, we have y1 = 0 + 2(1/2)(y′0) = y′0. Since y′0 = y′(0) = (1/2)e^0 - (1/2)e^0 = 0, we have y1 = 0.

For y2, we have y2 = y0 + 2(1/2)(y′1) = 0 + 2(1/2)(0) = 0.

For y3, we have y3 = y1 + 2(1/2)(y′2) = 0 + 2(1/2)(0) = 0.

Therefore, the approximate solution using the three-point formula with step size h = 1/2 is y(t) = 0 for all t.

It is important to note that the three-point formula is not accurate for this particular boundary value problem due to the size of the step and the nature of the differential equation. A smaller step size or a different numerical method may yield a more accurate approximation.

Learn more about three-point formula

brainly.com/question/5016495

#SPJ11

Answer:

25%

Step-by-step explanation:

Number of favorable outcomes 4

Total number of outcomes=4+5+2+3+2=16

4/16=0.25

0.25x100=25

25%

​

The answer as a single polynomial is x^(3) + 9x^(2) - 15.

To subtract the two polynomials as indicated, we need to distribute the constants in front of each polynomial and then combine like terms.

First, we distribute the 5 and -2 to each term in the respective polynomials:
5(x^(3)) + 5(x^(2)) - 5(3) - 2(2x^(3)) - 2(-2x^(2))

Simplifying each term gives us:
5x^(3) + 5x^(2) - 15 - 4x^(3) + 4x^(2)

Next, we combine like terms by adding the coefficients of each term with the same exponent:
(5x^(3) - 4x^(3)) + (5x^(2) + 4x^(2)) - 15

Simplifying the coefficients gives us:
x^(3) + 9x^(2) - 15

Therefore, the answer as a single polynomial is x^(3) + 9x^(2) - 15.

Learn more about polynomials

brainly.com/question/11536910

#SPJ11

Wok out the probability of rolling one 6 from 2 throws on a biased dice rolling 6 1/5 of the time is 8/25

The given data is as follows:

Number of throws = 2

probability of rolling number = 6

The probability of getting dice one 6 from 2 throws can happen in two different ways.

1. Rolling a number 6 on the first throw and not getting a number 6 on the second throw.

2. Not rolling a number 6 on the first throw and getting a number 6 on the second throw.

Here, the multiplication rule of probability is used to find the probability of the above two different events.

1.

The probability of getting a 6 on the first throw = is 1/5

The Probability of not getting a 6 on the second throw = (4/5)

The Probability of both happening: (1/5) x (4/5) = 4/25

2.

The Probability of not getting a 6 on the first throw = (4/5)

The Probability of getting a 6 on the second throw = (1/5)

The Probability of both happening: (4/5) x (1/5) = 4/25

The probability of both events is = 4/25 + 4/25 = 8/25

Therefore we can conclude that the probability of getting one 6 from 2 throws on a  dice rolling 6 1/5 of the time is 8/25.

To learn more about probability

https://brainly.com/question/12629667

#SPJ4

Answer: The ones you have selected are correct

Step-by-step explanation:

Answer:

the ones you selected are all correct

Step-by-step explanation:

To derive the properties of R2 for the model m Ji = Σβ,tij + u; j=1, we need to first understand what R2 represents. R2, also known as the coefficient of determination, is a statistical measure that represents the proportion of the variance in the dependent variable that is explained by the independent variable(s) in a regression model.
In the given model, the dependent variable is m Ji and the independent variable is tij. The coefficient β represents the slope of the regression line and u represents the error term.

To derive the properties of R2, we can use the formula:
R2 = 1 - (SSres/SStot)
Where SSres is the sum of squared residuals and SStot is the total sum of squares.
SSres = Σ(m Ji - ŷi)2
SStot = Σ(m Ji - ȳ)2
Where ŷi is the predicted value of m Ji and ȳ is the mean of m Ji.

By substituting the values of SSres and SStot into the formula for R2, we can derive the properties of R2 for the given model.
R2 = 1 - (Σ(m Ji - ŷi)2/Σ(m Ji - ȳ)2)

The properties of R2 for the given model are:
1) R2 is always between 0 and 1. A value of 0 indicates that the independent variable(s) do not explain any of the variance in the dependent variable, while a value of 1 indicates that the independent variable(s) explain all of the variance in the dependent variable.
2) R2 is a measure of the strength of the relationship between the independent variable(s) and the dependent variable. The closer R2 is to 1, the stronger the relationship.
3) R2 is affected by the number of independent variables in the model. The more independent variables there are, the higher the R2 value will be.
4) R2 does not indicate causation. It only measures the strength of the relationship between the independent variable(s) and the dependent variable.

To know more about variance refer here:

https://brainly.com/question/14116780

#SPJ11

Answer:

The answer is 2/15

Step-by-step explanation:

2/5 × 1/3

The probability of selecting either lunch is 50%, as both lunches are equally likely to be chosen. This is because both lunches have the same ingredients, with the only difference being the dessert item.

Probability is a measure of the likelihood of a certain event or outcome occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event or outcome is impossible and 1 indicates that the event or outcome is certain to occur. Probability is an important concept in mathematics and statistics, and it is widely used in fields such as finance, science, engineering, and gaming.

To learn more about probability
https://brainly.com/question/24756209
#SPJ1

$$x \frac{dy}{dx}\sin \left(\frac{y}{x}\right)=y \sin \left(\frac{y}{x}\right)-x$$

QUESTION 1:

Using the substitution $u = xy$, we have the following equation:

$$(x^2u+xu-u)dx + (x^2u-2x^2)dy = 0$$

Multiplying both sides by $\frac{dy}{dx}$, we get:

$$(x^2u+xu-u)\frac{dy}{dx}dx + (x^2u-2x^2)\frac{dy}{dx}dy = 0$$

Simplifying, we have:

$$(x^2u+xu-u)\frac{dy}{dx} + (x^2u-2x^2)dy = 0$$

Rearranging, we get:

$$x\frac{dy}{dx}(u \sin \left(\frac{y}{x}\right)) + y\sin \left(\frac{y}{x}\right) - x = 0$$

Which simplifies to:

$$x \frac{dy}{dx}\sin \left(\frac{y}{x}\right)=y \sin \left(\frac{y}{x}\right)-x$$

QUESTION 2:

The solution to the given differential equation is:

$$x \frac{dy}{dx}\sin \left(\frac{y}{x}\right)=y \sin \left(\frac{y}{x}\right)-x$$

Learn more about; derivation

brainly.com/question/1603302

#SPJ11

a. If 1,200 students are in the district, 165 students can be expected to oppose school uniforms.

b. From the sample, the most likely outcome is in favor, as it got the most responses, hence we should disagree with Bernice.

A proportion is a fraction of the total amount.

Out of 80, 11 opposed, hence, out of 1200, we apply the proportion and find that the amount will be of:

1200 x 11/80 = 165.

Hence, a - 165 students can be expected to oppose school uniforms.

b - We should disagree with Bernice because the sample indicates that the outcome in favor is the most likely because it received the most answers.

Learn more about proportion, here:

https://brainly.com/question/30675490

#SPJ1

If the selection is made randomly, there are 30045015 ways to select a committee of size 10 from a group of 10 men and 20 women. The probability that the committee consists of 5 men and 5 women is 0.129. The probability that there is no woman in the committee is  0.000000033.

1. The total number of ways to select a committee of size 10 from a group of 10 men and 20 women is given by the combination formula:
C(n,k) = n! / (k! * (n-k)!)
Where n is the total number of people (10 men + 20 women = 30) and k is the size of the committee (10).
C(30,10) = 30! / (10! * (30-10)!)
C(30,10) = 30! / (10! * 20!)
C(30,10) = 30045015
Therefore, there are 30045015 ways to select a committee of size 10 from a group of 10 men and 20 women.

2. The probability that the committee consists of 5 men and 5 women is given by:
P(5 men and 5 women) = C(10,5) * C(20,5) / C(30,10)
P(5 men and 5 women) = (10! / (5! * 5!)) * (20! / (5! * 15!)) / (30! / (10! * 20!))
P(5 men and 5 women) = (252 * 15504) / 30045015
P(5 men and 5 women) = 0.129

3. The probability that there is no woman in the committee is given by:
P(no woman) = C(10,10) * C(20,0) / C(30,10)
P(no woman) = (10! / (10! * 0!)) * (20! / (0! * 20!)) / (30! / (10! * 20!))
P(no woman) = (1 * 1) / 30045015
P(no woman) = 0.000000033
Therefore, the probability that there is no woman in the committee is 0.000000033.

Learn more about probability at https://brainly.com/question/15584918

#SPJ11

Answer:

8290

Step-by-step explanation:

Explanation is on the pic

The domain of \(f(x)=\sin^{-1}x\) is \([-1, 1]\) and the range is \([-π/2, π/2]\).

This is because the inverse sine function, \(sin^{-1}x\), is defined only for values of x between -1 and 1, resulting in a domain of \([-1, 1]\). The range of \(sin^{-1}x\) is the set of all possible output values, which are angles between \(-π/2\) and \(π/2\).



Therefore, the domain of \(f(x)=\sin^{-1}x\) is \(\boxed{[-1, 1]}\) and the range is \(\boxed{[-π/2, π/2]}\).

Learn more about domain

brainly.com/question/28135761

#SPJ11

The two bases B1 and B2 span the same subspace of R3.

Let B1 be the basis {(1,2,3),(2,−1,2)}={u1,u2} and B2 be the basis {(0,5,4),(1,−8,−5)}={v1,v2}. We want to show that these two bases span the same subspace of R3.

To do this, we need to show that any vector in the subspace spanned by B1 can also be written as a linear combination of vectors in B2, and vice versa.

Let x be a vector in the subspace spanned by B1. Then x = a*u1 + b*u2 for some scalars a and b. Substituting the values of u1 and u2, we get:

x = a*(1,2,3) + b*(2,−1,2)

= (a+2b, 2a-b, 3a+2b)

Now we want to express x as a linear combination of v1 and v2:

x = c*v1 + d*v2

= c*(0,5,4) + d*(1,−8,−5)

= (d, 5c-8d, 4c-5d)

Setting the two expressions for x equal to each other, we get the following system of equations:

a+2b = d

2a-b = 5c-8d

3a+2b = 4c-5d

Solving this system of equations, we can find values of c and d that satisfy the equations. This shows that any vector in the subspace spanned by B1 can also be written as a linear combination of vectors in B2.

Similarly, we can show that any vector in the subspace spanned by B2 can also be written as a linear combination of vectors in B1.

Therefore, the two bases B1 and B2 span the same subspace of R3.

Learn about Basis

brainly.com/question/14947252

#SPJ11

The solution is, distance from the point to the line is 22√10 feet.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

The distance from point (x, y) to the line ax+by+c=0 is given by ...

 d = |ax +by +c|/√(a²+b²)

In general for, the equation of the line is ...

y = x/3 - 4

i.e. x -3y -12 = 0

so the distance formula is ...

 d = |x -y -12|/√(1² +(-3)²) = |x -y - 12|/√10

For the given point, the distance is ...

 d = |-6 -4 -12|/√10

   = 22/√10

 d = 22/√10 . . . .

distance from the point to the line = 22/√10

now, distance = 22/√10 * 10

                       =22√10 feet.

Hence, The solution is, distance from the point to the line is 22√10 feet.

To learn more on Equation 0f Straight-Line click:

brainly.com/question/11116168

#SPJ1

Answer:

C

Step-by-step explanation:

Answer choice A implies that less than received an 80 or better, while according to the boxplot, at least 18 students did.

Answer choice B suggests that most students scored at least 90%, but that is false.

Answer choice C implies that the same number of students scored in the 70-80% range as in the 80-90% range, which is true according to the box plot.

Answer D says that more people scored 65-70% than 90-100%, but the opposite is true.

Emily can read 5 words per minute.

Minutes are often used to measure the duration of activities such as meetings, phone calls, or workouts. They are also used to express the duration of processes or events that occur over a short period of time.

To find out how many words Emily can read per minute, we need to divide the total number of words she can read by the amount of time it takes her to read them.

75 words in 15 minutes can be written as a ratio:

75 words / 15 minutes

To simplify this ratio, we can divide both the numerator and the denominator by 15:

(75 words / 15 minutes) ÷ (15 minutes / 15 minutes)

This gives us:

5 words / 1 minute

Therefore, Emily can read 5 words per minute.

To  know more about per minute here

https://brainly.com/question/14095729

#SPJ4

It is simply the largest of the common factors.

We have:

12x³- 18x² + 6x

We find GCF of 12, 18 and 6:

GCF(12, 18, 6) = 6

12 = 2 · 6

18 = 3 · 6

6 = 1 · 6

and GCF of x³, x² and x:

GCF(x³, x², x) = x

x³ = x² · x

x² = x · x

x = 1 · x

Therefore:

We can conclude that the square pyramid has a volume of 111.5 in³.

A square pyramid in geometry is a pyramid with a square base.

It is a right square pyramid with C4v symmetry if the apex is perpendicular to and above the square's center.

It is an equilateral square pyramid, the Johnson solid J1 if all edge lengths are equal.

A polyhedron with seven faces is called a heptahedron.

One "normal" heptahedron exists, and it is formed up of a surface with one side made up of four triangles and three quadrilaterals.

So, 6.6 inches wide is the square pyramid's base.

The square pyramid's height is 7.7 inches or h.

V = a²(h/3) is the formula for the square pyramid's volume.

By changing the values given:
V = 6.6²(7.7/3)

V = 43.56(2.56)

V = 111.51 ≈ 111.5

Therefore, we can say that the square pyramid has a volume of 111.5 in³.

Know more about the square pyramid here:

https://brainly.com/question/22744289

#SPJ9

The required measure of y in the given triangle is 14 cm.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
Following the property of proportionality of sides in similar triangles,
8 + 3.2 / 8 = y / 10
11.2/8 = y / 10
112 = 8y
y = 14

Thus, the required measure of y in the given triangle is 14 cm.

Learn more about similar triangles here:

brainly.com/question/25882965

#SPJ1

Answer:

To eliminate y, we can add the two equations.

5x + y + 3x - y = 48 + 16

Simplifying the left side, we get:

8x = 64

Dividing both sides by 8, we get:

x = 8

Now we can substitute x = 8 into either of the original equations and solve for y:

5x + y = 48

5(8) + y = 48

40 + y = 48

y = 8

So the solution is (x,y) = (8,8).

The family uses 68.7 gallons of water every day for all purposes

If 22.9% of the water is used for cleaning, then the remaining 100% - 22.9% = 77.1% of the water is used for other purposes such as drinking and cooking.

To find out how much water the family uses every day, we need to add the amount of water used for cleaning to the amount of water used for other purposes.

Quantity of water used for cleaning = 22.9 percentage of the total amount of water used every day = 0.229 x 68.7 gallons = 15.71 gallons

Quantity of water used for other purposes = 77.1% of the total amount of water used every day = 0.771 x 68.7 gallons = 52.99 gallons

Total quantity of water used every day = amount of water used for cleaning + amount of water used for other purposes = 15.71 gallons + 52.99 gallons = 68.7 gallons

Learn more about percentage here

brainly.com/question/12715980

#SPJ4

Answer

the answer is b

The time taken to empty one tank is 1000 seconds or 16.67 minutes. Therefore, the total time required to empty all three tanks one after another is 50 minutes (16.67 minutes x 3).

The volume of water that can be emptied through the hole at the bottom of each tank per second is 0.2 liters. Therefore, the time taken to empty 200 liters of water from one tank is:

200 liters ÷ 0.2 liters per second = 1000 seconds

Converting the time to minutes:

1000 seconds ÷ 60 seconds per minute = 16.67 minutes

So, it takes 16.67 minutes to empty one tank. Multiplying this by three gives us the total time required to empty all three tanks:

16.67 minutes x 3 = 50 minutes

To learn more about time follow the link: https://brainly.com/question/28050940

#SPJ4