If the area of the rectangle is 42 square units, what is the area of the shaded part?

Option A. The set of side measurement that can be used to form a triangle is given as A. 13, 19, 7

A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.

If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices. In Euclidean geometry, a triangle is a two-dimensional shape that is represented by three non-collinear points in a single plane.

How to get the measurement that can produce a triangle.

a + b > c  = 13 + 19 > 7

a + c > b  =  13 + 7 > 19

b + c > a  = 7 + 9 > 13

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The number of points that are expected to lie inside the circle is 785.

A circle is a closed two-dimensional figure. In a circle, all points are equidistant from the centre.

As per the given question, the circle is inscribed in a square,

⇒ The area of the circle   =   π × r × r

                                           =   π × 1 × 1

∴ The area of the circle    =   π

⇒ The area of the square   =   s × s

                                             =   2 × 2

∴The area of the square    =    4  

The probability that a randomly selected point inside the square will lie inside the circle,

p   =   π / 4

The probability that a randomly selected point inside the square will lie outside the circle,

q   =  1 - p

q   =  1 - ( π / 4 )

⇒ Binomial trial with n   =   1000 and  p   =   π / 4,

Number of points expected to lie inside the circle(N)  =   n × p

                                                                                         =   1000 × ( π / 4 )

                                                                                         =   1000 × ( 3.14 / 4 )

                                                                                         =   1000 × ( 0.785 )

                                                                                  N    =   785  

Therefore, 785 expected points lie inside the circle.  

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The complete question is

Answer: 56 square

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

locations of A are 7, 17

Step-by-step explanation:

since B is positioned at 12 and AB = 5 , then

A = 12 - 5 or 12 + 5 = 7 , 17

Dividing 50x⁴ - 50x³ + 12x² + 10x - 2 by 5x - 3 with the long division method will result to a quotient of 10x³ - 4x² + 2 and a remainder of 1.

The method of long division involves the following steps:

We sall divide the 50x⁴ - 50x³ + 12x² + 10x - 2 by 5x - 3 by applying the long division method as follows;

50x⁴ divided by 5x equals 10x³

5x - 3 multiplied by 10x³ equals 50x⁴ - 30x³

subtract 50x⁴ - 30x³ from 50x⁴ - 50x³ + 12x² + 10x - 2 will result to -20x³ + 12x² + 10x - 2.

This process is repeated until we have a remainder of 1.

Therefore, by the long division method, we have quotient of 10x³ - 4x² + 2 and a remainder of 1.

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Answer:

The numbers that we use are expressed in base 10. Every 10 1s equals 1 ten For example, if you are adding 5 + 4, you get: 0101 + 0100.

The sum of the ages of the children would be 3x - 94 years.

We have the total sum of the ages of pam ,dion and their children  

as 5x - 99

here , x is the age of Dion .

we see , pam is five years younger than Dion , so

age of Pam = x - 5

Now as the sum of all the ages = 5x - 99

therefore ,

Age of Dion + Age of Pan + Age of children = 5x - 99

x + x - 5 + Age of children = 5x - 99

2x - 5 + Age of children = 5x - 99

therefore ,

Age of children = 3x - 94

So  the age of their children would be 3x - 94 years

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432 ways are there to paint each of the integers 2, 3,..., 9 either red, green, or blue so that each number has a different color from each of its proper divisors.

A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle. It claims that if there are n ways to do something and m ways to do something else after that, then there are n m n*m methods to do both of these acts.

Here,

(1) All prime number can take any of three colors, except one of 2 or 3 as both are connected via 6..

so 2, 5, 7 can have 3 ways each - 3*3*3 = 27 ways

(2) Let us take the multiples of 2..

4 can take any of the remaining 2 colors, while 8 would take the remaining colour. As like 4, 6 can also take any of 2 colors other than the colour of integer 2.

Thus 2*2*1=4

3 is restricted because of 6, so it cannot have the same color as 6 and therefore 3 can have any of the remaining 2 colors.

We could also have taken 3 colors for 6, and then 2 and 3 would have 2 colors each and overall 2*2*3.. We are still getting the same

Only integer left is 9, so it will take any of the 2 colors other than that of 3, so 2 ways..

Total 2*2=4

Combined way of  integers = 27∗4∗4=432 ways

There are 432 different methods to paint the numerals 2, 3,..., 9 red, green, or blue so that each number has a different hue from each of its suitable divisors.

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a) The length of segment CD is; CD = 10 cm

b) The length of segment AB is; AB = 5 cm

c) Another segment with same length as segment AB is;

Segment AC

From the attached image, we see that Segment AE is a radius of the circle with center of A.

Now, any segment with origin from the center of the Circle that goes on to hit the circumference of the circle, is also a radius, and would be equal in length to segment AE.

a) Segment CD divides the circle into 2 equal parts and as such it will be the diameter of the circle.

Diameter = 2 × radius.

Diameter; CD = 2 × AE

CD = 2 × 5

CD = 10 cm

b) AB is a radius as defined earlier and as such; AB = AE

Thus; AB = 5 cm

c) The other segments that are also radius of the circle and have the same length as segment AB are;

Segment AC

Segment AD

Segment AG

Segment FA

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The amount of fat in Cherry ice-cream is 24 grams.

The amount of fat in the Mint Chocolate Chunk ice-cream is 12 grams.

Writing data into equations using Algebra,3C + M = 84...(1)C + 3M = 60...(2)

Multiplying equation (2) by 3 and then subtracting equation (1) from

the result gives, 3 * (C +3M) = 3 × 603C + 9M = 180...(3)(3C + 9M = 180) - (3C + M = 84) = 8M =96M= 12

The amount of fat in the Mint Chocolate Chunk ice-cream, M = 12  

grams C + 12*3 = 60C = 60-36 = 24

The amount of fat in Cherry ice-cream C = 24 grams As a result, Cherry ice cream contains 24 grams of fat and Mint Chocolate Chunk ice cream contains 12 grams of fat.

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Answer: 25 degrees

Step-by-step explanation:

Assuming that both triangles are to be connected and that they form a rectangle,

angle x can be found by subtracting 65 degrees from 90 degrees.

(all corners of rectangle=90 degrees)

90-65=25

The given function shifted 3 units left is log(x+3), vertical compression by factor 2 is 2log(x+3), Reflection across the y-axis is 2log (-x+3) and shifted down by 5 units is 2log(-x+3)-5.

Given the parent function with base 10.

We want to find the given transformations.

The given parent function is y=log(x)

Firstly, we want to shift the given parent function 3 units left means we will add 3 in the parent function, we get

y=log(x+3)

Now, we want to do vertical compression by a factor of 2 means we will multiply the above function with 2, we get

y=2log(x+3)

Further, we want to reflected the above function across the y-axis means we will multiply the x with minus, we get

y=2log(-x+3)

Furthermore, we want to shift the above function down with 5 units means we will subtract 5 from the above function, we get

y=2log(-x+3)-5

Hence, the given parent function y=log(x) when shifted 3 units left is log(x+3), vertical compression by factor 2 is 2log(x+3), Reflection across the y-axis is 2log (-x+3) and shifted down by 5 units is 2log(-x+3)-5.

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The compound interest calculated for 10 years annually, semi-annually, quarterly, monthly, and daily are (a) $2195.05,  (b) $2206.18  (c) $2211.88 (d) $2215.75, and, (e) $2217.63

The formula for Compound Interest is

Amount = Principal X (1 + r/n100)ⁿˣ

where,

Principal = original mount

n = no. of times the interest is applied

t = time period

Here,

Principal = $1400

x = 10

r = 4.6

a)

Since it is compounded annually, the interest will be given 10 times in 10 years. therefore, once a year

Hence,

n = 1

Amount = 1400 X (1 + 4.6/100)¹⁰

= 1400 X (104.6/100)¹⁰

= 1400 X (1.046)¹⁰

= $2195.05

b)

Since the interest is compounded semi-annually here, it will be calculated twice a year.

Hence, n = 2

Therefore we get

Amount = 1400 X (1 + 4.6/200)²⁰

= 1400 X (204.6/200)²⁰

= 1400 X (1.023)²⁰

= $2206.18

c)

Since it is compounded 4 times a year now,

n = 4

Hence we get

Amount = 1400 X (1 + 4.6/400)⁴⁰

= 1400 X (1.0115)⁴⁰

= $2211.88

d)

Here, the interest is calculated 12 times a year

Hence we get

Amount = 1400 X (1 + 4.6/1200)¹²⁰

= 1400 X (10038)¹²⁰

= $2215.75

e)

Here we are told to ignore leap years, hence we are only going to consider a year to have 365 days.

Hence,

n = 365

Therefore, we get

Amount = 1400 X (1 + 4.6/36500)³⁶⁵⁰

= 1400 X (1 + 4.6/36500)³⁶⁵⁰

= 1400 X (1.00012)³⁶⁵⁰

= $2217.63

Correct Question

If 1400 dollars is invested in an account for 10 years. find the value of the investment at the end of 10 years if the interest is:

(a) 4.6% compounded annually

(b) 4.6% compounded semiannually

(c) 4.6% compounded quarterly

(d) 4.6% compounded monthly

(e) 4.6% compounded daily (ignore leap years)

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The total number of miles for the four trips is 25 miles.

Given that;

Linda traveled for one hour each day for four days at a speed that made her cover one mile in an even number of minutes. After the first day, she started to lose speed, and it took her 5 minutes longer to complete a mile than the day before. Her journey distance was also an integer amount of miles throughout the four days.

We know that,

Distance is a product of speed and time. We need to find the distance here with the use of the given conditions, time is 1 hour.

Speed = Distance / Time

Hence, speed is 1 mile per x minutes because we want to distance by multiplying the time and speed together yielding 60 min * 1 mile / x mins.

Minutes cancel out, so now we have 60/x as our distance for the first day.

The distance for the given case;

⇒ [tex]\frac{60}{x},\frac{60}{x+5},\frac{60}{x+10},\frac{60}{x+15}[/tex]

It is given that x = 5;

⇒ [tex]\frac{60}{5},\frac{60}{10},\frac{60}{15},\frac{60}{20}[/tex]

= 12 + 6 + 4 + 3

= 25

The total number of miles for the four trips is 25 miles.

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The vertex of the equation given as .f(x) = |2x + 3| is (-3, 0)

The vertex of a function or an equation is the minimum or the maximum point on the function

From the question, we have the equation of the function to be

f(x) = |2x + 3|

The above function is an absolute value function

An absolute value function is represented as

f(x) = a|x - h| + k

Where the vertex is represented as

Vertex = (h, k)

By definition, a graph that has a vertex would have an obvious maximum or minimum point on it

By comparing the equations f(x) = a|x - h| + k and f(x) = |2x + 3| to determine the vertex, we have

(h, k) = (-3, 0)

This means that

Vertex = (-3, 0)

Hence, the vertex of the equation is (-3, 0)

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The Central Limit Theorem gives the idea that a large number of sample means or proportions will approximate a normal distribution, regardless of the distribution of the population from which they were drawn .

Central Limit Theorem : In probability theory , the Central Limit Theorem establishes that , in many situations , when independent random variables are summed up , their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed .

The Central Limit Theorem gives the idea that a large number of sample means or proportions will approximate a normal distribution, regardless of the distribution of the population from which they were drawn .

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Answer:

1/28 kilo

Step-by-step explanation:

sb help me on my recent please

If he arranges them into 6 equal rows, 4 posters will be in each row.

One of the fundamental arithmetic operations in mathematics is the division, which is the process of dividing a group of items into equal pieces. Every day, we might employ the division approach in various situations. Fraction division differs significantly from natural number division. We must change the division operator into a multiplication operator when dividing fractions. Therefore, the dividend should be multiplied by the inverted divisor.

Given,

Total posters = 24

Arranging them into 6 equal rows,

Dividing:

24÷ 6

Reciprocating,

24 × 1/6

4

If he arranges them into 6 equal rows, 4 posters will be in each row.

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The steps and reason to prove the angle theorems is; Table 3

The internal angles of the given triangle are given as;

a, b, c and d.

Now, we know that the sum of interior angles in a triangle is equal to 180°;

∠a + ∠b + ∠c = 180°

Now, ∠c and ∠d are angles that form a straight line and as such they sum up to 180° as they are supplementary angles.

∠c + ∠d = 180°

Thus, by transitive properties, we can say that;

∠a + ∠b + ∠c = ∠c + ∠d

Therefore by subtraction property of equality we have;

∠a + ∠b = ∠d

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The initial 4 gallons and the fractions of [tex]\frac{1}{2}[/tex] and [tex]1\frac{1}{4}[/tex] gallons of paint used on the first day indicates;

A fraction is the representation of a number in quotient form such that the value of the number is obtained by dividing the numerator by the denominator.

The amount of paint Lyle and Ming started painting the room with = 4 gallons

Amount of paint Lyle used on the first day = [tex]\dfrac{1}{2}[/tex] gallons of paint

The amount of paint Ming used on the first day =  [tex]1\frac{1}{4}[/tex] gallons of paint

Required; The amount of paint remaining after the first day of painting

The paint left after the first day of painting, V, is the difference between the amount of paint with which the painting was started and the amount used by Lyle and Ming on the first day

Therefore; [tex]V = 4 - \left(\dfrac{1}{2} + 1\dfrac{1}{4} \right) = 4 - \left(\dfrac{1}{2} +\dfrac{5}{4} \right) = 4 - \dfrac{7}{4}[/tex]

[tex]V = 4 - \dfrac{7}{4} = \dfrac{16-7}{4} = \dfrac{9}{4} = 2\dfrac{1}{4}[/tex]

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The car that is 16 feet long has a length of 8 inches on the scale.

Scale is used to represent the relationship between a measurement on a model and the corresponding measurement on the actual object.

Therefore, the particular car is 16 feet long. A model of it was built with a scale of 1 in: 2 ft. The length of the car can be found as follows:

2 feet = 1 inches

16 feet = ?

cross multiply

length of the model car = 16 / 2

Therefore,

length of the model car =  8 inches

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ΔBGC is right because Line EG is perpendicular-to CC'.

A reflection image or reflection point is the mirror image of a figure in the axis or plane of reflection.

Each point of the original figure (the pre-image) has an image that is the same distance from the reflection line as the original point, but is on the other side of the line. This transformation is known as a reflection over line. The size and form of the image in a reflection are identical to those of the pre-image.

Given:

On the line of reflection will be the midpoints of the segments connecting a triangle vertex with its reflected image. The segment will be parallel to the reflection's line.

A triangle will be considered correct in this situation if it has a leg that is a part of the segment connecting the reflected points and a leg that is on the line of reflection. Such a triangle is the BGC.

Hence, BGC is right triangle.

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Answer: D

Step-by-step explanation: Trust

Answer:

The two numbers are [tex]3[/tex] and [tex]-16[/tex].

Step-by-step explanation:

Two numbers that, when multiplied, result in a product of [tex]-48[/tex]:

[tex]x \cdot y = -48[/tex]

Same two numbers when added get a sum of [tex]-13[/tex]:

[tex]x + y = -13[/tex]

Solve for x in the summation identity:

[tex]y = -13 - x[/tex]

Plug the value back into the product identity and solve for [tex]x[/tex]:

[tex]x \cdot (-13-x) = -48\\-13x - x^2 = - 48\\x^2 + 13x = 48\\x^2 + 13x - 48 = 0\\(x-3)(x+16) = 0[/tex]

The roots we found for [tex]x[/tex] were:

[tex]x = 3\\x = -16[/tex]

Our two numbers are [tex]3[/tex] and [tex]-16[/tex]. We can test this:

[tex]3 + (-16) = -13\\3 * -16 = -48[/tex]

Answer:

Step-by-step explanation:

NOSEEEEEE

The probability that a carpet that is 7 ft × 12 ft contains no flaws is 0.732  

The Normal, Binomial, and Poisson Distributions are the three types of continuous and discrete data-based distributions used in probability and statistics. The distribution of unusual occurrences is another name for the Poisson distribution. This is mostly used to forecast the likelihood of future events based on how frequently the past events occurred. It offers the chance that a specific number of events might happen during a particular time frame.

The formula for Poisson distribution is given below:

       P(x) = (e^-x * m^x) / x!  

Here we have,

flaws in a carpet tend to occur randomly and independently at a rate of one every 270 square feet  

Given the dimensions of carpet = 7 feet × 12 feet  

=> area of the carpet = 84 feet²

=> the expected mean of defects m = [1/270]*84 = 0.311

Now use the Poisson formula  

P[x] = e^-m × m^x / x!

=> P(x = 0) = e^-(0.31) × 0.31^(0) / 0!

= (0.732 × 1)/1 = 0.732

Therefore,

The probability that a carpet that is 7 ft × 12 ft contains no flaws is 0.732  

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a) The mean distribution is 5.295.

b) The standard deviation is 0.1026

c) The probability that the child will be older than 5 years old is 0.7657

d) The probability that the child's age is between 4.84 and 5.34 is  0.4504

e) At the 9th percentile, the age of the child is 5.739 years old.

Given interval distribution is

4.74 - 5.85.

a) Firstly, we will find the mean distribution,

Mean distribution = Sum of intervals / Number of intervals

= 4.74+5.85 / 2

= 5.295.

Hence, the mean distribution is 5.295.

b) Now, we will find the standard deviation,

We use the formula:

SD = [tex]\sqrt{\frac{(b-a)^{2} }{12} }[/tex]

b = 5.85

a = 4.74

SD = [tex]\sqrt{\frac{(5.85-4.74)^{2} }{12} }[/tex]

SD = [tex]\sqrt{\frac{(1.11)^{2} }{12} }[/tex]

SD = 0.1026

Hence, the standard deviation is 0.1026

c) The probability that the child will be older than 5 years will be

p(older than 5) = 5.85 - 5 / 5.85 - 4.74

= 0.85 / 1.11

= 0.7657

Hence, the probability that the child will be older than 5 years old is 0.7657

d) The probability that the child will be between 4.84 and 5.34 years old will be

p(between 4.84 and 5.34) = 5.34 - 4.84 / 5.85 - 4.74

= 0.5 / 1.11

= 0.4504

Hence, the probability that the child's age is between 4.84 and 5.34 is  0.4504

e) If the child is at the 9th percentile, the age will be

At the 9th percentile = 4.74 + 9/100 ×(5.85 - 4.74)

= 4.74 +(0.9)(1.11)

= 4.74 + 0.999

= 5.739

Hence, at the 9th percentile, the age of the child is 5.739 years old.

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The height of the candle after 15 hours of burning is 17 cm.

According to the question,

We have the following information:

Height of the candle after 11 hours of burning = 19.4 cm

Height of the candle after 23 hours of burning = 12.2 cm

Now, we will find the rate at which the height of the candle is decreasing. It means that we will find the decrease in height per centimeter.

Difference between hours and height:

23-11 = 12 hours

19.4-12.2 = 7.2 cm

So, we have:

12 hours = 7.2 cm

1 hour = 7.2/12

1 hour = 0.6 cm

So, the height is decreasing at the rate of 0.6 cm per hour.

Now, we have to find the height after 15 hours.

Height at 11 hours = 19.4 cm

Difference between 15 hours and 11 hours is 4 hours.

Change in height = 0.6*4 cm

Decrease in height = 2.4 cm

So, the height after 15 hours:

19.4-2.4

17 cm

Hence, the height of the candle after 15 hours of burning is 17 cm.

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Answer: The ladder reaches 4.8 ft up the wall

Step-by-step explanation:

Sin 53°=0.80

Cos 53°=0.60

Tan 53°=1.33  

Cos 58°/1 = X/8

0.60/1 = X/8

X=4.8  

We know that the sum of all the interior angles of the polygon with sides n is (n - 2)*180.

It is given in the question that,

Sum of all the interior angles of the polygon is 800.

Hence, according to the data given in the question, we can write,

(n - 2)*180 = 800

n - 2 = 800/180

n - 2 = 40/9

n = 40/9 + 2

n = 58/9 = 6.44

As number of sides should always be in integer form, it is not possible to have the sum of all the interior angles of the polygon to be 800 degrees.

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