Given:
The arithmetic mean of three consecutive even integers is 20.
To find:
The equation that can be used to find the integers.
Solution:
Let the three consecutive even integers are x, x+2 and x+4.
We know that,
[tex]\tex{Mean}=\dfrac{\text{Sum of observations}}{\text{Number of observations}}[/tex]
The arithmetic mean of three consecutive even integers is:
[tex]\tex{Mean}=\dfrac{x+(x+2)+(x+4)}{3}[/tex]
It is given that, mean = 20. So,
[tex]\dfrac{x+(x+2)+(x+4)}{3}=20[/tex]
Therefore, the correct option is E.
Factor 125q^6 − r^6s^3.
Answer:
(5 q^2 - r^2 s) (25 q^4 + 5 q^2 r^2 s + r^4 s^2)
Step-by-step explanation:
Factor the following:
125 q^6 - r^6 s^3
Hint: | Express 125 q^6 - r^6 s^3 as a difference of cubes.
125 q^6 - r^6 s^3 = (5 q^2)^3 - (r^2 s)^3:
(5 q^2)^3 - (r^2 s)^3
Hint: | Factor the difference of two cubes.
Factor the difference of two cubes. (5 q^2)^3 - (r^2 s)^3 = (5 q^2 - r^2 s) ((5 q^2)^2 + 5 q^2 r^2 s + (r^2 s)^2):
(5 q^2 - r^2 s) ((5 q^2)^2 + 5 q^2 r^2 s + (r^2 s)^2)
Hint: | Distribute exponents over products in (5 q^2)^2.
Multiply each exponent in 5 q^2 by 2:
(5 q^2 - r^2 s) (5^2 q^(2×2) + 5 q^2 r^2 s + (r^2 s)^2)
Hint: | Multiply 2 and 2 together.
2×2 = 4:
(5 q^2 - r^2 s) (5^2 q^4 + 5 q^2 r^2 s + (r^2 s)^2)
Hint: | Evaluate 5^2.
5^2 = 25:
(5 q^2 - r^2 s) (25 q^4 + 5 q^2 r^2 s + (r^2 s)^2)
Hint: | Distribute exponents over products in (r^2 s)^2.
Multiply each exponent in r^2 s by 2:
(5 q^2 - r^2 s) (25 q^4 + 5 q^2 r^2 s + r^(2×2) s^2)
Hint: | Multiply 2 and 2 together.
2×2 = 4:
Answer: (5 q^2 - r^2 s) (25 q^4 + 5 q^2 r^2 s + r^4 s^2)
Find the slope of the table
Answer:
The slope should be -5/8
Step-by-step explanation:
The equation used to find the slope using a table is:
[tex]\frac{y2-y1}{x2-x1}[/tex]
To get the values, take two points from the table. For example:
(8, -5) and (16, -10)
Write and classify them as (x1, y1) and (x2, y2). Knowing that these values equal the numbers, put the numbers in the equation above, and you should find the slope.
PLS HELP PLSSSSSSS QUICK
What are three different ratios that are equivalent to 7;3
Answer:
7:3 7/3 and 3 to 6
Step-by-step explanation:
Answer:
3 over 7 (FRACTION) 7.3(Decimal) and 7 times 3(Muliplication)
Step-by-step explanation:
You know: 13 + 7 = 20. Therefore: 13 + 7 + 2 = 20 + 2. Which Property of Equality was illustrated?
A. Subtraction Property of Equality
B. Multiplication Property of Equality
C. Division Property of Equality
D. Addition Property of Equality
Answer:
d
Step-by-step explanation:
What is f(-8) for the function f?
F= 11(x-24)/2
Answer:
-176.........................
What does this mean f(5)=-10
How many four-digit numbers can you make with these three integers?
0, 1, 2
Answer:
I would think 2222
Step-by-step explanation:
Between the three numbers, that four-digit number is the greatest.
(Apologies if not correct)
Jayden recently learned that the atmosphere is made of gases. Which is NOT a way in whichgases are helpful to life on Earth?A.It provides carbon monoxide to help plants growB.It protects us from the Sun's harmful raysC.It allows us to breatheD.It protects us from meteors
Answer:
A. It provides carbon monoxide to help plants grow.
Step-by-step explanation:
The only incorrect option is that carbon monoxide is required by plant, but the correct statement would be carbon dioxide is required my plants, for its growth, which helps to perform the process of photosynthesis.
The rest of the statements are correct.
As, the atmosphere acts as a blanket, which protects the earth from the harmful rays of the sun.
And, atmosphere constitute of various gases, which enables the living organisms to breath.
And, the atmosphere protects from any meteors entering from space.
Brad is hoping to package exactly 48 baseballs together. He sees the side of a box in his storeroom that is 2 x 3. What is he hoping the other dimension is? please help me out! I need the eqation and answer and a drawing of it too! Please help me out!
The given dimensions of the base of the box are 2 x 3 units.
Let h be the height of the box.
So, the volume of the box = 2 x 3 x h ...(i)
The shape of baseball is spherical and one baseball fits in a cubical box having the minimum dimensions equal to the diameter of the spherical ball.
Assuming the diameter of the baseball is d units.
So, the volume occupied by one baseball= volume of the cubical box having the side [tex]d[/tex] units.
[tex]=d^3[/tex] cubic units
So, the volume required to pack 48 baseballs
[tex]= 48 d^3 \cdots(ii)[/tex]
Assuming that all the baseballs fit in the box, i.e peripheral balls in every horizontal and vertical layer touched the box as shown in the figure.
So, the length, 3 units and the width, 2 units, must be the integral multiple of the diameter, [tex]d[/tex] units, of the baseball. i.e
The length, [tex]3 = ad\cdots(iii)[/tex]
The width, [tex]2=bd\cdots(iv)[/tex]
The height, [tex]h=cd\cdots(iv)[/tex]
where [tex]a,b[/tex] and [tex]c[/tex] belong to the natural number.
This required volume must be equals to the volume of the box.
From equations (i) and (ii),
[tex]2\times 3\times h=48d^3[/tex]
[from (iii) and (iv)]
[tex]\Rightarrow abhd^2=48d^3[/tex]
[tex]\Rightarrow h=\frac{48d^3}{6abd^2}[/tex]
[tex]\Rightarrow h=\frac{48}{ab}d[/tex]
On comparing with the equation (iv)
[tex]c=\frac{48}{ab}\cdots(v)[/tex]
Now, if the diameter of the baseball is unity,i.e, d=1 unit
( integer) and (integer) [from (iii) and (iv)]
(also an integer) [from (v)]
Now, the height of the box,
[tex]h=8 \times 1= 8[/tex] unit.
Hence, the other dimension of the box, is 8 units corrosponding to the unity diameter of the baseball.
Note the height of the box depends on the diameter of the baseball, so it will have infinite possible value for different value of the diameter.
For example, the value of height for d=1 unit has been shown.
and another example may be if units, then (integer) and (integer)
(also an integer) [from (v)]
Now, the height of the box,
[tex]h=2 \times 0.5= 1[/tex] unit. [from (iv)]
Here, the height of the box is 2 units corrosponding to 0.5 unit diameter of the baseball.
The possivle values of d can be taken for which [tex]a,b[/tex] and [tex]c[/tex] must be integers.
13t+6=12t +21
What value of/ makes the equation true?
Answer:
t=15
Step-by-step explanation:
which of the following is the numerical coefficient of x2y2
Step-by-step explanation:
1) Option II (1)
2) Option III (-5)
3) IV (None of these)
4) III (-4)
Answer:
1. The numerical coefficient of x^2y^2 is 1
2. -5
3. Monomial
4. -4(I know its x squared)
Step-by-step explanation:
1. We know if we multiply any number or variable with 1 it remains same.
here there is no number before (x^2)(y^2) so we assume it as 1.
Hence the answer is 1.
2. numerical coefficient is a constant multiplier of the variables in a term. In the term -5x2y, the numerical coefficient is -5. In the expression ax2 + bx + c, the numerical coefficient of the x2 term is "a" and the numerical coefficient of the x term is "b". "c" is properly referred to as the constant term.
3. in monomial there is only one term and pqr is only one term. binomial requires two terms like abc, pqr. and trinomial requires three terms like abc, pqr, mno.
4. -1^2 - 5 = -1 - 5 = -4 I know in rules of subtracting integer it equals to -4
To subtract integers, change the sign on the integer that is to be subtracted.
If both signs are positive, the answer will be positive.
If both signs are negative, the answer will be negative.
If the signs are different subtract the smaller absolute value from the larger absolute value.
Which list shows the numbers below in order from least to greatest? −5.9, −234, 5.78, 58%−5.9, −234, 5.78, 58% −234, −5.9, 58%, 5.78−234, −5.9, 58%, 5.78 −5.9, −234, 58%, 5.78−5.9, −234, 58%, 5.78 58%, −234, 5.78, −5.958%, −234, 5.78, −5.9
convet one solar day into second
Answer:
f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)
Step-by-step explanation:
4r – 4s+ 4 = - 4
4r + s - 2t=5
- 3r - 3s - 41= -16
Help please
Answer:
r=-2.00000
s=2.00000
A total of $68.75 was spent on pizza and sodas at the party. Let n be the number of pizzas purchased. Set up an equation involving n that models the scenario. Solve it and state both the number of pizzas and the number of sodas that were bought.
Answer:
n + s = $68.75
Step-by-step explanation:
Amount spent on pizza and soda = $68.75
Number of pizza = n
The soda = s
Then the total amount soe t can be modeled thus :
(number of pizzas + number of soda) = total amount spent
n + s = $68.75
If the price of each slice of pizza and unit of soda was given, we could have been able to calculate the amount spent on each of soda and pizza.
The function g(x) is a transformation of the cube root parent function,
f(3) = Vz. What function is g(x)?
g(x)
O A. g(x) = 1 + 2
O B. g(x) = x + 2
O c. g(x) = 273
OD. g(Q) = v
PREVIOUS
Answer:
C
Step-by-step explanation:
Apex
The value of function of g (x) is,
⇒ g (x) = 2∛z
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The function g(x) is a transformation of the cube root parent function,
The function is,
⇒ f (x) = ∛z
Now, After translation we get;
The value of function of g (x) is,
⇒ g (x) = 2∛z
Thus, The value of function of g (x) is,
⇒ g (x) = 2∛z
Learn more about the function visit:
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Which graph shape would represent the connected
points in Celeste's function table?
A. A straight line that slopes up from left to right
B. A straight line that slips down from left to right
C. A symmetrical V shape that opens down
D. A symmetrical face shape that opens up
Answer:
I believe the answer would be A
Step-by-step explanation:
There is no possible slope being involved so B, C, or D couldn't be the answer.
Answer:
A. A straight line that slopes from left to right.
Step-by-step explanation:
y = mx + b
Determine which postulate or theorem can be used to prove that
AABC= ADCB.
A. SSS
B. ASA
C. SAS
D. AAS
Answer:
[tex]\triangle ABC \cong \triangle DCB[/tex] by AAS
Step-by-step explanation:
According to the following two triangles, [tex]\triangle ABC[/tex] and [tex]\triangle DCB[/tex] are congruent by Angle-Angle-Side (AAS), because there are two angles shown and share a side, which is in the middle between triangles.
Cindy deposited $350 into a savings account. As long as the account balance remains at or above $200, she does not have to pay a service fee for the account. For how long can she withdraw $30 a month without having to pay service fees? A) 5 months B) 6 months C) 7 months D) 8 months E) 9 months
Answer:
5 months
Step-by-step explanation:
Cindy deposited $350 into a savings account
The acct balance remains above $200
We are required to find the number of months that it will take to $30 a month
Let y represent the number of months
y × 30 < 350-200
30y < 150
Divide both sides by the coefficient of y which is 30
30y/30 < 150/30
y < 5
Hence the number of months required is 5 months
Help!! Show all work
Answer:
I used a math calculator by a math calculator service
Step-by-step explanation:
Estimate the sum 59.6 + 51.4
Answer:
111
Step-by-step explanation:
Answer:
111
Step-by-step explanation:
Two pounds of raw materials are needed to produce one product. The desired ending balance of raw materials is 10% of the of the next month's production needs. (Refer to your answer in Activity Sheet 05). The beginning inventory of raw materials is 4,000 pounds and raw material cost per unit is P 0.50/per pound.
Answer:
Purchases= production + desired ending inventory - beginning inventory
Step-by-step explanation:
Giving the following information:
Two pounds of raw materials are needed to produce one product.
The desired ending balance of raw materials is 10% of the next month's production needs.
The beginning inventory of raw materials is 4,000 pounds.
The raw material cost per unit is $0.50 per pound.
To calculate the direct material purchase required for a given month, we need the production for each month. I will provide the formula and a small example to guide an answer.
To calculate the purchase required, we need to use the following formula:
Purchases= production + desired ending inventory - beginning inventory
For example:
Production:
January= 5,000 units
February= 4,500 units
Direct material purchases January:
Production= 5,000*2= 10,000
Desired ending inventory= (4,500*2)*0.1= 900
Beginning inventory= (4,000)
Total purchase in pounds= 6,900
Total direct material cost= 6,900*0.5= $3,450
Abe is going to plant 54 oak trees and 27 pine trees.
Abe would like to plant the trees in rows that all have the same number of trees and are made up of only one type of tree.
What is the greatest number of trees Abe can have in each row?
Answer: There are 27 trees he can plant in one row. There is one pine tree and 2 oak trees in each row
Step-by-step explanation:
Does a triangle with these side lengths exist 15,12,9
Answer:
Yes it does exist
Step-by-step explanation:
You must be able to add any two sides and get a number greater than the third side in order to be considered a triangle.
In this case that is possible.
Hope this helps!
What is true about segment R S and T U, if Point T has coordinates four, negative five. and U has coordinates (9, 2)?
Answer:
d
Step-by-step explanation:
Which expression is equivalent to 1/4x+3−1/3x+(−2)?
Answer:
7/12x+5
Step-by-step explanation:
PLEASE ANSWER ASAP
1.) the sum of two numbers is 42, the difference is 30. find the two numbers
2.) the perimeter of a rectangle is 62cm, the length is 1cm more than twice the width, what are the dimensions of the rectangle?
3.) in blue river terry can row 36km downstream in three hours, but it takes him 6 hours to row the same distance upstream, find the rate he rows in still water and the rate of the current.
4.) the cost of 8 avocados and 3 tomatoes is $8.39, the cost of 4 avocados and 12 tomatoes is $11.44. find the cost of each avocado and each tomato.
5.) coffee is worth $2.95 a pound was mixed with coffee worth $3.50 a pound to produce a blend worth $3.30 a pound. how much of each coffee was used to produce 44 pounds of blended coffee?
Answer:
1.) The two numbers are 36 and 6.
2.) 42cm + 20cm = 62cm
3.) 3km/hr = rate of current
4.) Each cost 0.79 cents
5.) Mixed is 16 lbs
Blended is 28 lbs
Step-by-step explanation:
Anoushka needs to stain the circular wooden deck in the backyard. The deck has a diameter of 30 feet. A gallon of stain covers approximately 250 square feet. Each gallon is $33.99. How much will Anoushka spend in order to stain the deck? Use 3.14 to approximate .
Answer:
$101.97
Step-by-step explanation:
Diameter of circular wooden deck = 30 ft
Radius of the deck = ½ of diameter = ½*30 = 15 ft
Area of deck = πr² = 3.14*15² = 706.5 ft²
1 gallon covers 250 ft² (1 gallon = 250 ft²)
Let x be the number of gallons that will cover 706.5 ft² of the deck
Thus:
1 gallon = 250 ft²
x = 706.5 ft²
Cross multiply
1*706.5 = 250*x
706.5/250 = x
2.826 = x
Number of gallons to cover the deck is approximately 3 gallons (approximated to nearest whole number). Since the we can't buy a gallon that is not full, we approximate to give us 3 gallons.
1 gallon cost $33.99 (1 gallon = $33.99)
3 gallons cost: 3*33.99 = $101.97
For the function f(x) = (x - 2)2 + 4, identify the vertex, domain, and range. (2 points) a The vertex is (-2, 4), the domain is all real numbers, and the range is y ≥ 4. b The vertex is (-2, 4), the domain is all real numbers, and the range is y ≤ 4. c The vertex is (2, 4), the domain is all real numbers, and the range is y ≤ 4. d The vertex is (2, 4), the domain is all real numbers, and the range is y ≥ 4.
Answer: The vertex is (2, 4), the domain is all real numbers, and the range is y ≥ 4.
Step-by-step explanation:
Answer: The correct answer is D (The vertex is (2, 4), the domain is all real numbers, and the range is y ≥ 4.)
Step-by-step explanation: