The length of a rectangle is 5 units more than the width. The area of the rectangle is 36 square units. What is the length, in units, of the rectangle?

The equation, (x - 10)² + (y - 5)² = 144, represents a circle with center (10, 5) and radius 12.

From the question, we are to determine the center and radius of the circle represented by the given equation

From the given information, the given equation is

(x - 10)² + (y - 5)²= 144

To determine the center and the radius of the circle we will compare the given equation to the standard form of the equation of a circle:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius.

The equation

(x - 10)² + (y - 5)²= 144

can be written as

(x - 10)² + (y - 5)²= 12²

By comparison,

h = 10, k = 5 and r = 12

Hence, the center of the circle is (10, 5) and the radius is 12

Learn more on Determining the center and radius of a circle here: https://brainly.com/question/26757548

#SPJ1

Answer: 21 cups of sugar, 7 cakes

Solve the following proportion:

3/5=x/35

Cross multiply:

5x=35(3)

5x=105

x=21 cups of sugar

3 cups of sugar= 1 cake

21 cups of sugar= x cakes

Cross multiply:

3x=21

21/3

7 cakes

Answer:

$217.99

Step-by-step explanation:

To calculate your electricity bill, you need to multiply the number of kilowatt-hours (kWh) used by the rate per kWh.

Using the given information:

Number of kWh used = 2205

Rate per kWh = $0.09884

To calculate the bill:

Bill = Number of kWh used x Rate per kWh

= 2205 kWh x $0.09884/kWh

= $217.99

Therefore, your electricity bill would be $217.99 if you used 2205 kWh at a rate of $0.09884 per kWh.

Answer:

To calculate your bill for using 2205 kWh of electricity at a rate of $.09884 per kWh, you can use the following formula:

Bill = kWh used x Rate per kWh

Plugging in the values given, we get:

Bill = 2205 x 0.09884

Simplifying the calculation, we get:

Bill = 217.5354

Rounding to two decimal places, the bill would be $217.54.

Hope This Helps!

The width of the rectangle is 6 centimeters

We know that the area of a rectangle is given by the formula

A = L x W

where A is the area, L is the length, and W is the width.

In this problem, we are given the length of the rectangle (L) as 9 centimeters and the area (A) as 54 square centimeters. We can use these values to find the width (W) of the rectangle.

We can start by substituting the given values into the formula

54 = 9 x W

Next, we can solve for the width (W) by dividing both sides of the equation by 9

54 / 9 = W

Simplifying the left-hand side, we get

W = 6 centimeter

Learn more about area here

brainly.com/question/20693059

#SPJ4

I have solved the question in general, as the given question is incomplete.

The complete question is:

The length of a rectangle with area 54 square centimeters is 9 centimeters. What is the width of the rectangle

The probability that flood volume exceeds its mean value by more than one standard deviation is approximately 0.000.In rounded form, it is 0.000 (to three decimal places).Hence, the required probability is approximately 0.000.

Given that the flood volume follows a normal distribution. We are supposed to find the probability that flood volume exceeds its mean value by more than one standard deviation.

To find the probability, we need to standardize the variable, X.

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

We can standardize the variable X with the help of the following formula:

Z = (X - μ) / σ

Where Z is the standard score,

X is the raw score,

μ is the population mean, and

σ is the population standard deviation.

Now, we need to find the value of Z.

Z = (X - μ) / σZ = (20 - 10) / 2

Z = 5P(X > 20) = P(Z > 5)

From the z-table, we can find that the probability of Z being greater than 5 is very close to 0.

for such more question on probability

https://brainly.com/question/24756209

#SPJ11

The approximate percentage that the price of the computer was reduced is 12.5%.

A number can be expressed as a fraction of 100 using a percentage. The letter "%" stands for it. We may compare numbers of various sizes quickly and efficiently using percentages to compare a quantity to its entire or total.

To find the approximate percentage that the price of the computer was reduced, we can use the following formula:

percentage decrease = (original price - new price) / original price x 100%

Substituting the given values, we get:

percentage decrease = (399 - 349) / 399 x 100%

percentage decrease = 50 / 399 x 100%

percentage decrease ≈ 12.5%

Therefore, the approximate percentage that the price of the computer was reduced is 12.5%.

To know more about fraction, visit:

https://brainly.com/question/10354322

#SPJ1

Answer:

x = 12 , -2

Step-by-step explanation:

For the first Question ,

we Know that by VOA , The angles are equal to 40*
and by being a linear pair , we get 180 - 110 = 70*

By exterior angle property , 40 + 70 = 9x - 2

= 110 = 9x - 2

9x = 108

x = 108/9 = 12



For the second question ,

By VOA , we know that the interior angles of the triangle are x+74 , 37 + x and 73


By Angle - sum Property , x+ 74 + 37 + x + 73 = 180

                                               2x + 184 = 180
                                                2x = 180 - 184
                                                2x = -4 , so x = -2

Therefore, the coordinates of A are (1, 3) and (2, 4). Therefore, the area of the shaded region is (1/2) square units.

In mathematics, area is the measure of the amount of surface enclosed by a two-dimensional shape or object. It is the size of a surface, and is typically measured in square units such as square meters (m²), square centimeters (cm²), square feet (ft²), or square inches (in²).

Here,

First, we need to find the coordinates of the point where the line and the curve meet (point A).

Substituting y = x(4 – x) into y + 2x = 5, we get:

x(4 – x) + 2x = 5

Simplifying and rearranging, we get:

x² – 3x + 2 = 0

Factoring, we get:

(x – 1)(x – 2) = 0

Therefore, x = 1 or x = 2.

When x = 1, y = 3, and when x = 2, y = 4. Therefore, the coordinates of A are (1, 3) and (2, 4).

To find the area of the shaded region, we need to find the integral of the curve y = x(4 – x) between x = 1 and x = 2, and subtract the area under the line y + 2x = 5 between the same limits.

The equation y + 2x = 5 can be rewritten as y = -2x + 5.

Integrating y = x(4 – x) between x = 1 and x = 2, we get:

∫(1 to 2) x(4 – x) dx = (8/3) – (2/3)

= 2

Integrating y = -2x + 5 between x = 1 and x = 2, we get:

∫(1 to 2) (-2x + 5) dx = (3/2)

Therefore, the area of the shaded region is:

=2 - (3/2)

= (1/2) square units

To know more about area,

https://brainly.com/question/22469440

#SPJ1

Atticus asks Calpurnia to go with him to tell Helen Robinson about the death of her husband. Option B is the correct answer.

Helen Robinson was Tom Robinson's widow in To Ki-ll a Mockingbird, a novel by Harper Lee. Despite the fact that she is not a major character in the story, she plays a significant role in the novel's plot. When Bob Ewell accuses Tom Robinson of ra-pe, Atticus Finch is hired to defend him, and Helen Robinson appears in the story.

When Tom Robinson, a black man, was accused of rapi-ng a white woman, Mayella Ewell, he was arrested and imprisoned in the local jail. He was sentenced to death, but he attempted to flee and was subsequently sh-ot and kill-ed by a group of guards. When the news of his death reaches Atticus, he goes to tell Helen Robinson that her husband had died.  Atticus, recognizing that it will be difficult for her to receive such news, offers to accompany her and asks Calpurnia to come along with him.

Calpurnia was the Finch family's black housekeeper in the novel To K-ill a Mockingbird. She is one of the few African American characters in the book who has a speaking role, and she serves as a motherly figure to Scout and Jem. Throughout the novel, she serves as a bridge between the white and black communities, and she plays a crucial role in the story's resolution.

You can learn more about To Kill a Mockingbird. at

https://brainly.com/question/1509680

#SPJ11

Issues with the quality of data, finding appropriate data, determining which data to collect, handling big data and research issues like low response rates are some of the factors that may influence the collection of data.

1) Issues with the quality of data. Raw data often contains errors, inconsistencies, and other problems. Although data collection measures are designed to prevent or minimize these issues, they are not foolproof. Therefore, collected data usually undergoes data profiling to identify problems and data cleansing to correct them.

2) Finding appropriate data. With various systems to navigate, gathering data for analysis can be a complex task for data scientists and other users within an organization. Data curation techniques make it easier to find and access data. For instance, this may involve creating a data catalog and searchable indexes.

3) Determining which data to collect. This is a crucial issue for both upfront collection of raw data and when users collect data for analytics applications. Collecting unnecessary data adds time, cost, and complexity to the process. However, leaving out valuable data can limit a data set's business value and impact analytics results.

4) Handling big data. Big data environments usually involve a mixture of structured, unstructured, and semistructured data in large volumes. This makes the initial data collection and processing stages more complicated. Additionally, data scientists frequently need to filter sets of raw data stored in a data lake for specific analytics applications.

5) Research issues like low response rates. In research studies, a lack of responses or willing participants raises concerns about the validity of the data that is collected. Other research challenges include training people to collect the data and establishing adequate quality assurance procedures to ensure data accuracy.

To learn more about data, click here:

brainly.com/question/14926605

#SPJ4

3.a. The slope of the line is -2.

b. The y-intercept of the line is 17.

c. The equation of the line is y=-2x+17.

4. The correlation coefficient is -2.

5. When the number of losses is 20, the week is 6.

6. When the week is 15, the number of losses is -13.

It is calculated by dividing the vertical change (rise) between two points by the horizontal change (run) between the same two points.

3.a. The slope of the line is -2.

This can be determined by calculating the change in the y-values

(15-12=3,

12-10=2,

10-7=3,

7-6=1,

6-3=3,

and 3-1=2)

and dividing by the change in the x-values

(1-2=-1,

2-3=-1,

3-4=-1,

4-5=-1,

5-6=-1,

and 6-7=-1),

which gives us (3+2+3+1+3+2)/-6=-2.33=-2

b. The y-intercept of the line is 17.

This can be determined by finding the y-value when x=0.

Since there is no x=0 value in the table, we can use the equation of the line to calculate the y-value when x=0.

When x=0, y=17.

c. The equation of the line is y=-2x+17.

4. The coefficient of correlation is -2.

This can be determined by using the slope of the line, which is -2.

The coefficient of correlation is equal to the slope of the line, which is -2.

5. When the number of losses is 20, the week is 6.

This can be determined by using the equation of the line and solving for x when y=20.

When y=20,

-2x+17=20,

so 2x=3 and x=3/2, which is 6 weeks.

6. When the week is 15, the number of losses is -13.

This can be determined by using the equation of the line and solving for y when x=15.

When x=15,

y=-2(15)+17

=-13.

For more questions related to coefficient

https://brainly.com/question/27969435

#SPJ1

Twenty percent of the students in a class of 400 are planning to go to graduate school. The standard deviation of this binomial distribution is 8.

The binomial distribution is a type of probability distribution that computes the probability of a given number of successes in a fixed number of independent tests with two possible results: success and failure. Furthermore, the following are the features of the binomial distribution:

The trial is identical, with two possible outcomes: success and failure.

The probability of success (p) and failure (q = 1 - p) remains constant throughout the trials.

All trials are independent of one another.

The formula for a standard deviation for binomial distribution is given by:

[tex]$\sqrt{npq}$$[/tex]

Where n is the sample size, p is the probability of success, and q is the probability of failure.

Therefore, given that the percentage of students planning to go to graduate school is 20%, the probability of success (p) is 0.2, and the probability of failure (q) is 0.8. The sample size (n) is 400.

Thus, the standard deviation can be calculated as follows:

[tex]$$\sqrt{npq} = \sqrt{400\times 0.2\times 0.8} \approx 8$$[/tex]

Therefore, the standard deviation of this binomial distribution is 8.

To know more about the "standard deviation": https://brainly.com/question/24298037

#SPJ11

Answer:

Step-by-step explanation:

The area of a Circle is (Pie)r^2

Area of the Semi-circle will be (Pie)r^2 /2

In this particular case, the given radius = 98cm.

Therefore, the Area will be (Pie)(98)^2 /2

= (22/7)*(98)^2 /2

=15,092 sq. cms. which will be our final answer.

Answer:

The value of the function f at t = 7, will be 11.

Step-by-step explanation:

What is a function?

A statement, principle, or policy that creates the link between two variables is known as a function.

The function is given as,

f = 2t – 3

Then the value of the function f at t = 7, will be

f = 2 x 7 – 3

f = 14 – 3

f = 11

Answer:

f = 11

Step-by-step explanation:

i got it right on khan academy lol

The exact value of x is 12.97.

In geometry, a bisector refers to a line or plane that divides a geometric figure into two equal parts. Specifically, a bisector divides an angle into two equal angles, a line segment into two equal parts, or a plane figure into two equal areas.

There are two types of bisectors:

Angle bisector: A line or ray that divides an angle into two equal angles is called an angle bisector. The point where the bisector intersects the angle is known as the vertex of the angle.

Segment bisector: A line, ray, or line segment that divides a line segment into two equal parts is called a segment bisector. The point where the bisector intersects the line segment is known as the midpoint of the line segment.

We can use the angle bisector theorem to find the value of x. According to the angle bisector theorem, the length of the segment bisecting an angle in a triangle is proportional to the lengths of the two sides adjacent to that angle.

Let's call the point where ST intersects QS point U. Then, by the angle bisector theorem, we have:

QU / QR = SU / SR

Substituting the given values, we get:

QU / 20 = x / 16

Multiplying both sides by 20, we get:

QU = (20x) / 16 = (5x) / 4

Similarly, we have:

SU / QS = TU / TR

Substituting the given values and simplifying, we get:

SU / 12 = x / 20

Multiplying both sides by 12, we get:

SU = (12x) / 20 = (3x) / 5

Now, we can use the fact that QRS is a triangle to find the remaining side length:

QR + RS = QS

20 + 16 = 12 + SU + QU

36 = 12 + (3x/5) + (5x/4)

Multiplying both sides by 20, we get:

720 = 240 + 12x + 25x

720 = 37x + 240

37x = 480

x = 480/37

So the value of x is approximately 12.97 (rounded to the nearest hundredth).

To know more about intersects visit:

https://brainly.com/question/13792156

#SPJ1

T3=R1

T4=R2}==>TUR=TSR

RT=RT

so: S=U

The axis of symmetry of the function h(x) is x = 5. So, option D is correct.

The axis of symmetry of a quadratic function is a vertical line that divides the parabola into two symmetric parts. The axis of symmetry is always a vertical line passing through the vertex of the parabola.

In algebraic terms, the axis of symmetry of a quadratic function of the form [tex]f(x) = ax^2 + bx + c[/tex] is given by the equation:

[tex]x = -\frac{b}{2a}[/tex]

Where a and b are the coefficients of the quadratic expression.

Let's consider the given question:

To find the axis of symmetry of the quadratic function [tex]h(x) = 6x^2 - 60x + 147[/tex], we can use the formula [tex]x = -\frac{b}{2a}[/tex], where a and b are the coefficients of the quadratic expression.

In this case, a = 6 and b = -60, so the axis of symmetry is:

[tex]x = -\frac{(-60)}{2*(6)}[/tex]

[tex]x = 5[/tex].

To know more about axis of symmetry

brainly.com/question/22495480

#SPJ4

Answer: required ratio is 1;3

Step-by-step explanation:

Since we have given that

Ratio of the number of 5 p coins to the number of 10 p coins = 2:3

So, the number of 5p coins be '2x'

Let the number of 10p coins be '3x'.

Value of 5p coins = 5p x 2x =10px

Value of 10p coins = = 10p x 3px=30px

So, the ratio of value of 5p coins to the value of 10p coins is given by

10px:30px

1:3

Answer: -25/21

Step-by-step explanation:

[tex](4x+5)/5 + (x-3)/4 = -1\\= > 4(4x+5) + 5(x-3) = -1*5*4\\= > 16x + 20 + 5x - 15 = -20\\= > 21x + 5 = -20\\= > 21x = -20 - 5\\= > 21x = -25\\= > x = -25/21[/tex]

Answer:

The constant of variation in the given problem is 9.8

GIVEN

w = 2,116.8

m = 120

h = 1.8

SOLUTION

w=kmh

2116.8 = k(120)(1.8)

2116.8=216k

9.8=k

The values of x and y in the cyclic quadrilateral are 107 degrees and 75 degrees

From the question, we have the cyclic quadrilateral

In a cyclic quadrilateral, opposite angles are supplementary, meaning they add up to 180 degrees. This property is known as the "Opposite Angles Theorem."

For example, angles A and C are opposite angles, and they are both subtended by diameter BD.

Similarly, angles B and D are opposite angles, and they are both subtended by diameter AC.

Therefore, we can state that in a cyclic quadrilateral, the sum of opposite angles is 180 degrees

So, we have

x = 180 - 73 = 107

y = 180 - 105 = 75

Hence, the value of x is 107 degrees

Read more about cyclic quadrilateral at

https://brainly.com/question/29704807

#SPJ1

Check the picture below.

[tex]\sin(43^o )=\cfrac{\stackrel{opposite}{y}}{\underset{hypotenuse}{18}}\implies 18\sin(43^o )=y\implies 12.28\approx y[/tex]

Make sure your calculator is in Degree mode.

I think we need to (4 divided by 5)+2

4 divided by 5= 0.8

0.8+2

=2.8

answer: 2.8

the probability that both drivers are wearing their seatbelts is 0.64, or 64%.

P(A and B) = P(A) x P(B|A)

The probability of both drivers wearing seatbelts can be calculated as follows, assuming that one driver's use of a seatbelt has no effect on the other driver's use of a seatbelt and that the probability of a driver wearing a seatbelt is independent of the other driver:

Let P(S) be the probability that a driver wears a seatbelt, then P(not S) is the probability that a driver does not wear a seatbelt.

Given that 4 out of every 5 drivers wear seatbelts, we have P(S) = 4/5 = 0.8 and P(not S) = 1 - P(S) = 1 - 0.8 = 0.2.

Let A be the event that the first driver wears a seatbelt, and B be the event that the second driver wears a seatbelt. We need to find the probability of both A and B occurring, which is denoted as P(A and B).

he probability of the first driver wearing a seatbelt is P(A) = P(S) = 0.8,

and the probability of the second driver wearing a seatbelt given that the first driver is wearing a seatbelt is P(B|A) = P(S) = 0.8 because the two drivers are stopped at random.

Using the multiplication rule for independent events, we have:

P(A and B) = P(A) x P(B|A)

= 0.8 x 0.8

= 0.64

Therefore, the probability that both drivers are wearing their seatbelts is 0.64, or 64%.

know more about probability visit :

https://brainly.com/question/11234923

#SPJ1

The equatiοn οf the circle will be [tex]x^{2}+y^{2} -6x-16=0[/tex]

A clοsed rοund shaped figure which cοntains nο cοrners is called circle. It has center called (h, k)  and radius r. Rοund clοck, car tire, wheels are the examples οf circle.

If the center and radius is given then the equatiοn οf circle is:

[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex] ------------- (1) where (h, k) centre and r radius.

Here center οf the circle is (3,0) and radius οf the circle is 5

putting h= 3 , y=0  and r=5 in equatiοn (1) we get

    [tex](x-3)^{2} + (y-0)^{2} =5^{2}[/tex]

⇒ (x²- 6x+9) +y²=25

⇒ x²+y²-6x+9-25=0

⇒x²+y²-6x-16=0

Hence the equatiοn οf circle is x²+y²-6x-16=0.

To learn more about circle

https://brainly.com/question/11833983

#SPJ1

the answer is (D) 3/10. we know that the arrow landed on the red section 15 times out of 50 total spins. So we can find by  the experimental probability of landing on the red section

what is probability ?

Probability is a measure of the likelihood or chance that a particular event will occur. It is expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to happen. A probability of 0.5 means that the event is equally likely to occur or not occur.

In the given question,

The experimental probability of an event is defined as the ratio of the number of times the event occurred to the total number of trials. In this case, we want to find the experimental probability of landing on the red section.

From the given data, we know that the arrow landed on the red section 15 times out of 50 total spins. So the experimental probability of landing on the red section is:

P(Red) = Number of red spins / Total number of spins

= 15/50

= 3/10

Therefore, the answer is (D) 3/10.

To know more about  probability , visit:

https://brainly.com/question/30034780

#SPJ1

Answer:

Step-by-step explanation:

The median of a data set is the middle number.

The middle number in a data set of 9 will be the 5th number, with 4 on either side.

e.g.

1 2 3 4 5 6 7 8 9

5 is the middle number, as there are four on either side

Answer:

4.85 ft

Step-by-step explanation: