The expression 4x + 13 represents the time it takes a commuter to travel in the morning to work. The expression 10x – 2 represents the time it takes a commuter to travel in the evening from work. What is the total travel time?

14x + 15
14x + 11
6x + 11
6x + 15

Answer: 85.41 percent

Step-by-step explanation:

2882.45 / 3374.60 = 0.8541 or 85.41%

Answer:

85.416%

Step-by-step explanation:

#CarryOnLearning

The rate of interest per annum will be 3.6%.

The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.

Given, Isabelle takes out a loan that gathers compound interest.

At the start, the loan amount is £5500

after the 1-year loan amount is £5698.00

After the 2-year loan amount is £5903.13

thus,

P = 5500

For t = 1 year A = 5698.00

since interest is annually thus, the value of n is 1

So, from the formula

5698 =  5500( 1 + r)

5500r = 5698 -5500

r = 198/5500

r = 0.036

or

rate of interest, r = 3.6%

Learn more about compound interest here:

https://brainly.com/question/29335425

#SPJ1

The expressions that are equivalent to 2(-2m+7)-9m are C: 2(-8m+6m+7)-9m and D: 2(-6m+4m+7)-9m.

To see why, let's simplify the original expression:

2(-2m+7)-9m = -4m+14-9m = -13m+14

Now let's simplify the other expressions:

(-2m+7)2-9m = -4m+14-9m = -13m+14

2(-8m+6m+7)-9m = -16m+12m+14-9m = -13m+14

2(-6m+4m+7)-9m = -12m+8m+14-9m = -13m+14

So we can see that the expressions 2(-8m+6m+7)-9m and 2(-6m+4m+7)-9m are equivalent to the original expression.

You can learn more about equivalent expressions at

https://brainly.com/question/24734894

#SPJ11

The mean and the standard deviation of the binomial variable are given as follows:

The binomial distribution formula gives the probability of obtaining a specific number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is constant throughout the trials.

The mass probability formula(PMF) is given by the equation presented as follows:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters, along with their meaning, are listed as follows:

The parameter values for n and p in this problem are given as follows:

n = 3, p = 0.6.

The mean of the binomial distribution is given by the following equation:

E(X) = np.

Hence:

E(X) = 3 x 0.6

E(X) = 1.8.

The standard deviation of the binomial distribution is given by the following equation:

[tex]\sqrt{V(X)} = \sqrt{np(1 - p)}[/tex]

Hence:

[tex]\sqrt{V(X)} = \sqrt{3 \times 0.6 \times 0.4}[/tex]

[tex]\sqrt{V(X)} = 0.8485[/tex]

More can be learned about the binomial distribution at https://brainly.com/question/24756209

#SPJ1

All of the possible outcomes in which Hana wins the game is {6, 8, 10, 12, 14, 16}.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that it is certain to occur.

To win the game, the sum of the two spinners must be an even number greater than 6. Let's list all the possible outcomes:

So the possible outcomes in which Hana wins the game are: 2 + 4 = 6, 2 + 8 = 10, 4 + 2 = 6, 4 + 4 = 8, 4 + 6 = 10, 4 + 8 = 12, 6 + 2 = 8, 6 + 4 = 10, 6 + 6 = 12, 6 + 8 = 14, 8 + 2 = 10, 8 + 4 = 12, 8 + 6 = 14, and 8 + 8 = 16.

Therefore, all of the possible outcomes in which Hana wins the game is {6, 8, 10, 12, 14, 16}.

To know more about probability visit:

https://brainly.com/question/13604758

#SPJ1

The measurement of variability that would be best to use for the distribution is Interquartile Range, the correct option is (b).

The best measurement of variability to use depends on the distribution of the data and the purpose of the analysis.

If the distribution is skewed or contains outliers, the median and interquartile range would be better measures of variability than the mean and standard deviation.

The median is less affected by extreme values, and

The interquartile range is a robust measure of spread that is not influenced by outliers.

The mean and mean absolute deviation may be appropriate if the data are approximately symmetric and do not contain outliers.

Therefore, The best measurement of variability is (b) Interquartile range.

Learn more about Distribution here

https://brainly.com/question/30912587

#SPJ4

it definitely should be (-2,3)

Answer:

14

Step-by-step explanation:

The width of the rectangular field is 51 m. To find the width of the rectangular field, we can use the formula for the perimeter of a rectangle, which is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.

Given:
P = 294 m
L = 96 m

Substituting the given values into the formula, we get:

294 = 2(96) + 2W

Simplifying the equation, we get:

294 = 192 + 2W

Subtracting 192 from both sides of the equation, we get:

102 = 2W

Dividing both sides of the equation by 2, we get:

W = 51

To know more about perimeter refer to-

brainly.com/question/6465134#
#SPJ11

a) There are 128 subsets of A with 8 elements. This is because the number of subsets of a set with n elements is 2 ^ n. Therefore, the number of subsets of A with 8 elements is 2 ^ 8 = 128.

b) There are 82 subsets of A with 8 elements that have only numbers. This is because there are 10 numbers in A and each of these numbers can be included or excluded from the subset of 8 elements. Therefore, the number of subsets of A with 8 elements that have only numbers is 2 ^ 10 = 1024.

c) There are 46 subsets of A with 8 elements that have only letters. This is because there are 6 letters in A and each of these letters can be included or excluded from the subset of 8 elements. Therefore, the number of subsets of A with 8 elements that have only letters is 2 ^ 6 = 64.

d) There are 28 subsets of A with 8 elements that have 2 letters. This is because there are 6 letters in A and each of these letters can be included or excluded from the subset of 8 elements twice. Therefore, the number of subsets of A with 8 elements that have 2 letters is 2 ^ 12 = 4096.

Know more about subsets here

https://brainly.com/question/17514113#

#SPJ11

The area of the rhombus is 16√39 sq. cm.

A four-sided polygon with equal-length sides is known as a rhombus. A rhombus is an unique kind of parallelogram, like a square, in which the opposing sides are parallel and congruent. Yet, a rhombus lacks right angles, unlike a square.

Given that, sides = 10cm and the diagonal = 16 cm.

Using the Pythagorean theorem, we can find the length of the other diagonal as follows:

a^2 + b^2 = c^2

(10/2)^2 + b^2 = 16^2/4

25 + b^2 = 64

b^2 = 39

b = √39

The length of the other diagonal is 2*√39 cm.

Now, we can use the formula for the area of a rhombus:

A = (d1d2)/2 = (162√39)/2 = 16√39

Hence, the area of the rhombus is 16√39 sq. cm.

Learn more about rhombus here:

https://brainly.com/question/27870968

#SPJ1

The area of the rhombus is approximately 62.4 cm².

A rhombus is a quadrilateral with four sides of equal length. It is also known as a diamond or a lozenge. A rhombus has two pairs of parallel sides, and opposite angles are equal to each other. The diagonals of a rhombus bisect each other at right angles, meaning they cut each other in half and form a right angle at their intersection point.

The properties of a rhombus are similar to those of a square, but unlike a square, a rhombus does not have right angles. However, a square can be considered a special case of a rhombus, where all four angles are right angles.

The area of a rhombus can be calculated using the formula:

Area = (diagonal 1 x diagonal 2) / 2

where diagonal 1 and diagonal 2 are the lengths of the two diagonals of the rhombus.

Let's use the Pythagorean theorem to find the length of the shorter diagonal. We know that a rhombus has two pairs of congruent right triangles. Let's call the length of the shorter diagonal d.

Using Pythagorean theorem:

(10/2)² + (d/2)² = (16/2)²

5² + (d/2)² = 8²

25 + (d/2)² = 64

(d/2)² = 39

d/2 = √(39)

d = 2 * √(39)

Now we can use the formula for the area of a rhombus:

Area = (diagonal1 * diagonal2) / 2

Area = (10 * 2 * √(39)) / 2

Area = 10 * √(39)

Therefore, the area of the rhombus is approximately 62.4 cm².

To know more about area visit:

https://brainly.com/question/27683633

#SPJ1

Answer:

Step-by-step explanation:

Assuming that the number of ingredients per pie is constant, we can write an expression for the total number of ingredients and pies baked in the two years as:

Total number of ingredients = (129 x ingredients per pie) + (b x ingredients per pie)

Total number of pies baked = 129 + b

So, if we let "i" represent the number of ingredients per pie, we can write the expression as:

Total number of ingredients = (129 x i) + (b x i)

Total number of pies baked = 129 + b

Note that without knowing the value of "i," we cannot simplify this expression any further.

The probability that the first two bulbs are of the same colour and the last two are of different colours is 25/48.

The probability that the first two bulbs are of the same colour and the last two are of different colours is calculated as follows:

Given:

n(B) = 3 (Number of blue bulbs)

n(G) = 4 (Number of green bulbs)

n(R) = 5 (Number of red bulbs)

Formula: P(A) = n(A) / n(S)

Where,

P(A) = Probability of event A

n(A) = Number of favorable outcomes

n(S) = Number of possible outcomes

The probability of selecting two bulbs of the same colour is calculated as:

P(SS) = n(B) * n(B) / n(S)

= 3 * 3 / 12

= 1/4

The probability of selecting two bulbs of different colour is calculated as:

P(DD) = n(B) * n(G) * n(R) * n(R) / n(S)

= 3 * 4 * 5 * 5 / 12

= 25/12

Therefore, the required probability is calculated as:

P(SSDD) = P(SS) * P(DD)

= 1/4 * 25/12

= 25/48

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ4

Given:

5yd

To find:

The area of the hexagon

Solution:

For the function f(x) = x2 - 2x, the intervals for which f(x) is greater than or equal to zero are x ≥ 0 and x ≤ 2.

We can solve this equation by setting f(x) equal to zero and solving for x:
x2 - 2x = 0
x(x - 2) = 0
x = 0 or x = 2

Therefore, the intervals for which f(x) is greater than or equal to zero are x ≥ 0 and x ≤ 2.

Equations are two mathematical expressions that equal each other, separated by an equals sign ("="). In equations, we can find data that may or may not be known.

For more information about function, visit:

https://brainly.com/question/25638609

#SPJ11

Answer:

Step-by-step explanation:

The Domain is (x) values that a certain line covers on a graph.

This line is a segment, so it has a very specific domain.

The domain is written in the form of =>     [tex]a\leq x\leq b[/tex]

    - In which (a) and (b) are the smallest and largest numbers on the domain, respectively.

Here, the line starts at (-11,6) and goes all the way to (2,1)

From here - we take out the y-values to get that the x-values go from (-11) to (2)

That means that the domain. of this here line, is:

[tex]Domain = -11\leq x\leq 2[/tex]

The exact value of sin(6/11π) is -sin(6/11π).

The exact value of sin(6/11π) can be found by using the reference angle of 6/11π. The reference angle is the acute angle formed by the terminal side of the given angle and the x-axis. In this case, the reference angle is (6/11π) - π = (-5/11π).

To find the exact value of sin(-5/11π), we can use the fact that sin(-θ) = -sin(θ). So, sin(-5/11π) = -sin(5/11π).

Next, we can use the fact that sin(θ) = sin(π - θ) to find the exact value of sin(5/11π). So, sin(5/11π) = sin(π - 5/11π) = sin(6/11π).

Therefore, the exact value of sin(6/11π) is -sin(6/11π).

In conclusion, the exact value of sin(6/11π) is -sin(6/11π).

Learn more about Exact value

brainly.com/question/12060967

#SPJ11

From the given information provided, the number of students who brought a packed lunch and did not visit the gift shop is 32.

The number of students who brought a packed lunch and did not visit the gift shop can be calculated by subtracting the number of students who visited the gift shop from the number of students who bought a packed lunch:

32 - 0 = 32

A frequency tree is a visual representation of data that shows how the total number of individuals or items is distributed among different categories or groups. It is commonly used in statistics and probability to organize and analyze data in a hierarchical structure.

Learn more about frequency here: brainly.com/question/27820465

#SPJ1

An abscissa is a line that is drawn perpendicular to the vertical axis, or y-axis, of a graph. It is usually measured in the form of a number, and it is used to determine the position of points, lines, and shapes on a graph. Abscissas are also referred to as the x-coordinates of a graph, and they can be used to plot and analyze data.

Quadrants are the four sections of a coordinate plane formed by the intersection of the x-axis and the y-axis. Quadrants are labeled I, II, III, and IV, with Quadrant I being the upper right-hand corner, Quadrant II being the upper left-hand corner, Quadrant III being the lower left-hand corner, and Quadrant IV being the lower right-hand corner. Quadrants are commonly used to graph equations and to identify points on a coordinate plane.

Learn about Quadrants here https://brainly.com/question/28587485

#SPJ1

The sales price of the item after the 15% discount is $850.

The original price of the item is $1,000 and the discount rate is 15%. To find the amount of the sales price, we need to calculate the amount of the discount and subtract it from the original price.

Step 1: Calculate the amount of the discount by multiplying the original price by the discount rate.
Discount = Original Price x Discount Rate
Discount = $1,000 x 0.15
Discount = $150

Step 2: Subtract the amount of the discount from the original price to find the sales price.
Sales Price = Original Price - Discount
Sales Price = $1,000 - $150
Sales Price = $850

Therefore, the sales price of the item after the 15% discount is $850.

Learn more about Original price

brainly.com/question/731526

#SPJ11

Answer:₹14.40

Step-by-step explanation:

36x2=72

24x2=48

72+48=120x12=1440/100 =14.40

The simplification of the radical expression √9. is 3.

Radical expressions are simplified by taking them down to their most basic form and, if feasible, altogether deleting the radical. When a radical expression appears in the denominator of an algebraic expression, the radical expression is simplified by multiplying the numerator and denominator by the appropriate radical expression (for example, conjugate in the case of a binomial and the same radical in the case of a monomial).

The given expression is √9.

The given expression can be written as:

√(3)(3) = 3

Hence, the simplification of the radical expression √9. is 3.

Learn more about radical expressions here:

https://brainly.com/question/3796764

#SPJ1

The domain of \(f(x)=\tan ^{-1} x\) is \(\mathbb{R}\) and the range is \((-\frac{\pi}{2}, \frac{\pi}{2})\).

Explanation:

The domain of a function is the set of all possible input values for which the function is defined. The inverse tangent function, \(f(x)=\tan ^{-1} x\), is defined for all real numbers, so the domain is \(\mathbb{R}\).

The range of a function is the set of all possible output values for which the function is defined. The inverse tangent function, \(f(x)=\tan ^{-1} x\), has a range of \((-\frac{\pi}{2}, \frac{\pi}{2})\). This is because the tangent function has a period of \(\pi\), and the inverse tangent function is the inverse of the tangent function restricted to the interval \((-\frac{\pi}{2}, \frac{\pi}{2})\).

Therefore, the domain of \(f(x)=\tan ^{-1} x\) is \(\mathbb{R}\) and the range is \((-\frac{\pi}{2}, \frac{\pi}{2})\).

Learn more about

brainly.com/question/28135761

#SPJ11

√9 - 3x⁄x + 4x2 - x3⁄2 + y2 - 2xy + 2⁄2 + 9 - x2⁄2 from 0 to √9

To find the area bounded by the given functions, we will need to solve the following integrals:

1. Integral of √9 - 3x⁄x from 0 to √9
2. Integral of 4x2 - x3⁄2 from 0 to √9
3. Integral of y2 - 2xy + 2⁄2 from 0 to √9
4. Integral of 9 - x2⁄2 from 0 to √9

The area bounded by the given functions is then equal to the sum of the four integrals, or:

Area = √9 - 3x⁄x + 4x2 - x3⁄2 + y2 - 2xy + 2⁄2 + 9 - x2⁄2 from 0 to √9

Learn more about integration

brainly.com/question/18125359

#SPJ11

Answer:

log(2)+log(3)+2log(x)

you should try downloading an app called math away

i don't know if it's right but I got the answer from a reliable source

The pair of equations is y = 25x + 8 and y = 12 + 5x where 'x' is the number of months and 'y' is the total cost.

A system of equations refers to a set of two or more equations that need to be solved simultaneously. The solution of a system of equations is a set of values that satisfy all the equations in the system.

To represent the following situations use variables like x, y, z.. etc. to represent the number of months and total cost and form the equations.

Here we have

An online video streaming service offers two plans for unlimited streaming.

Plan A has a one-time $8 membership fee and is $25 per month.  

Let Plan A run for 'x' number of months and 'y' be the total cost

Total cost for 'x' months, y = 25x + 8  

=> y = 25x + 8

Plan B has a $12 membership fee and is $5 per month.

Let Plan B run for 'x' number of months and 'y' be the total cost

Total cost for 'x' months, y = 12 + 5x

=> y = 12 + 5x

Therefore,

The pair of equations is y = 25x + 8 and y = 12 + 5x where 'x' is the number of months and 'y' is the total cost.

Learn more about Equations at

https://brainly.com/question/29071782

#SPJ1

The solutions to the quadratic equation are x = -1/3 and x = -8.

To solve the quadratic equation 3x^2 + 1 = -25x - 7 by factoring, we first need to rearrange the equation so that all the terms are on one side of the equal sign:

3x^2 + 25x + 8 = 0

Next, we need to find two numbers that multiply to give us 8 (the constant term) and add to give us 25 (the coefficient of the x term). These numbers are 20 and 1, so we can factor the trinomial as follows:

(3x + 1)(x + 8) = 0

Now we can use the zero product property to set each factor equal to zero and solve for x:

3x + 1 = 0 or x + 8 = 0

x = -1/3 or x = -8

So the solutions to the quadratic equation are x = -1/3 and x = -8.

Learn more about quadratic equation

brainly.com/question/30098550

#SPJ11

The simplified expression is 1/(9a²b⁵).

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

To simplify the given expression, we need to cancel out any common terms in the numerator and denominator. We can do this by dividing both the numerator and denominator by the highest power of a and b that they have in common. Here are the steps:

1. (4a²b₂²)/(15ab³)*(5a³b⁶)/(12a⁴b⁷)
2. Cancel out the common terms in the numerator and denominator:
= (4/15)*(5/12)*(a²/a⁴)*(b²/b⁷)*(a³/a⁴)*(b⁶/b⁷)
3. Simplify the terms:
= (1/9)*(1/a²))*(1/b⁵)
4. Multiply the terms together:
= 1/9a²b⁵

So the simplified expression is1/(9a²b⁵)

To learn more on Expression:

brainly.com/question/10413253

#SPJ11

We can conclude that the measure of length AB is 23.46 ft and the measure of length BC is 9 ft.

Sine formula is used to calculate the sine angle of a right-angled triangle which is the ratio of the opposite side and the hypotenuse.

Given is that a 40-ft-wide house has a roof with a 6-12 pitch (the roof

rises 6 ft for a run of 12 ft). The owner plans a 14-ft-wide addition that will

have a 3-12 pitch to its roof.

We can write the measure of length AB as -

AB = 6 + √(9 + 296)

AB = 6 + 17.46

AB = 23.46 ft

We can write the measure of length BC as -

BC = 6 + 1/4 x 12

BC = 6 + 3

BC = 9 ft

Therefore, we can conclude that the measure of length AB is 23.46 ft and the measure of length BC is 9 ft.

To solve more questions on length measurements, visit the link-

https://brainly.com/question/30956532

#SPJ1

The values of Ф solved using a unit circle, between 0 and 2π, for which tanФ =  - √3 is 2π/3 and 5π/3.

What is a circle?

A circle is a shape made up of all points in a plane that are at a specific distance from the centre point. In other words, it is the path a moving point in a plane takes to move around a curve while maintaining a constant distance from another point. The circle has an area and a perimeter and is a two-dimensional figure. The distance around a circle, or its circumference, is referred to as the perimeter of the circle. The region enclosed by a circle in a 2D plane is said to be its area.

The complete question is given below.

Given,

tan Ф = - √3

We have to find all values of Ф between 0 and 2π using a unit circle.

The unit circle for trigonometric calculations is given below.

from the unit circle,

tan 60 = √3

In quadrant 2,

tan ( 180 - 60) = - tan 60

tan 120 = - tan 160 = -√3

In quadrant 3,  tangent values are positive.

In quadrant 4

tan (360 - 60) = - tan 60

tan 300 = -tan 60 = -√3

Also,

tan 120 = tan 2π/3

tan 300 = tan 5π/3

Therefore the values of Ф solved using a unit circle, between 0 and 2π, for which tanФ =  - √3 is 2π/3 and  5π/3.

To learn more about unit circles, follow the link.

https://brainly.com/question/14346076

#SPJ1