Solve the following proportion: k/4=33/20

The statements DF=EG, EF=DG and ∠DEG ≅ ∠FGE are true for parallelogram DEFG.

a quadrilateral is a four-sided polygon, having four edges and four corners.

DEFG is a parallelogram.

A parallelogram is a simple quadrilateral with two pairs of parallel sides.

The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

DF=FG is a true statement.

The diagonal passing through a parallelogram are equal in length.

EF=DG is a true statement

The opposite sides of a parallelogram are equal.

∠DEG ≅ ∠FGE are congruent angles.

Because the opposite angles of a triangle are equal in meausure.

Hence, the statements DF=EG, EF=DG and ∠DEG ≅ ∠FGE are true for parallelogram DEFG.

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Answer:

I think the answer is c

Step-by-step explanation:

Answer:

yesss it does

Step-by-step explanation:

CONGRATULATIONSSSSS

Answer:

Incorrect

Step-by-step explanation:

10x10x10x10 or 10 to the 4th power has 4 0's and 1,000 only has 3. So, 10x10x10x10=10,000

The volume of the cylinder rounded to the nearest cm is,

V₁ = 9,646.1 cm³

We know the following:

Cylinder volume: V₁ = π r² h

Ball (sphere) volume: V₂ =4/3 π r³

where:

V - volume

r - radius of base of cylinder and diameter of ball

h - height of cylinder.

Here, We have,

D = 16 cm ⇒ r = 16 ÷ 2 = 8

π = 3.14

a) Since balls touch all sides of cylinder (as shown in image), it can be concluded that height of cylinder is equal to sum of diameters of 3 balls and that radius of base of cylinder is equal to radius of ball:

h = 3 × r = 3 × 16 cm = 48 cm

r = 8 cm

So,

V₁ = π r² h

V₁ = 3.14 × (8 cm)² × 48 cm

V₁ = 9,646.1 cm³

Thus, The volume of the cylinder rounded to the nearest cm is,

V₁ = 9,646.1 cm³

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Answer:

32÷4 = 8 (minutes per mile)

Step-by-step explanation:

48÷8=6 miles

brainly pls

Amelia ride a distance of 6 miles in 48 minutes if she rode her bike 4 miles in 32 minutes.

Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.

We have been given that Amelia rode her bike 4 miles in 32 minutes.

At this rate, we have to determine the distance in miles she rides in 48 minutes.

Let the total distance traveled by Amelia would be x in 48 minutes.

We can write a ratio as

4 miles : 32 minutes = x miles : 48 minutes

⇒ 4 / 32 = x / 48

⇒ (4)(48) / 32 = x

⇒ 192 / 32 = x

⇒ x = 6

Therefore, the total distance traveled by Amelia would be 6 miles in 48 minutes.

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\(\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies SA=4\pi (4)^2\implies SA\approx 201.1~in^2 \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies V=\cfrac{4\pi (4)^3}{3}\implies V\approx 268.1~in^3\)

In the given situation the sample space has 16 elements and the sample space is:

1H   2H    3H    4H    5H    6H    7H    8H

1T    2T    3T     4T    5T     6T     7T    8T

A sample space is a set of potential results from a random experiment.

The letter "S" is used to denote the sample space.

Events are the subset of possible experiment results.

Depending on the experiment, a sample area could contain a variety of results.

There are just two possible results when we toss a coin: either head or tail.

So, S = H, T, where H is the head and T is the tail, will be the sample space.

As a result, we are aware that there will be a total of 2n outcomes available if there are 'n' coins.

So, the coin has 2 outcomes which are H and T.

And the spinner has 8 outcomes which are 1 - 8.

Then, the sample space would be as follows:

1H   2H    3H    4H    5H    6H    7H    8H

1T    2T    3T     4T    5T     6T     7T    8T

So, the sample space has a total of 16 elements.

Therefore, in the given situation the sample space has 16 elements and the sample space is:

1H   2H    3H    4H    5H    6H    7H    8H

1T    2T    3T     4T    5T     6T     7T    8T

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Answer:

75%

Step-by-step explanation:

Think about quarters

1=25

2=50

3=75.......3/4

4=100

Answer:

75% hope this helps since 75/100

9514 1404 393

Answer:

  r = 2

Step-by-step explanation:

"A varies inversely with r cubed" means the relation is of the form ...

  A = k/r³

We can find the value of k as ...

  k = Ar³ = 72·5³ = 9000 . . . . . . . multiply the above relation by r³

And we can solve this for r to get ...

  r³ = 9000/A . . . . . . divide by A

  r = ∛(9000/A) . . . . . take the cube root

So, for A = 1125, we have ...

  r = ∛(9000/1125) = ∛8

  r = 2

Answer: In decimal form, 14.85

Answer in fraction form: 297/20

Step-by-step explanation:

If Gavin contributes towards a Pension fund (7,5% of his Basic Salary), then his net salary will be reduced by the amount he contributed towards pension fund i.e. R652.5.

1.1 Name of employee is Gavin Pillay. 1.2 UIF stands for Unemployment Insurance Fund. UIF is a benefit to provide short-term relief to workers who lose their jobs, or can't work due to illness, maternity or adoption leave. 1.3 The UIF paid by Gavin is calculated correctly.

Firstly, we need to calculate Gross Salary of Gavin, which is given as: Basic Salary + Overtime + M = R8700 + R1200 + R3201 = R13101Then, calculate total deductions from gross salary.

Total Deductions = PAYE + UIF = R1200 + 87 = R1287Hence, Gavin's net salary = Gross salary - Total Deductions = R13101 - R1287 = R11814Therefore, UIF paid by Gavin is calculated correctly as R87.1.4 This payslip is for the month of May i.e.

31/05/2023.1.5 Basic salary of Gavin = R8700. Deduct 7.5% of his basic salary to calculate his pension fund contribution. Pension Fund Contribution = 7.5/100 x R8700 = R652.5.1.6

Total deductions of Gavin includes PAYE, UIF and pension fund contribution.

Therefore, Total Deductions = PAYE + UIF + Pension Fund Contribution = R1200 + R87 + R652.5 = R1939.5.1.7

Gavin's age can not be determined as his date of birth is not provided.1.8 Address of Gavin's workplace is 21 Halsted Road, Pietermaritzburg?

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The probability that a randomly selected person from this sample was a friend of the bride OR of the groom is 0.9875.

Given that, at a wedding each guest asked the 80 guests whether they were a friend of the bride or of the groom.

What is the probability?

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

Total Number of Guests which forms the Sample Space, n(S)=80

Let the event (a friend of the bride) =A

Let the event (a friend of the groom) =B

n(A) =59

n(B)=50

Friends of both bride and groom,

So,

n(A∪B)=n(A)+n(B)-n(A∩B)

n(A∪B)=59+50-30

n(A∪B)=79

The number of Guests who was a friend of the bride OR of the groom = 79

Thus,

P(A∪B)=n(A∩B)/n(S)

= 79/80

= 0.9875

Hence, the probability that a randomly selected person from this sample was a friend of the bride OR of the groom is 0.9875.

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The inequality relation  -q > -7  can be represented in the form of q as q < 7

The numbers in set A = { -8 , -7.1 , -7 , -6.9 , -6 , -2 , 0 , 2 , 6 , 6.9 }

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be A

The value of A is - q > - 7

Now , multiplying by (-1) on both sides of the equation , we get

( -1 ) ( -q ) > ( -1 ) ( - 7 )

The inequality relation will change the sign from > to < and ,

q < 7

So , the value of the inequality relation A is q < 7

Now , all the values in the number line which satisfy the inequality equation q < 7 are given in set A

The numbers in set A = { -8 , -7.1 , -7 , -6.9 , -6 , -2 , 0 , 2 , 6 , 6.9 }

Hence , The inequality relation  -q > -7  can be represented in the form of q as q < 7 and numbers in set A = { -8 , -7.1 , -7 , -6.9 , -6 , -2 , 0 , 2 , 6 , 6.9 }

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Answer:

y^-1= x +8

Step-by-step explanation:

this may be helpful for you

Answer:

second option

Step-by-step explanation:

\(shaded~area\\(x-1)^2+y^2<25\\and\\(x+4)^2+y^2<16\)

Answer:

A

Step-by-step explanation:

edge

not sure if this is the right question so i dont know if we're thinking about the same question...

Answer:

1 1/14

you have to multiply by the reciprocal of the second fraction

Answer:

potatoe

Step-by-step explanatio

Answer:

Step-by-step explanation:

Given the following complex numbers, we are to expressed them in the form of a+bi where a is the real part and b is the imaginary part of the complex number.

1) (2-6i)+(4+2i)

open the parenthesis

= 2-6i+4+2i

collect like terms

= 2+4-6i+2i

= 6-4i

2)  (6+5i)(9-2i)

= 6(9)-6(2i)+9(5i)-5i(2i)

= 54-12i+45i-10i²

= 54+33i-10i²

In complex number i² = -1

= 54+33i-10(-1)

= 54+33i+10

= 54+10+33i

= 64+33i

3) For the complex number 2/(3-9i), we will rationalize by multiplying by the conjugate of the denominator i.e 3+9i

= 2/3-9i*3+9i/3+9i

=2(3+9i)/(3-9i)(3+9i)

= 6+18i/9-27i+27i-81i²

= 6+18i/9-81(-1)

= 6+18i/9+81

= 6+18i/90

= 6/90 + 18i/90

= 1/15+1/5 i

4) For (3 − 5i)(7 − 2i)

open the parenthesis

= 3(7)-3(2i)-7(5i)-5i(-2i)

= 21-6i-35i+10i²

= 21-6i-35i+10(-1)

= 21-41i-10

= 11-41i

  Simplified form of the given expressions will be,

1). 6 - 4i

2). 64 + 33i

3). \(\frac{1}{15}+\frac{1}{5}i\)

4). \(\frac{31}{53}-\frac{31}{53}i\)

1). In a complex number (a + bi),

    a = Real part of the complex number

   bi = Imaginary part

     Expression given in the question → (2 - 6i) + (4 + 2i)

Rule to solve the given expression,

"Add real part and imaginary part of two complex numbers separately"

(2 - 6i) + (4 + 2i) = (2 + 4) + (-6i + 2i)

                         = 6 + (-4i)

                         = 6 - 4i

  Therefore, simplified form of the given expression will be (6 - 4i).

2). Given expression → (6 + 5i)(9 - 2i)

Rule to solve the expression → i² = -1

(6 + 5i)(9 - 2i) = 6(9 - 2i) + 5i(9 - 2i)

                       = 54 - 12i + 45i - 10i²

                       = 54 - 12i + 45i + 10 [Since, i² = -1]

                       = (54 + 10) + (45i - 12i)

                       = 64 + 33i

     Therefore, simplified form of the given expression will be (64 + 33i).

3). Given expression → \(\frac{2}{3-9i}\)

Multiply numerator and denominator with the conjugate of (3 - 9i) to convert the expression into (a + bi).

\(\frac{2}{3-9i}= \frac{2(3+9i)}{(3-9i)(3+9i)}\)

       \(=\frac{2(3+9i)}{3^2-(9i)^2}\)

       \(=\frac{6+18i}{9-81(-1)}\)

       \(=\frac{6+18i}{9+81}\)

       \(=\frac{6+18i}{90}\)

       \(=\frac{6(1+3i)}{90}\)

       \(=\frac{1}{15}+\frac{1}{5}i\)

    Therefore, simplified form of the given expression will be \(\frac{1}{15}+\frac{1}{5}i\)

4). Given expression → \(\frac{(3-5i)}{(7-2i)}\)

Multiply numerator and denominator with the conjugate of the denominator.

\(\frac{(3-5i)}{(7-2i)}=\frac{(3-5i)(7+2i)}{(7-2i)(7+2i)}\)

         \(=\frac{3(7+2i)-5i(7+2i)}{7^2-(2i)^2}\)

         \(=\frac{21+4i-35i-10i^2}{49-4(-1)}\)

         \(=\frac{21-31i+10}{53}\)

         \(=\frac{31-31i}{53}\)

         \(=\frac{31}{53}-\frac{31}{53}i\)

  Therefore, simplified form of the given expression will be \(\frac{31}{53}-\frac{31}{53}i\).

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Answer:

area of a circle = pi*r^2

3 = pi*r^2

r^2 = 3/pi

r = √(3/pi)

diameter = 2*r = 2*√(3/pi)

The Surface Area of cylinders are: 100 yd² , 264 m², 226  mm²

The Surface Area of Can is 219 cm².

We know the formula for Surface Area of Cylinder

= 2πrh

1. Radius = 2 yd

Height = 8 yd

So, Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 2 x 8

= 100 yd²

2. Radius = 7 m

Height = 6 m

So, Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 6 x 7

= 264 m²

3. Radius = 3 mm

Height = 12 mm

So,  Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 3 x 12

= 226  mm²

4. Radius = 3.5 cm

Height = 10 cm

So, Surface Area of Can

= 2πrh

= 2 x 3.14 x 3.5 x 10

= 219 cm²

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Answer:

The 95% confidence interval for the mean tuition for all colleges and universities in the United States is between $15718 and $22882.

Step-by-step explanation:

Sample size greater than 30, which means that we use the normal distribution to find the interval.

We have that to find our  level, that is the subtraction of 1 by the confidence interval divided by 2. So:

α = (1 - 0.95) / 2

  = 0.025

Now, we have to find z in the table as such z has a pvalue of . So it is z with a pvalue of 1 - 0.025 = 0.975.

So, z = 1.96

Now, find M as such

M = z * (σ / √n )

In which σ is the standard deviation of the population and n is the size of the sample.

M = 1.96 * ( 10800 / √35 )

M = 3581.72

M ≈ 3582

The lower end of the interval is the sample mean subtracted by M. So it is 19300 - 3582  = $15718.

The upper end of the interval is the sample mean added to M. So it is  19300 + 3582  = $22882.

The 95% confidence interval for the mean tuition for all colleges and universities in the United States is between $15718 and  $22882.

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Answer:

138/3

46

Step-by-step explanation:

Answer:

414

Step-by-step explanation:

138+138+138=414

Answer:

C) 4+9i

Step-by-step explanation:

A complex number is represented as: \(a + bi\).

Where:  \(a \to\) Real part and      

\(bi \to\) Imaginary part

From the given numbers, \(4 + 9i\) is a complex number

The given numbers are:

\(-7\)

\(2 + \sqrt 3\)

\(4 + 9i\)

\(\pi\)

By comparing \(a + bi\) with the given numbers;

We can conclude that: \(4 + 9i\) is a complex number

Because it has a real part (4) and an imaginary part (9i)

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The probability of selecting a girl and a boy for the class committee can be calculated by considering the total number of outcomes and the number of favorable outcomes.

Identify the number of girls and boys in the class. In this case, there are 5 girls and 7 boys.

Determine the total number of students in the class. That is 5 + 7 = 12.

Determine the number of ways to select two students from the class.

Here we can use the combination formula, which is written as C(n, r), where n is the total number of items and r is the number of items to be chosen.

In our case, n = 12 (total number of students) and r = 2 (number of students to be selected).

C(12, 2) = 12! / (2!(12-2)!) = 66.

Determine the number of favorable outcomes.

In this case, we want to select one girl and one boy. We multiply the number of girls by the number of boys: 5 x 7 = 35.

To find the probability, we divide the number of favorable outcomes (35) by the total number of outcomes (66):

Probability = Number of favorable outcomes / Total number of outcomes = 35 / 66 = 5/6.

So, the probability of selecting a girl and a boy for the class committee is 5/6.

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Answer:

The inequality are  8x + 14y ≤ 2000 and x + y ≤ 200

Step-by-step explanation:

The sneaker’s cost = $8

Selling price of sneaker = $10

Cost of sandals = $14

Selling price of sandals = $17

Let the sneaker is x and sandals are y. It is given that total spending amount will not exceed $2000. So the inequality is:

8x + 14y ≤ 2000

since it is given that total number of x and y will not exceed 200 so the inequality that shows number of shoes purchased each year is:

x + y ≤ 200

The value of the variable 'x' is 11. Then the length of BC will be 47.

An axis is a term used to describe a line on which points are located, particularly if that line is connected to a triangle or other geometric shape. Since two factors determine a line, two points are transparently collinear. If the points are in a line, then the points are collinear points.

Let A, B, and C be the collinear points. Then the condition of the collinear will be

AB + BC = AC

If AC = 72, AB = 2x + 3, and BC = 5x - 8. Then the value of x is calculated as,

2x + 3 + 5x - 8 = 72

7x - 5 = 72

7x = 77

x = 11

Then the length of BC will be given as,

BC = 5(11) - 8

BC = 55 - 8

BC = 47

The value of the variable 'x' is 11. Then the length of BC will be 47.

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The pressure by the statue exerted on the floor will be 1200 N per square meter.

The term pressure is defined as the force per unit area.

The formula is igven below.

P = F /A

A bronze statue weighs 2400 N and has a base that is 4 m by ½ m.

Then the base area will be

A = 4 x 1/2

A = 2 square meters

Then the pressure will be

P = 2400 / 2

P = 1200 N per square meter.

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