A quilter created the following shape to use in a block for a new quilt.

A six-sided figure with a large base of 13 inches. The side to the right of the base is 7 and one-half inches. The small side parallel to the base is 5.18 inches. There are two sides that form a point at a right angle. The smaller is 5 inches, and the larger is 6 inches.
What is the area of the shape for the quilt block?

sixty-three and three fourths in2
one hundred twelve and one half in2
one hundred twenty-seven and one half in2
225 in2

Answer:

Step-by-step explanation:

To show that point O is the center of the circle that passes through points D, E, and F, we can use the property of perpendicular bisectors. The perpendicular bisectors of two chords of a circle bisect the chord and pass through the center of the circle. Since the perpendicular bisectors of DE and EF intersect at point O, it follows that O must be the center of the circle that passes through points D, E, and F.

This property can also be proven using the Pythagorean theorem. Let the radius of the circle be r and let the midpoints of DE and EF be M1 and M2, respectively. Then, OM1 = OM2 = r, and the distance between M1 and M2 is equal to the distance between D and F. By the Pythagorean theorem, the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse, so we have:

OM1^2 + (M1M2)^2 = r^2 + r^2 = 2r^2

Since OM1^2 + (M1M2)^2 is equal to 2r^2, it follows that the distance between M1 and M2 is equal to the diameter of the circle. This means that M1 and M2 are the midpoints of the diameter of the circle, so they must both lie on the circumference of the circle. This, in turn, means that O is the center of the circle that passes through points D, E, and F.

Carrie is slicing sticker sheets to fit four present bags. There will be an equal quantity of stickers in each bag.

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The percentage of gratuity paid is 20%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Amount for the bill = $50

Amount paid = $60

The amount of gratuity.

= 60 - 50

= $10

Now,

The percentage of gratuity.

= 10/50 x 100

= 20%

Thus,

The percentage of gratuity is 20%.

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The point estimate of the population mean is 6

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

Measurements: 5, 10, 2, 7, and 6.

Sample size = 5

The point estimate of the population mean is the sample size of the mean

Using the above as a guide, we have the following:

Sample mean  = Sum/Count

substitute the known values in the above equation, so, we have the following representation

Sample mean  = (5 + 10 + 2 + 7 + 6)/5

Evaluate

Sample mean = 6

Hence, the estimate is 6

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P(12,8)

Move  8 units to the left (X) and  12  units down(Y).

P'(12-8, 8-12)

P'(4, -4)

If you don't how to do translation try plotting (12,8).

Answer:

Step-by-step explanation:

y = -3

The required pair of the like fraction among the given fraction is given as 1/3 and 2/6.

A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers.

Here,
For pairs of fraction area given we have to determine that fair of like fraction,
So we have to simplify the fraction given in the pair,
1. 4/6 and 5/6 = 2/3 and 5/6which not like pair of fraction, Similarly pairs  [1/2 and 3/4] and [1/10and2/100] are not like fractions.

Now,
3. pair 1/3and2/6 is like fractions because 1/3 = 2/6 (=1/3)

Thus, the required pair of the like fraction among the given fraction is given as 1/3 and 2/6.

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➡ There are 22 hundredths. That is enough to make a tenth.

What is the arithmetic operations?

Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional  operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th century, Italian mathematician Giuseppe Peano formalized arithmetic with his Peano axioms,[disputed – discuss] which are highly important to the field of mathematical logic today.

The four basic mathematical operations are Addition, subtraction, multiplication, and division.

To find the total volume of the slime, we need to add 1.5 and 0.72:

1.5 + 0.72 = 2.22

There are 22 hundredths, which is enough to make a tenth.

Hence, the answer is:

➡ There are 22 hundredths. That is enough to make a tenth.

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The area of a rectangle with side lengths 5/8ft. and 1/3 ft is: D. 5/24 ft².

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

Substituting the given points into the area of rectangle formula, we have the following;

Area of rectangle = 5/8 × 1/3

Area of rectangle = 5/24 square feet.

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In the given triangle, ∠F=29°, d>15 and e<15.

What exactly is a triangle?

Triangles are polygons in geometry that have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is a three-sided polygon. A triangle's three angles added together equals 180°. A single plane contains the triangle. The triangle is classified into six forms based on its sides and angles.

A triangle is categorised into three categories based on its sides, namely:

Scalene Triangle - Each side has a distinct length.

Isosceles Triangle - A triangle with two sides of equal length and one side of a different length.

Equilateral Triangle - A triangle has three sides that are of the same length.

A triangle is categorised into three categories based on its angles, namely:

Acute Angle Triangle - A triangle with all of its angles smaller than 90°.

Obtuse Angle Triangle - A triangle with one of its angles larger than 90°.

Triangle with a Right Angle - A triangle with one of its angles equal to 90°.

Now

As sum of all angles of triangle=180°

∠F+127°+24°=180°

∠F=180-151

∠F=29°

and In a triangle Largest angle is opposite to largest side and smallest angle is opposite to smallest side.

Then the sides e and d will be as following d>15 and e<15.

hence,

          In the given triangle, ∠F=29°, d>15 and e<15.

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Answer:

69

Step-by-step explanation:

if it bisects that mean both angles are equal which tells us we can just divide the whole angle by 2

angle BOA is 138

so when you divide 138 by 2 you get 69

hope it helped

please mark brainiest

The solution is 0.3486 or 34.86%, chance that exactly one other guest has the same birthday as you.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

For each guest, the probability that they share a birthday with you is 1 in 365. Aside from you, there are 499 guests.

Therefore, this problem can be modeled by a binomial probability model with probability of success 1/365.

The probability of exactly 1 success in 499 trials is given by:

P(x=1) = 0.3486

There is a 0.3486 or 34.86% chance that exactly one other guest has the same birthday as you.

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The g-intercept of the function g(n) is 0.

The n-intercepts of the function g(n) are n = 0, n = -3, and n = -7.

What is a function?

In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the range), such that each input is related to exactly one output.

To find the g-intercept of a function, we need to determine the value of g when n = 0. So, to find the g-intercept of the function g(n) = 2n⁴+ 20 n³ + 42n², we can simply substitute n = 0 into the function:

g(0) = 2(0)⁴ + 20 (0)³ + 42(0)² = 0

Therefore, the g-intercept of the function g(n) is 0.

To find the n-intercepts of a function, we need to determine the values of n for which g(n) = 0. In other words, we need to solve the equation 2n⁴+ 20 n³ + 42n² = 0.

We can factor out a common factor of 2n² to simplify the equation:

2n²(n² + 10n + 21) = 0

This equation is true when either 2n² = 0 (which implies n = 0), or when n² + 10n + 21 = 0. The quadratic equation n² + 10n + 21 = 0 can be factored as (n + 3)(n + 7) = 0, so its solutions are n = -3 and n = -7.

The n-intercepts of the function g(n) are n = 0, n = -3, and n = -7.

Hence,

The g-intercept of the function g(n) is 0.

The n-intercepts of the function g(n) are n = 0, n = -3, and n = -7.

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Answer:

Option D.

Step-by-step explanation:

Negative correlation also called an " inverse correlation " is a relation between 2 variables where-by they behave in opposite manner. When one variable moves ---> in an increasing /\ direction, the other variable moves in a decreasing \/ direction.

Thus, Option D.

Answer:

0.0152 is the probability that the first 5 locations are in water and the last 2 locations are on land.

The distance between the point P and the plane through the points Q, R, and S is 60/23.

The distance of a point P(x1, y1, z1) from a plane that passes through the points Q(x2, y2, z2), R(x3, y3, z3), and S(x4, y4, z4) can be found using the following formula:

d = |(A * x1 + B * y1 + C * z1 + D) / sqrt(A^2 + B^2 + C^2)|

Where A, B, and C are the coefficients of the plane's normal vector and D is the constant term in the equation of the plane. The normal vector can be found by taking the cross product of the vectors Q-R and Q-S:

n = (Q-R) x (Q-S)

The coefficients of the normal vector can be found using the following equations:

A = n1

B = n2

C = n3

D = -(A * x2 + B * y2 + C * z2)

Substituting the values of Q, R, and S, we have:

Q-R = (5-0, 0-(-1), 3-7) = (5, 1, -4)

Q-S = (7-5, 5-0, 0-3) = (2, 5, -3)

The cross product of Q-R and Q-S is:

n = (1 * -3 - 5 * -4, -3 * 5 - 2 * -4, -2 * 1 - 5 * 5) = (-23, 29, 17)

So,

A = -23

B = 29

C = 17

D = -(A * x2 + B * y2 + C * z2) = -(-23 * 5 + 29 * 0 + 17 * 3) = -109

Finally, substituting the values of x1, y1, and z1:

d = |(A * x1 + B * y1 + C * z1 + D) / √(A^2 + B^2 + C^2)|

= |(-23 * 3 + 29 * 1 + 17 * 7 + -109) / √(-23^2 + 29^2 + 17^2)|

= |(-69 + 29 + 119 -109) / √(-23^2 + 29^2 + 17^2)|

= |60 / √(-23^2 + 29^2 + 17^2)|

= |60 / √(529)|

= 60 / 23

So the distance between the point P and the plane through the points Q, R, and S is 60/23.

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Answer:

Step 1: Construct a circle through three points not on a line.

a) Points D, E, and F are not in a line. To construct a circle through points D, E, and F, begin by

drawing line segments DE and EF. Then construct the perpendicular bisectors of DE and EF, and

name the point of intersection of the perpendicular bisectors O. How do you know that point O

is the center of the circle that passes through the three points?

Answer:

Step-by-step explanation:

To show that point O is the center of the circle that passes through points D, E, and F, we can use the property of perpendicular bisectors. The perpendicular bisectors of two chords of a circle bisect the chord and pass through the center of the circle. Since the perpendicular bisectors of DE and EF intersect at point O, it follows that O must be the center of the circle that passes through points D, E, and F.

This property can also be proven using the Pythagorean theorem. Let the radius of the circle be r and let the midpoints of DE and EF be M1 and M2, respectively. Then, OM1 = OM2 = r, and the distance between M1 and M2 is equal to the distance between D and F. By the Pythagorean theorem, the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse, so we have:

OM1^2 + (M1M2)^2 = r^2 + r^2 = 2r^2

Since OM1^2 + (M1M2)^2 is equal to 2r^2, it follows that the distance between M1 and M2 is equal to the diameter of the circle. This means that M1 and M2 are the midpoints of the diameter of the circle, so they must both lie on the circumference of the circle. This, in turn, means that O is the center of the circle that passes through points D, E, and F.

Answer:

The solution is 23/500 or 0,046

Step-by-step explanation:

6 3/14÷250+5 2/7÷250

= 6 3/14×1/250+5 2/7×1/250

= (87/14×1/250)+(37/7×1/250)

= (87/3500)+(37/1750)

= 87+37(2)/3500

= 87+74/3500

= 161/3500

= 161÷7/3500÷7

= 23/500

= 0,046

The system of equations defined by the supply and demand models solved for equilibrium price is $9 and equilibrium quantity is 3000 units

Supply:

p=0.003x

x = p/0.003

x = 1/0.003p

Demand:

p= -0.008x+330

-0.008x = p - 330

x = (p - 330)/-0.008

Equilibrium price

Equate supply and demand price

0.003x = -0.008x+330

0.003x + 0.008x = 330

0.011x = 330

x = 330/0.11

x = 3,000

Substitute into

p=0.003x

p = 0.003(3000)

p = $9

Consequently, the equilibrium quantity and price is 3000 units and $9

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Answer:

no

Step-by-step explanation:

15+32 you would first add the tens

5+2=7

then the ones

1+3 =4

you're answer would then be 47 as the ones come before the tens

Step-by-step explanation:

[tex] \frac{1}{ \sin(x ) } - \frac{1}{ \csc(x) } = \csc(x) - \sin(x) [/tex]

[tex] \frac{ \csc(x) - \sin(x) }{ \csc(x) \sin(x) } [/tex]

[tex] \csc(x) - \sin(x) = \csc(x) - \sin(x) [/tex]

The relation is a direct variation

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

10 inches in 6 hours

80 inches in 2 days

Convert 2 days to hours

So, we have the following representation

10 inches in 6 hours

80 inches in 72 hours

For the relation to be a direct variation, the following must be equal

6/10 = 72/80

Evaluate

0.6 = 0.6

Hence, the relation is a direct variation

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Complete question

Determine if the following relation represents a direct variation

10 inches in 6 hours

80 inches in 2 days

The given system of linear equations has a unique solution.

A linear equation is an algebraic equation in which each term has an exponent of 1 and when graphed, the result is always a straight line.

Given that, a system of linear equations, ​ y = 5x+1 and y = -2x-8, we are asked to find how many solutions do they have,

The rule for a system of linear equations, ​a₁x+b₁y+c₁ = 0 and a₂x+b₂y+c₂ = 0 are :-

​a₁ / a₂ ≠ b₁ / b₂, and the lines intersect at one only point.

a₁ / a₂ = b₁ / b₂ ≠ c₁ / c₂, and the lines are parallel.

a₁ / a₂ = b₁ / b₂ = c₁ / c₂, and the lines overlaps.

Checking for the given equations,

y = 5x+1 and y = -2x-8

Converting into standard form of the linear equations,

5x-y +1 = 0 and 2x+y+8 = 0

5/2 ≠ -1

The equation is following the rule of unique solution, also the graph is intersecting at one point, [graph is attached]

Hence, the given system of linear equations has a unique solution.

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Answer:

One solution

Step-by-step explanation:

Statistics is referred to as a discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

This is referred to as information that has been translated into a form that is efficient for movement or processing.

Statistics involves using information that has been translated into a form that is efficient for movement or processing through different tools such as mean standard deviation etc.They help to provide more details about a set of data which makes it use very important.

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Answer:

15^4

Step-by-step explanation:

An exponent refers to the number of times a number is multiplied by itself,

so 15 multiplied 3 more times by itself (15 * 15 * 15 * 15) its 15^4.

[tex]15^{4} .[/tex]

When working with positive non fractional exponents, we state that a number A elevated to the n power is that number A in a multiplication of itself n times. For example, when we write [tex]7^{3}[/tex] we're stating that the seven is being multiplied 3 times: [tex]7*7*7[/tex].

As you may see, the expression "15*15*15*15" is just the number 15 being multiplied by itself four times. Hence, we could say that the number 15 to the power of 4. Thus, we can rewrite it as:

[tex]15^{4} .[/tex]

Answer:

Step-by-step explanation:

here's a step-by-step explanation with more detail:

The equation X^2 + X + 8 = 0 can be solved using the Quadratic Formula:

X = (-b ± √(b^2 - 4ac)) / 2a,

where a = 1, b = 1, and c = 8.

Plugging in the values, we get:

X = (-1 ± √(1^2 - 4 * 1 * 8)) / 2 * 1

X = (-1 ± √(-31)) / 2

Since the square root of a negative number is not a real number, the solution to the equation must be expressed using complex numbers. In this case, the square root of -31 can be expressed as the imaginary unit i times the square root of 31.

X = (-1 ± i * √31) / 2

So, the two solutions to the equation are:

X = (-1 + i * √31) / 2 and X = (-1 - i * √31) / 2

And these are the two solutions expressed in terms of the imaginary unit i.

a) The value of z-score is -0.299.

c) The IQR value is measure of spread of data,  IQR = 4.25.

d) There is outliers since observations are not less than 30.375 and greater than 47.375.

The z-score is an example of a standardised score. The standard deviation of a data point's divergence from the mean of the distribution is calculated using a z-score.

Given:

Sample Data = 31.5, 36.0, 37.8, 38.5, 40.1, 42.2, 34.2, 36.2, 38.1, 38.7, 40.6, 42.5, 34.7, 37.3, 38.2, 39.5, 41.4, 43.4, 35.6, 37.6, 38.4, 39.6, 41.7, 49.3

(a) The value of z-score is calculated as follows,

μ = [tex]\sum _{i=1}^n[/tex]/ n = 933.1 /24 = 38.88

σ = 3.61

So, z = X - μ / σ  

 = 37.8 - 38.88/3.61

 = −  0.299

(b) Quartile:

Q₁ = ( n+1/4)th value

= (24+1/4)th

= 6.25th

=  36.2 + 0.25 x ( 37.3 −  36.2 )  

= 36.47

and, M = ( n+1/2)th value

= (24+1/2)th

= (24+1/4)th

=  12.5 t h

= 38.4 + 38.5/2

= 38.45

Q₃ = 3( n+1/4)th

= 3(24+1/4)th

= 18.75 t h  

= 40.6 + 0.75 x ( 41.4  −  40.6 )  

= 41.2

(c) Interquartile​ range

=  Q ₃ −  Q ₁  

= 41.2  −  36.47  

= 4.25

(d) Lower fences =  Q₁− 1.5 ( I Q R )  

                           =  36.75 −  1.5  ( 4.25 )  

                           =   30.375  

Upper fences = Q ₃+1.5

                      =  41 + 1.5( 4.25 )  

                      = 47.375

Hence, there is outliers since observations are not less than 30.375 and greater than 47.375.

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Answer:

[tex]\frac{1}{10}[/tex]

Step-by-step explanation:

Answer:

3w= 17.98-6.88

3w=11.1

w =3.7

Step-by-step explanation:

After subtracting divide both side by 3

Answer:

w = 3.70

Step-by-step explanation:

Given that,

6.88 + 3w= 17.98 ..........(1)

Now subtracting both sides by 6.88 in equation (1), We have

6.88 + 3w - 6.88 = 17.98 - 6.88

or, 3w + 0 = 11.1

or, 3w = 11.1

Again dividing both sides by 3 in the above equation, We have

[tex]\frac{3w}{3}=\frac{11.1}{3} = 3.70[/tex]

Hence the required answer is w = 3.70

The length of the dotted line would be 7.922 ft.

What is the diameter of the circle?

The diameter of a circle is the distance across the circle through its center. It is equal to twice the length of the radius, which is the distance from the center of the circle to any point on the circle.

In mathematical terms, if d represents the diameter of a circle, and r represents its radius, we have the formula:

d = 2r

In the given circle, for finding the inner diameter we have to remove the thickness of the circle from outer diameter, we get

q = 17.708 - 4.893 - 4.893

By solving this, we get

q = 7.922

Hence, the length of the dotted line would be 7.922 ft.

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