Set of six numbers has an average of 42. When three of this numbers were removed the remaining three numbers had an average of 72. What was the sum of the removed numbers?

Answer:

see explanation

Step-by-step explanation:

Any point that lies on the line is a solution to the equation.

Thus

(0, 1 ), (2, 0 ), (- 2, 2), (4, - 1 ) are all solutions

Answer:

[tex]\boxed{(6, -2)}[/tex]

Step-by-step explanation:

Any of the points that lies on the line is the solution to the equation of the line.

(-2, 2), (0, 1), (2, 0), (4, -1), (6, -2) are all solutions.

Answer:

see below

Step-by-step explanation:

y>−5/4x+5

The y intercept is 5

The x intercept is

0 = -5/4x +5

-5 = -5/4x

-5 *-4/5 =- 5/4x *-4/5

4 =x

The x intercept is (4,0)

The line is dotted since there is no equals sign

We shade above the line

Answer:

Negative StartFraction 1 Over 27 EndFraction

(-1/27)

Step-by-step explanation:

Given expression

(P^-5)(p^-4)(q^3)

When

P=3 and q=-9

(P^-5)(p^-4)(q^3)

=(3^-5)(3^-4)(-9^3)

=(1/3^5)(1/3^4)(-9^3)

=(1/243)(1/81)(-729)

Multiply all numerators

We have,

= (-729)/(243)(81)

Multiply all denominators

= -729/19,683

= -1/27

Negative StartFraction 1 Over 27 EndFraction

Answer:

-1/27

Step-by-step explanation:

Answer:

The salary of the governor of state A is $171,575 and the salary of the governor of state B is $117,830.

Step-by-step explanation:

If the governor of state A's salary is "x" and the governor of state B's salary is "y", then:

[tex]x = y + 53,745[/tex]

If the total of their salaries is $289,405, then the sum of x and y should be equal to that number.

[tex]x + y = 289,405\\[/tex]

Applying the first expression on the second allows us to solve for y as shown below.

[tex]y + 53745 + y = 289405\\2y = 289405 - 53745\\2y = 235660\\y = 117830[/tex]

Using this data on the first expression allows us to solve for the first governo's salary.

[tex]x = 117830 + 53745 = 171575[/tex]

The salary of the governor of state A is $171,575 and the salary of the governor of state B is $117,830.

Answer:

~226.195cm 2

Step-by-step explanation:

1. Because the shaded region is exactly one half of the circle, this means the Shaded area = 1/2 larger circle area

2. Calculate the area of the circle using the radius

3. Use that halved to get your final answer.

Hope this helped! Comment if you have any questions. :)

Answer:

The best fit is A. Linear model

Step-by-step explanation:

Given:

Monthly Rate = $20, Number of customers = 5000

If there is a decrease of $1 in the monthly rate, the number of customers increase by 500.

To find:

The type of model that best fits the given situation?

Solution:

Monthly Rate = $20, Number of customers = 5000

Let us decrease the monthly rate by $1.

Monthly Rate = $20 - $1  = $19, Number of customers = 5000 + 500 = 5500

Let us decrease the monthly rate by $1 more.

Monthly Rate = $19 - $1  = $18, Number of customers = 5500 + 500 = 6000

Here, we can see that there is a linear change in the number of customers whenever there is decrease in the monthly rate.

We have 2 pair of values here,

x = 20, y = 5000

x = 19, y = 5500

Let us write the equation in slope intercept form:

[tex]y =mx+c[/tex]

Slope of a function:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\dfrac{5500-5000}{19-20}\\\Rightarrow -500[/tex]

So, the equation is:

[tex]y =-500x+c[/tex]

Putting x = 20, y = 5000:

[tex]5000 =-500\times 20+c\\\Rightarrow c = 5000 +10000 = 15000[/tex]

[tex]\Rightarrow \bold{y =-500x+15000}[/tex]

Let us check whether (18, 6000) satisfies it.

Putting x = 18:

[tex]-500 \times 18 +15000 = -9000+15000 = 6000[/tex] so, it is true.

So, the answer is:

The best fit is A. Linear model

Answer:

m∠D = 94°

Step-by-step explanation:

Quadrilateral ABCD is also called a cyclic quadrilateral or a quadrilateral that is inscribed in a circle.

Opposite angles in a cyclic Quadrilateral are supplementary, i.e the sum of two opposite angles in a Quadrilateral = 180°

m∠A + m∠C = 180°

m∠A = 74°

74° + m∠C = 180°

m∠C = 180° - 74°

m∠C = 106°

In a cyclic quadrilateral, the total sum of the angles outside the circle = 360°

i.e =

m∠AB + m∠BC + mDC + mAD = 360°

m∠DAB= ( m∠C) × 2

= 106° × 2 = 212°

m∠DAB = m∠AD + m∠AB

m∠AD = 79°

212° = 79° + m∠AB

m∠AB = 212° - 79°

= 133°

m∠ABC = m∠AB + m∠BC

m∠AB = 133°

m∠BC= 55°

m∠ABC = 133° + 55°

= 188°

We are asked to find m∠D

m∠D = 1/2m∠ABC

m∠ABC = 188°

m∠D = 1/2 × 188°

m∠D = 94°

Therefore, m∠D = 94°

Answer:

Part 2:

The shape of a banana cut in 45° angle is that of a curve that is closed with the appearance of a flattened circle or an oval similar to an ellipse therefore having two focal points

The drawing of the angle cross section of a cylinder representing the banana is attached

Part 3:

When the banana is cut in half, perpendicular to the base of the banana, the shape formed is circular withe the center of the banana being about the same location as the center of the circle

The drawing of the perpendicular cross section of a cylinder representing the banana is

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Cylinders:

Ratio of radii = 1 : 4

Radius of two cylinders are: r , 4r

Ratio of height = 3 :1

Height of two cylinders are: 3h , h

Lateral surface area of cylinder =  2πrh

Ratio of lateral surface area= 2π* r * 3h   : 2π* 4r * h

                                             = 3 : 4

Step-by-step explanation:

-2x + 3 – (5 – 6x)

=-2x + 3 - 5 + 6x

= 4x - 2

Answer:

4x - 2

Step-by-step explanation:

We have to combine the like terms which are -2x and 6x. We will get 4x. Next, we have to subtract 3 - 5 and we get -2. This brings us to the conclusion of 4x - 2.

Answer:

[tex] \theta = 210^\circ [/tex] or [tex] \theta = 330^\circ [/tex]

Step-by-step explanation:

[tex] 4 \sin \theta - 1 = -3 [/tex]

[tex] 4 \sin \theta = -2 [/tex]

[tex] \sin \theta = \dfrac{-2}{4} [/tex]

[tex] \sin \theta = -0.5 [/tex]

For sin θ = 0.5, the reference angle is θ = 30 deg.

[tex] \sin 30^\circ = 0.5 [/tex]

[tex] \theta = 210^\circ [/tex] or [tex] \theta = 330^\circ [/tex]

Answer:

44

Step-by-step explanation:

96 divided by 4 add 5 times 2 squared equals 44

Answer:

44

Step-by-step explanation:

BIDMAS

B: Brackets

I: Indices

D: Division

M: Multiplication

A: Addition

S: Subtraction

96 divided by 4 + 5 x 2^2

96 divided by 4 + 5 x 4

96 divided by 4 = 24

24 + 5 x 4

24 + 20

24 + 20 = 44

Answer:

I think its 90

Step-by-step explanation:

Answer:

E=90

Step-by-step explanation:

because EFG=JKL                                                                                                                                          E=J                      F=K                   G=L

Answer:

No

Step-by-step explanation:

Let's calculate sinA and sinB.

sinA = opposite / hypotenuse = 12 / 20

sinB = opposite / hypotenuse = 16 / 20

Since 12 / 20 ≠ 16 / 20, she is incorrect.

Answer:

(4,7.5)

Step-by-step explanation:

Reflect (-4,7.5) at the y-axis

Answer:

A. Volume: 819, Surface Area: 598

B. Surface area

C. Volume

Step-by-step explanation:

Sorry I'm late, but here I go.

The volume of a rectangular prism is [tex]lwh[/tex] or [tex]bh[/tex]. (l being length, w being width, and h being height.)

So if we multiply the 3 values of 13, 9, and 7, we get 819. This is the volume.

To find the surface area, we can take note that 4 sides are the exact same, and the remaining two are the same. Let's find the area of the top/bottom of the prism.

[tex]13\cdot9=117[/tex]

Since there are two, bottom and top:

[tex]117\cdot2 = 234[/tex].

Now, there are the remaining 4 sides. Let's find the area of one then multiply it by 4.

[tex]13\cdot7=91\\91\cdot4=364[/tex]

Adding 364 and 234 gets up 598, so this is the surface area.

If we are painting something, the surface area is being painted, as we can't paint inside the box. However if we fill up the box with something (concrete in this case), it will be the volume.

Hope this helped!  

Answer:

a.

v= 819 cm3

sa= 542 cm2

b. surface area

c. volume

Step-by-step explanation:

Volume of a rectangular prism: Length x width x height

Replacing with the values given:

V = 13 x 9 x 7 = 819 cm3

Surface area = S = 2 × (W × L + L × H + H × W)

S = 2 ( [9x13]+ [13 x7] +[7x9]) = 2 ( 117+91+63)= 542 cm2

b . Surface area, because we only have to paint the exterior of the brick.

c. Volume, because is the amount of concrete that the brick has.

Answer:

The median number of words in Luis's essays is 205.5.

Step-by-step explanation:

To find the median number of words in Luis's essay, first arrange the values in the data set in ascending order:

177, 178, 189, 198, 198, 213, 221, 236, 245, 253.

Because the number of values in the data set is an even number (10), the median is the mean of the two middle values, the fifth and sixth values, in the data set. The fifth and sixth values are 198 and 213, respectively. So,

median .

The median number of words in Luis's essays is 205.5.

The median number of words in Luis's essays is 231.

The median is defined as the value range. To get it, arrange the numbers in ascending order from smallest to largest, then hide one number on either end until you reach the center.

The number of words in Luis's essays arranged in order from smallest to largest is:

177, 178, 189, 198, 198, 210, 213, 221, 228, 231, 231, 236, 236, 244, 245, 245, 245, 253, 259, 286

Since there are 20 numbers in the list, the median will be the average of the 10th and 11th numbers:

Median = [(n/2)th term + ((n/2) + 1)th term]/2

Median = [(20/2)th term + ((20/2) + 1)th term]/2

Median = [10th term + 11th term]/2

Median = [231 + 231]/2

Median = 462/2

Median = 231

Therefore, the median number of words in Luis's essays is 231.

Learn more about the median of data here:

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The complete question is as follows:

Luis and Darcy are required to write essays for their English class. The table shows the number of words t wrote for 10 randomly chosen essays. Complete the steps below to compare the number of words in Luis’s and Darcy's essays using the mean and the median. Luis Darcy 178 231 213 210 198 245 245 259 236 286 198 245 221 231 253 244 189 236 177 228. What is the median number of words in Luis’s essays?

v = 17 is your answer as an intergers or as a decimal rounded to the nearest tenth

Answer:

A 99% confidence level is saying that you are 99% positive that you null hypothesis will not be rejected. The critical value that comes with the confidence level is the Z-score. The Z-score can usually be found using the Z-score table found online. The Z-score for 99% confidence is 2.575. If they give you the Z-score and tell you to find it on a right tail graph you subtract the given z-score from alpha which is .5 and find what you got on the z-score table.

Ex: Given Z-score- 0.0079

.0079 - .5(alpha)=  0.4921.

The closest area to 0.4921 is 0.4922 at z = 2.42.

Hope this helps

Answer:

Option d

Step-by-step explanation:

Continuous data are data that can take on any values within a range while discrete data can only take on particular values.

Thus for this case study, the number of police cars in different cities are usually not specific and may vary, thus this data is continuous.

Answer:

The total loss experienced by Pak kamil is RM74

Step-by-step explanation:

The cost of 10 kg and  6 kg of vegetables = RM 136

The cost of 4 kg fish and 2 kg of vegetables = RM 54

Amount for which the fish was sold = RM8 per kilogram

Amount for which the vegetables was sold = RM0.50 per kilogram

The total mass of the fish = 10 kg + 4 kg = 14 kg

The total mass of the vegetables = 6 kg + 2 kg = 8 kg

The amount for which the meat was sold = 14 kg × RM8/kg = RM112

The amount for which the fish was sold = 8 kg × RM0.50/kg = RM4

RM112 + RM4 = RM116

The total amount for which the fish and vegetable was sold = RM136 + RM54 = RM190

Therefore, the total loss experienced by Pak kamil = RM190 - RM116 = RM74.

Answer:

Circumference = πd

where d = diameter

Step-by-step explanation:

When using this formula you don't need to multiply by 2 like you do when using the radius because the diameter is twice the radius of a circle.

Answer:

There are actually two formulas c=πd or pi=c/d.

Step-by-step explanation:

This is how they relate to each other. Let's say you were to isolate for pi. So, for 2pir, we have to divide both sides by 2r or the diameter. 2r=d because the diameter is equal to having two radii or radiuses. When you isolate pi, you will see that pi= to the circumference, c, divided by the diameter, d. Therefore, you can say that the circumference is approximately 3.14 or pi times greater than the diameter. In fact, that is what pi is. It is a ratio that shows the relationship between the circumference and the diameter. In other words, pi=c/d. Hope this helps!

Answer:

-\frac{7}{6}

Step-by-step explanation:

We can use the slope formula for the segment that joins any two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]:

[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

which in our case gives:

[tex]slope=\frac{y_2-y_1}{x_2-x_1} = \frac{-2-5}{3-(-3)}=\frac{-7}{6} =-\frac{7}{6}[/tex]

Answer:

the height of the prism =3cm

Step-by-step explanation:

From the question :there is 30 square centimeters, we can deduce this is the area due to the unit

the volume is 90 cubic centimeters

Volume of prism = Area of base × height

We are to determine the height

90cm³ = 30cm² × height

divide both sides by 30cm²

height = 90cm³/30cm²

height = 3cm

Therefore the height of the prism is 3centimeters

Answer:

6

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

i checked on edge

Answer:

1: C) y = -x + 1

2: D) y = -3x + 8

Step-by-step explanation:

Well number 1,

c is the correct option because,

-2 -> 2

2+1 - 3

This rule applies for all the x values.

2,

X: -2, -1, 0, 1, 2

Y: 14, 11, 8, 5, 2

d is the correct option because -3*-2 is 6 + 8 = 14.

this rule applies for all x values.

Thus,

the answers are C and D.

Hope this helps :)

Answer:

80 dollars

Step-by-step explanation:

l=prt ⇒ p=l/rt

20=p(0.05)(5)

P=20/0.25=80 dollars

Answer:

The answer is $80

Step-by-step explanation:

I just got it right

Answer:

A. 7017

Step-by-step explanation:

common difference is 7

first term of the sequence is 24

by explicit formula a1 + ( n- 1)*d

24 + (1000-1)*7

24+999*7

24+6993

7017

Answer:

Hey there!

The surface area of the triangular pyramid can be expressed as: 4 times the area of one triangle.

The area of one triangle is 17.32, so the total surface area is 69.28.

Hope this helps :)

The surface area of the triangular pyramid will be equal to 692.8 square inches.

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.

Given that:-

The formula for the surface area of the pyramid is given as follows;-

SA =  Base area + (1/2) [ Perimeter  x  Slant height ]

SA =  [ (1/2) x  20  x 17.32)]  + (1/2) [ 60   x   17.32 ) ]

SA=  [  173.2   +  519.6 ]

SA = 692.8 squarer inches

Therefore the surface area of the triangular pyramid will be equal to 692.8 square inches.

To know more about a surface area follow

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