Kiran earns y dollars doing chores, and Priya earns 5/6 as much as Kiran. How much does Priya earn?

A) 6/5y
B) 5/6y
C)5.6y

It is not possible to reach the top of the ladder to the edge of the roof.

We can solve this problem using the Pythagorean theorem, which states that for a right triangle, the sum of the squares of the two shorter sides is equal to the square of the length of the hypotenuse (the longest side).

In this case, the ladder is the hypotenuse of a right triangle, and the distance from the base of the ladder to the house and the distance from the top of the ladder to the edge of the roof are the two shorter sides.

Let x be the distance from the top of the ladder to the edge of the roof. Then, we can write:

\(10^{2}\) = \((1.5)^{2}\) + \(x^{2}\) + \(12^{2}\)

Simplifying and solving for x, we get:

100 = 2.25 +\(x^{2}\) + 144

\(x^{2}\) = 100 - 2.25 - 144

\(x^{2}\) = -46.25

Since x represents a distance, which must be positive, this means that there is no solution to the equation. Therefore, it is not possible for Sammy to reach the edge of the roof with his 10-foot ladder while keeping the base of the ladder at least 1.5 feet from the base of the house.

Correct Question :

Sammy has a 10-foot ladder, which he needs to climb to reach the roof of his house. the roof is 12 feet above the ground. the base of the ladder must be at least 1.5 feet from the base of the house. how far is it from the top of the ladder to the edge of the roof?

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Answer: 15 + b

Step-by-step explanation:

15 is being increased by b and b could be any number so the expression will be  15 + b . Increase means is going up so you will be adding b.

The product of a scalar (number) with a lower triangular matrix is a lower triangular matrix.

In linear algebra, matrices are crucial, and one of the critical matrix types is the lower triangular matrix. A lower triangular matrix is a matrix that has elements on the diagonal and below the diagonal, while the upper triangle of the matrix has elements that are zero. Scalar multiplication is one of the fundamental operations in linear algebra, where a scalar or a number multiplies a matrix to produce a new matrix. The product of a scalar or number with a lower triangular matrix is a lower triangular matrix. The scalar multiplication distributes the scalar to all the elements of the matrix, and if the matrix is a lower triangular matrix, then its elements below the diagonal are already zero, which means that the scalar multiplication will not affect them. The scalar multiplication will only affect the elements on the diagonal of the matrix and still preserve the lower triangular structure of the matrix. To better understand this, let us consider a 3x3 lower triangular matrix L, given by:0 0 00 2 00 3 1. Let us multiply the matrix L by a scalar k; we have: kL = k[0 0 00 2 00 3 1] = [k*0 k*0 k*0k*0 k*2 k*0k*0 k*3 k*1] = [0 0 00 2k 00 3k k]The result is still a lower triangular matrix, and the scalar multiplication of k did not affect the lower triangular structure of the matrix.

In summary, when we multiply a lower triangular matrix by a scalar, we will still have a lower triangular matrix. The scalar multiplication does not affect the lower triangle structure of the matrix but only affects the elements on the diagonal. This property is crucial when we want to perform scalar multiplication of matrices, especially lower triangular matrices.

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The given unity feedback system is the type-1 system, which can be observed from the given open-loop transfer function G(s).

Steady state error is the difference between the input and the output as time approaches infinity. It is also the difference between the desired value and the actual output at steady-state.

The steady-state error is calculated using the error coefficient, which depends on the type of the system.Find the steady-state error if the input is 80u(t):The transfer function of the given system can be written as follows;G(s) = 80(8²)/(s+4)(8+6)(8+17)The type of the given system is the type-1 system.

As the input to the system is u(t), the error coefficient is given as,Kp = lims→0sG(s) = 80/4(6)(17) = 5/153The steady-state error can be found out by the following formula;

ess = 1/Kp = 153/5.

Therefore, the steady-state error of the given system if the input is 80u(t) is 153/5.Find the steady-state error if the input is 80tu(t):As the input to the system is tu(t), the error coefficient is given as,Kv = lims→0s²G(s) = 0The steady-state error can be found out by the following formula;ess = 1/Kv = ∞.

Therefore, the steady-state error of the given system if the input is 80tu(t) is infinity.Find the steady-state error if the input is 80t²u(t):As the input to the system is t²u(t), the error coefficient is given as,Ka = lims→0s³G(s) = ∞The steady-state error can be found out by the following formula;

ess = 1/Ka = ∞.

Therefore, the steady-state error of the given system if the input is 80t²u(t) is infinity.

By using the error coefficient formula, we have found that the steady-state error of the given system if the input is 80u(t) is 153/5, steady-state error of the given system if the input is 80tu(t) is infinity and steady-state error of the given system if the input is 80t²u(t) is infinity.

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The lowest and greatest values in the dataset, divided by two, make up the Mid-range. Thus, this provides us with the midrange value.

The mid-range or mid-extreme is the arithmetic mean of the highest and minimum values of the data set and is used in statistics as a measure of a sample's central tendency.

The difference between the greatest and minimum values, which is a measure of statistical dispersion, is strongly related to the mid-range.

The two measurements are complementary in that one can determine the sample's maximum and minimum values by knowing the range and the midpoint.

Therefore, the lowest and greatest values in the dataset, divided by two, make up the Mid-range. Thus, this provides us with the midrange value.

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Part A: percent of 70 is 10.

x% of 70 = 10

70x / 100 = 10

x = 1000 / 70

x = 14.28 %.

Part B: percent of 2.8 is 20.

x% of 2.8 = 20

2.8x/ 100 = 20

x = 2000/ 2.8

x = 714.28%

Part C: percent of 90 is 18.

x% of 90 = 18

90x/100 = 18

x = 1800 / 90

x = 2 %

Part D: percent of 10 is 55.

x% of 10 = 55

10x / 100 = 55

x = 5500/ 10

x = 550%.

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Answer: £180

Step-by-step explanation:

The interest gotten for the 10 years will be calculated as:

= Principal × Rate × Time

= 150 × 2% × 10

= 150 × 0.02 × 10

= 30

The amount he has in the bank account at the end of the 10 year will be:

= Principal + Interest

= £150 + £30

= £180

Answer:

32.7 degress

Step-by-step explanation:

In this question we are to find the value of the angle

The best way to do with the information given is the cosine rule

Mathematically that would be;

y^2 = x^2 + z^2 -2xzCosY

where x = 90 ft , y = 55ft and z = 50 ft

Plugging the values we have;

55^2 = 90^2 + 50^2-2(90)(50)CosY

-7575 = -9000cosY

cosY = 7575/9000

cosY = 0.841666666667

Y = cos^-1 0.841666666667

Y = 32.68 degrees which is 32.7 to the nearest tenth

Answer:

32.7

Step-by-step explanation:

If variables were found to be unrelated, the correlation coefficient would be close to 0 or,more precisely.

How is the correlation coefficient affected when variables are found to be unrelated or have no linear relationship?

When variables are found to be unrelated or have no linear relationship, the correlation coefficient would be close to zero or zero, indicating a weak or no correlation between the variables.

If variables were found to be unrelated, the correlation coefficient would be close to 0 or, more precisely, the correlation coefficient would be negligible or statistically insignificant. In other words, there would be little to no linear relationship between the variables.

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Answer:

thank you for the free points

Step-by-step explanation:

Answer:

13 gallons

Step-by-step explanation:

13.35 = 5 gallons of gas

1 gallon = 2.67

y = 2.67x

34.71 = 2.67x

\(\frac{34.71}{2.67} = \frac{2.67x}{2.67}\)

x = 13

Answer:

B

Step-by-step explanation:

I think...

Answer:

295 feet

Step-by-step explanation:

407- 112= 295 feet

hope this helps!

ibrahim

Answer:295 Feet

Step-by-step explanation: 407-112 = 295 feet

Try it.

(b) No, The branch manager's argument that dispatching buses every 0.5 minutes will reduce the average traveling time (a round trip) to 3.5 minutes is not correct.

To calculate the average time, we need to consider the time it takes for the bus to travel to the airport and back, as well as the time spent waiting for the bus.

If buses are dispatched every 3 minutes, and the average traveling time (a round trip) is 21 minutes, it means that passengers spend 18 minutes waiting for the bus (21 minutes - 3 minutes of traveling time).

If buses are dispatched every 0.5 minutes, the waiting time will be significantly reduced. However, the traveling time remains the same at 21 minutes for a round trip.

Therefore, the average traveling time will not be reduced to 3.5 minutes but will remain at 21 minutes (assuming the traveling time remains constant).

(c) The average traveling time, following the branch manager's suggestion of dispatching buses every 0.5 minutes, would still be 21 minutes.

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Complete question:

The Avis Company is a car rental company and is located three miles from the Los Angeles airport (LAX). Avis is dispatching a bus from its offices to the airport every 3 minutes. The average traveling time (a round trip) is 21 minutes.

(a) The branch manager wants to improve the service and suggests dispatching buses every 0.5 minute. She argues that this will reduce the average traveling time (a round trip) to 3.5 minutes. Is she correct? (Enter "Yes" or "No" in the following blank).

c. Following the branch manager's suggestion (dispatch busses every 0.5 min), what will the average traveling time be? average travelling time ____(mins) (enter the numbers only)

We need to know about z-score to solve the problem. The z-score of the soda is 0.6

A z-score tells you how many standard deviations away an individual data falls from the mean. We can calculate z-score from the standard deviation and mean of the data. In this question we know that the cost of a soda is $1.15 and the mean is $1.00 and the standard deviation is $0.25.We need to calculate the z-score of the soda with the given information.

z-score=x-μ/σ=1.15-1.00/0.25=0.15/0.25=0.6

Therefore the z-score of the soda is 0.6

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Given:

The bases of a trapezoid lie on the lines

\(y=2x+7\)

\(y=2x-5\)

To find:

The equation that contains the midsegment of the trapezoid.

Solution:

The slope intercept form of a line is

\(y=mx+b\)

Where, m is slope and b is y-intercept.

On comparing \(y=2x+7\) with slope intercept form, we get

\(m_1=2,b_1=7\)

On comparing \(y=2x-5\) with slope intercept form, we get

\(m_2=2,b_2=-5\)

The slope of parallel lines are equal and midsegment of a trapezoid is parallel to the bases. So, the slope of the bases line and the midsegment line are equal.

\(m=m_1=m_2=2\)

The y-intercept of one base is 7 and y-intercept of second base is -5. The y-intercept of the midsegment is equal to the average of y-intersects of the bases.

\(b=\dfrac{b_1+b_2}{2}\)

\(b=\dfrac{7-5}{2}\)

\(b=\dfrac{2}{2}\)

\(b=1\)

So, the y-intercept of the required line is 1.

Putting m=2 and b=1 in slope intercept form, we get

\(y=2x+1\)

Therefore, the equation of line that contains the midsegment of the trapezoid is \(y=2x+1\).

Answer:

35 - 4x = 3x + 10

Step-by-step explanation:

Given that :

Writing out the problem mathematically,

Let the number = x

35 - (4 * x) = (3 * x) + 10

35 - 4x = 3x + 10

-4x - 3x = 10 - 35

-7x = - 25

Hence x the equation which can be used to obtain the value of x is :

35 - 4x = 3x + 10

Answer:

The equation: 35 - 4x = 3x + 10

3.57

Step-by-step explanation:

Let

x = the unknown number

35 - 4x = 3x + 10

Collect like terms

35 - 10 = 3x + 4x

25 = 7x

Divide both sides by 7

x = 25 / 7

= 3.57 approximately

The unknown number, x is approximately 3.57

The equation: 35 - 4x = 3x + 10

Answer:

1400, 1575

Step-by-step explanation:

Two number: 175x , 175y   (x and y no more common factor)

LCM: 175xy = 12600

xy = 72

72: (1,72) (2,36) (3,24) (4,18) (6,12) (8,9) only (8,9) fit no common factor

Two number: 8*175 = 1400         9*175 = 1575

The amount of water you should pack per person when hiking is 2 liters.

option B.

Hiking is a type of exercise usually performed outdoor and it involves walking on trails or paths, typically in natural environments such as forests, mountains, or wilderness areas.

Both children and adult can preform hiking.

A general rule of thumb suggest that you should pack at least 2 liters of water per person per day for moderate hiking in moderate temperatures.

Some rules suggests 2 cups for adult (about 1/2 liter) and Children about 1-2 cups of water for every hour of hiking.

So based on the given options, we can choose 2 liters pack per person when hiking.

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Attached is a two-way frequency table, to help Hugo organize the results.

A two-way frequency table is a table used to organize and display the relationship between two categorical variables. It is constructed by counting the number of occurrences of each combination of categories and presenting the results in a table format.

1. Identify the categorical variables and list their possible categories.

cat, no cat, dog, no dog

2. Count the number of observations for each combination of categories.

cat = 17

no dog = 20

no cat no dog = 7

3. Organize the counts in a table with the categories of one variable as rows and the categories of the other variable as columns.

          | dog | no dog | total

cat      |        |              |   17  |

no cat |        |     7       |        |

total    |        |     20    |   41  |

4. Fill in the table with the counts of the observed combinations of categories.

cat but no dog = 20 - 7 = 13

both cat and dog = 17 -13 = 4

total no cat = 41 - 17 = 24

total dog = 41 - 20 = 21

dog but no cat = 24 - 7 = 17

          | dog | no dog | total

cat      |   4   |      13     |   17  |

no cat |   17  |     7       |   24  |

total    |   21  |     20    |   41  |

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The statement that is NOT true is "Line a and line b have the same slope."

In mathematics, slope refers to the measure of steepness of a line or a curve. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line or curve. In other words, slope is the amount by which the dependent variable (y) changes for a unit increase in the independent variable (x)

Given by the question.

Since lines a and b are parallel, they have the same slope. However, the statement that they have the same slope is true, so it cannot be the statement that is not true.

On the other hand, line c is perpendicular to both lines a and b, which means that its slope is the negative reciprocal of the slopes of lines a and b. Therefore, the product of the slopes of line c and line b is -1, and the product of the slopes of line a and line c is -1. Additionally, the sum of the slopes of line b and line c is 0, since the slopes are opposite reciprocals of each other.

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The formula for the cost if the line rental is £20 and the price of calls made is £15 will be 20 + 15p.

It should be noted that an expression is used to illustrate the relationship given between the variables.

In this case, the monthly phone contract is made up of the fixed line rental and the price represented by p.

The appropriate expression to illustrate this information will be:

= Fixed cost + Calls made

= 20 + 15(p)

= 20 + 15p

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Answer: 8

Step-by-step explanation:

a. Let be the side length of the square. The perimeter of the square is given by the formula: Perimeter = 4s, where s is the length of each side.       Solving for s, we get:

s = Perimeter / 4

b. Let be the diameter of the circle. The area of the circle is given by the formula:

Area = (π/4) × d², where d is the diameter. Substituting for d, we get:

Area = (π/4) × (2r)² = πr²

c. Let be the length of the string in inches. We know that 1 yard = 36 inches. Therefore, the length of the string in yards is given by the expression:

Length in yards = /36

d. i. If the Hare gives the Tortoise a 15-second head start, then the Tortoise has been running for 15 seconds when the Hare starts the race. When the Hare has been running for 26 seconds, the Tortoise has been running for:

26 - 15 = 11 seconds

ii. Let be the number of seconds since the Hare started the race. The number of seconds since the Tortoise began the race is less than . Therefore:

Tortoise's running time = - 15

iii. When the Tortoise has been running for 17 seconds, the Hare has been running for:

17 + 15 = 32 seconds

iv. Let be the number of seconds since the Tortoise started the race. The number of seconds since the Hare began the race is more than . Therefore:

Hare's running time = + 15

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Step-by-step explanation:

AD ≅ BC, Given

∠BCD ≅ ∠ADC, Given

CD ≅ CD, Reflexive property

ΔBCD ≅ ΔADC, SAS congruence

∠BDC ≅ ∠ACD, CPCTC

ΔECD is an isosceles triangle, definition of isosceles

DE ≅ CE, properties of isosceles triangles

Answer:

1. 36 \(m^{2}\)

2. 333.125 \(ft^{3}\)

3. 210 \(ft^{3}\)

4. Yes, Martina's estimate is reasonable.

Step-by-step explanation:

Numbering the rectangular surfaces, we have:

Area of a rectangle = length x width

For surface 1: Area = 2 x 2.4

                                = 4.8 \(m^{2}\)

For surface 2: Area = 3 x 2.4

                                = 7.2 \(m^{2}\)

For surface 3: Area = 3 x 2

                                = 6.0 \(m^{2}\)

For surface 4: Area = 3 x 2.4

                                = 7.2 \(m^{2}\)

For surface 5: Area = 2 x 2.4

                                = 4.8 \(m^{2}\)

For surface 6: Area = 3 x 2

                                = 6.0 \(m^{2}\)

Total surface area of the rectangular prism = (2 x 4.8) + (2 x 7.2) + (2 x 6.0)

                                        = 36 \(m^{2}\)

2. length = 10.25 ft

width = 5 ft

height = 6.5 ft

Thus,

volume = l x w x h

            = 10.25 x 5 x 6.5

            = 333.125 \(ft^{3}\)

3. length = 15 ft

width = 7 ft

height = 2 ft

So that,

volume = l x w x h

            = 15 x 7 x 2

            = 210 \(ft^{3}\)

4. For a rectangular prism, area of the opposite surfaces are equal. So that;

Area of rectangle = length x width

For surface 1: Area = 13.0 x 6

                               = 78.0 \(ft^{2}\)

For surface 2: Area = 13.0 x 8

                                = 104.0 \(ft^{2}\)

For surface 3: Area = 6 x 8

                                = 48 \(ft^{2}\)

Surface area of the prism = (2 x 78.0) + (2 x 104.0) + (2 x 48)

                                          = 460.0 \(ft^{2}\)

Therefore, Martina's estimate is reasonable.

From the given table and attached number line, we see that the lowest and highest record low temperatures are respectively; -34°F and -27°F

From the table attached, we see that the record low temperatures for several states graph the temperatures are;

AL = -27°F

AK = -29°F

CT = -32°F

NJ = -34°F

VA = -30°F

We can see that -34°F is the most negative temperature, therefore, it will be on the left most side of our number line.  

-27°F is greatest of our given negative temperatures. -27°F is a less negative temperature than our other given low temperatures, therefore, it will lie on the right most side of our number line.  

Other temperatures will lie between these two values according to their temperatures.    

-32 is second large negative temperature after -34, therefore, it will lie on the right side of -34.

-30 will lie on the right side of -32 and -29 will lie on the right of -32.

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Given:

solution :

so answer is 75.

Answer:

75

Step-by-step explanation:

Answer:

\(24\pi \: cm {}^{2} \)

Step-by-step explanation:

The area of a cone is

\(\pi \times r {}^{2} + \pi \times r \times \sqrt{ {r }^{2} + {h}^{2} } \)

The volume of the conical paper cup will be option (D) 24π

The steps are as follow:

r = base radius = 3 cm

h = height of cone = 8 cm

V = volume of cone = (1/3)πr²h.

V = (1/3)π*3²*8.

V = 24π

So, the volume of the conical paper cup will be option (D) 24π

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Answer:

the normal rice of saddle is  £275

Step-by-step explanation:

normal prices are reduced by 20% to get sale price

this can be shown that

normal price = 100%

and sale price is 80% of normal price (100%-20%)

therefore we can use cross multiplication

%                      amount( £)

80        :            220

100       :            x

80x = 22000

x = 22000/80

x = 275

the normal rice of saddle is  £275