Answer:
The first sequence has a common ratio of 2 while the second sequence has a common ratio of 4.
Step-by-step explanation:
Given the two sequences
[tex]\text{First Sequence:} \dfrac14, \dfrac12,$1, 2\\Second Sequence:\dfrac12$ , 2, 8, 32[/tex]
By observation:
In the first sequence:
[tex]\dfrac14 \times 2 = \dfrac12\\\dfrac12 \times 2 =1\\1 \times 2=2\\[/tex]
In the second sequence
[tex]\dfrac12 \times 4 =2\\ 2 \times 4=8\\8 \times 4=32[/tex]
We can see that both sequences are geometric sequences.
However, the first sequence has a common ratio of 2 while the second sequence has a common ratio of 4.
Maths * Henry is mixing concrete. To make concrete he needs to mix cement, sand and gravel in the ratio 4 : 3 : 1 by weight. Henry needs to make 120kg of concrete. He has 55kg of cement, 45kg of sand and 15kg of gravel. Which ingredient is Henry short of?
Answer:
His 55 kg of cement is 5 kg short of the 60 kg he needs.
Step-by-step explanation:
Let r be a ratio useful in determining how much of each ingredient Henry needs:
4/8 of the mix is cement, 3/8 is sand and 1/8 is gravel.
4/8 of the total 120 kg must then be 60 kg made up of cement;
3/8 must then be 45 kg made up of sand; and
1/8 must then be 15 kg made up of gravel
His 55 kg of cement is 5 kg short of the 60 kg he needs.
In a group of 17 pupils, 2 play the flute only. 11 play the piano only. 1 plays neither instrument. A student is selected at random. What is the probability the student plays both instruments?
Answer:
6
Step-by-step explanation:
idk
Here’s a graph of a linear function. Write the equation that describes that function. Express it in slope-intercept form.
Answer:
y=1/3x-3
Step-by-step explanation:
slope = (y2-y1)/(x2-x1)
Use the two points: (0,-3) (3,-2)
slope = (-3+2)/(0-3)
slope = -1/-3 = 1/3
y intercept = -3
Equation: y=1/3x-3
how many diagonals are there in a polygon of 6o sides
Answer:
9 diagonals
Bit by bit clarification:
Number of Diagonals = n(n-3)/2
For instance, in a hexagon, the complete sides are 6.
Along these lines, the complete diagonals will be 6(6-3)/2 = 9.
Answer:
9 diagonals hope its helpful
A bag contains 9 red marbles, 18 orange marbles, 2 yellow marbles, and 5 purple marbles. A marble is drawn at random from the bag. What is the probability that the marble drawn will not be orange?
Answer:
8/17
Step-by-step explanation:
total balls= 9 + 18 + 2 + 5 = 34
balls drawn should NOT be Orange.
so, 34 - 18 (as there are 18 orange balls)
16 balls
probability= 16/34 = 8/17
answer = 8/17
what do the following two equations represent? 4x+2y=10 and 4x-2y=-10
they represent linear equations
The two equations, 4x + 2y = 10 and 4x - 2y = -10, represent a system of linear equations.
Why is this so?The equations are written in standard form, where x and y are variables, and the coefficients 4, 2, -10, and -2 are constants. Each equation represents a linear relationship between x and y.
The coefficients in front of x and y determine the slope of the line, and the constants on the right side of the equations determine the y-intercept.
Solving this system of equations simultaneously can determine the values of x and y that satisfy both equations, representing the point(s) where the two lines intersect, if they intersect at all.
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A farmer has 3000 feet of fencing to use on a new enclosure. The new enclosure will go up against existing fencing so one side does not need additional fencing. If the farmer wants to subdivide the enclosure to have 3 pens, what is the maximum total area the farmer can enclose?
Answer:
375000 ft^2
Step-by-step explanation:
From the statement that we have that it would be 1 time the length and 2 times the width because one side is not necessary and also we must take into account that it would be divided by 3 equal enclosures therefore we will use 1000 feet (3000/3) so Therefore, the perimeter would be equal to:
1000 = l + 2 * w
we solve for w:
l = 1000 - 2 * w
Also the area is equal to:
A = w * l
replacing:
A = w * (1000 - 2 * w)
A = 1000 * w - 2 * w ^ 2
We derive:
A '= 1000 - 4 * w
Let's equal 0:
1000 - 4 * w = 0
w = 1000/4
w = 250
replacing and we calculate l:
l = 1000 - 2 * 250
l = 500
A = 250 * 500
A = 15,000 ft ^ 2
Which means that for each subdivision the maximum area would be 125000 square feet and the total would be:
125000 * 3 = 375000 ft ^ 2
What is x? Im having trouble
Answer:
These are two secant lines meaning we can use theorem 6-17 to find the value of x: 6x + 8x times 8x = 16 times 7
14x times 8x = 112
112x^2 = 112
x^2 = 1
x = 1
Answer:
x=1
Step-by-step explanation:
(whole secant) x (external part) = (whole secant) x (external part)
(9+7) *7 = (6x+8x)*8x
16*7 = 14x*8x
112 =112 x^2
Divide by 112
112/112 = 112x^2/112
1 = x^2
Take the square root
1 =x
Внешний диаметр полого шара равен 16 см. Толщина стенок 2 см Найти
объем материала, из которого изготовлен шар.
Answer:
Внешний радиус
Тогда внутренний радиус
Объем материала равен разности объемов внешнего и внутреннего шаров, то есть
Answer:
1239.25 cm³
Step-by-step explanation:
Outer diameter 16 cm
⇒ R= 8 cm
Inner radius
⇒ r= R- 2= 6 cm
The volume of the wall of 2 cm thickness:
⇒ 4/3πR³- 4/3πr³= 4/3*3.14*(8³-6³)= 1239.25 cm³
Find the area of the compound shapes below !Please help
Answer:
86cm
Step-by-step explanation:
Answer:
Step-by-step explanation:
the first figure is rectangle , so
length = 15cm, breadth = 6cm
therefore area = l * b = 15*6 = 90cm^2
second figure is also a rectangle so,
length = 12+6 =18 cm ( or 9+9) , breadth = 9cm
therefore area = l*b =18*9 = 162cm^2
third figure is a semicircle , so
d = 11+9 = 20 cm , r = d/2 =20/2 =10cm
area of semicircle = [tex]1/2[/tex] * [tex]\pi * r^2\\[/tex]
=1/2*22/7 *10*10
=1100/7 = 157 1/7 cm^2
if you add all the areas then you will get the requires area
hope it helps you
What expression has a positive value
Which is the best description of the equivalency of the two expressions?
Expression 1
Expression 2
5 x squared minus 2 x minus 4 + 6 x + 3
6 x squared minus 6 x + 6 minus x squared + 10 x minus 7
Answer:
The answer is option D
Took the quiz
Answer: They are equivalent because when x=2, the two expressions have the same value.
Step-by-step explanation:
The graph below shows the relationship between population density and pollution per person for 36 Japanese cities.
What is the best description of this relationship?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Positive linear association
(Choice B)
B
Negative linear association
(Choice C)
C
Nonlinear association
(Choice D)
D
No association
Graph:
Answer: D . No association
Step-by-step explanation:
The relationship between two variable is called correlation.
When two variables has positive correlation ( When one variable increases by increasing the other) then it reprsesents Positive linear association .When two variables has negative correlation ( When one variable decreases by increasing the other) then it reprsesents Negative linear association .When two variables in which change in one variable does not correspond with constant change in the other variable, then it represents Nonlinear association.If two variables are not interdependent such that if one increasing then there is no proportional change in the other variable, then we say there is no correlation.Hence, the correct option is D. No association.
Hi There. (Choice D) Is The Right Answer.
Step-by-step explanation:
please help will mark brainliest
Answer:
see below
Step-by-step explanation:
2* (4*8) = (2*4) * 8
This is the associative property of multiplication
Two hikers start a trip from a camp walking 15 miles due east. They turn north and walk 17 miles to a large pond. How far is the pond from base camp to the nearest tenth of a miles.
Answer:
22.7 miles
Step-by-step explanation:
The hikers start walking 15 miles due east and then they turn north and walk 17 miles to a large pond.
The shape of their journey can be represented as a right angled triangle, shown below.
To find the distance between the pond and the base camp, we need to find the hypotenuse of the triangle.
We can do this by using Pythagoras theorem:
[tex]hyp^2 = a^2 + b^2[/tex]
where a and b are the other two sides of the triangle. Therefore:
[tex]hyp^2 = 15^2 + 17^2\\\\hyp^2 = 514\\\\hyp = \sqrt{5`4} \\\\hyp = 22.7 miles[/tex]
The pond is 22.7 miles far from the base camp.
Solve: [4x + 2] + 6 =0
Select one
a. no solution
b. -1 or 2
O c. 1 or-2
o d. all real numbers
Answer:
Given
Step-by-step explanation:
4x+2+6=0
4x+2=-6
4x= -6-2
4x= -8
x = -8/4
= -2
Answer:
x = -2
Step-by-step explanation:
[4x + 2] + 6 =0
Combine like terms
4x+ 8 =0
Subtract 8 from each side
4x+8-8 = 0-8
4x = -8
Divide each side by 4
4x/4 = -8/4
x = -2
The proceeds of a $7,500.00, 10 percent simple discounted note for 85 days is
Answer:
7325.34
Step-by-step explanation:
is 262015 divisible between 4?
Answer:
No
Step-by-step explanation:
-a+(-b) where a= 6.05 and b= 3.611
Answer:
-9.661
Step-by-step explanation:
In the given equation, a and b are negative. The values of a and b are given. If you insert the values into the given formula, the values become negative because of "-" in front of the a and b values.
-a + (-b) = -6.05 + (-3.611)
Because the second value is negative, the plus sign references to adding BOTH negative values together so it is just the same as saying:
-6.05 - 3.611
This gives you -9.661
Hope this helps!
A boy saves up $79 for a gift for his friend. However, upon reaching the store, he realizes that he saved 257% of the actual amount he needed to buy the present. How much does the present cost? Round to the nearest cent.
Hint: This is a Part = Percent × Whole problem.
You're given the part (79) and the percent (257%, or 2.57).
Substitute these into the equation to find the whole.
Answer:
$30.74
Step-by-step explanation:
(8 + 2 x 6)2 =
the two at the end before the equals is a squared number is a small 2
The expression [tex](8 + 2 \times 6)^2[/tex], following PEMDAS, simplifies to 400.
Let's break down the steps in solving the expression [tex](8 + 2 \times 6)^2[/tex] in more detail (Follow PEMDAS).
Step 1: MultiplicationWe start by evaluating the multiplication operation, which is 2 x 6. The result of this operation is 12.
Step 2: AdditionNext, we evaluate the addition operation, which is 8 + 12. The sum of 8 and 12 is 20.
Step 3: SquaringFinally, we square the result of the addition, which is 20. Squaring a number means multiplying it by itself. In this case, [tex]20^2[/tex] means 20 multiplied by 20, which equals 400.
Therefore, the expression [tex](8 + 2 \times 6)^2[/tex] simplifies to 400.
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Kelly invested her savings of $4800. she invested part in mutual funds, at 9% per year, and the rest in GIC's, at 10% per year. at the end of the year, the interest from both investments is $457. how much did she invest at each rate?
Answer:
For the 9% she invested $2,300
For the 10% she invested $2,500
Step-by-step explanation:
Let the amount invested be $x and $y in both cases respectively
Since the total invested is $4,800
This means that;
x + y = 4800 ••••••••••••(i)
Now let’s have a look at the interests.
For the 9%
Interest would be 9/100 * amount invested
= 9/100 * x = 9x/100
For the 10%, interest would be
10/100 * y = 10y/100
Adding both will give a total of 457
9x/100 + 10y/100 = 457
multiply through by 100
9x + 10y = 45700 •••••••• (ii)
From equation i, we can write x = 4800 - y
we can substitute this into the second equation
9(4800-y) + 10y = 45700
43200 -9y + 10y = 45,700
43200 + y = 45,700
y = 45,700-43,200 = $2,500
Recall
x = 4800 -y
so x = 4800 -2500 = 2300
Which equation is equivalent to the following?
4x^2 + 4y^2 +16x – 24y = 34
Please answer it:(
Answer:
The correct answer is the third expression.
Step-by-step explanation:
We have the following equation:
[tex]4*x^2 + 4*y^2 + 16*x - 24*y = 34[/tex]
Let's organize it by variables, putting together the ones that have the same letter or no letter at all. We have:
[tex]4*x^2 + 16*x + 4*y^2 - 24*y = 34[/tex]
We can extract the common factor on the left side by dividing them by 4, we have:
[tex]4*(x^2 + 4*x) + 4*(y^2 - 6*y) = 34[/tex]
We need to complete the squares on the parenthesis without changing the value of the equation, to do that we will sum the proper values inside the parenthesis and those multiplied by four on the other side of the equation, we have:
[tex]4*(x^2 + 4*x + 4) + 4*(y^2 - 6*y + 9) = 34 + 16 + 36\\4*(x + 2)^2 + 4*(y - 3)^2 = 86[/tex]
The correct answer is the third expression.
The measure of angle 1 is (10 x + 8) degrees and the measure of angle 3 is (12 x minus 10) degrees. what is the measure of angle 2 in degrees?
Answer:
82 degrees
Step-by-step explanation:
First set 10x+8 equal to 12x-10 to find that the variable is equal to 9. Then solve for 10(9)+8 which equals 98. Since angle 1 is supplementary to angle two and supplementary angles add up to 180 degrees, subtract 98 from 180 to find that your answer is 82 degrees.
A contractor is building a circular swimming pool. The radius of the circle 12 feet. He needs to know the
circumference in order to buy tile to put around the edge of the pool.
What is the circumference if he uses n=2217 ?
Answer:
75.41 ftStep-by-step explanation:
This problem is on the mensuration of flat shape, a circle.
we know that the circumference of a circle is expressed as
[tex]C= 2\pi r[/tex]
Given that radius = 12 ft
The circumference can be solved for by substituting the value of r in the formula
C=2*3.142*12
C= 75.408ft
to 2 d.p the circumference is 75.41 ft
Ricky Major
3:05 AM (0 minutes ago)
to me
Fred is planning a fundraiser where he will collect $4.50 for every mile he runs. He will be running on a typical track, that has two straight lengths of 300 feet each, and two curved parts that are in the shape of semicircles with 200 foot diameters
He runs around the track exactly 15 times. To the nearest cent, how much money did he collect?
Answer:
Step-by-step explanation:
The diameter of each curved path is 200 feet. Since the two curved semi circular paths are equal, they would form a circle. It means that the distance around the two semi circular paths would be the circumference of the circle. Formula for determining the circumference of the circle is π × diameter. It becomes
200 × 3.14 = 628 feet
Total distance around the track would be
300 + 300 + 628 = 1228 feet
5280 feet = 1 mile
1228 feet = 1228/5280 = 0.23 mile
If he runs around the track exactly 15 times, it means that the number of miles covered is
0.23 × 15 = 3.45 miles
Since he will collect $4.50 for every mile he runs, the amount of money that he collected is
4.5 × 3.45 = $15.5
What is the value of the expression i To the power of 1 times I to the power of 2 times I to the power of 3 times I to the power of 4
Answer:
-1
Step-by-step explanation:
[tex]i^1\cdot i^2\cdot i^3\cdot i^4= \\\\i^{1+2+3+4}= \\\\i^{10}= \\\\-1[/tex]
Hope this helps!
The formula for the slant height of a cone is t equals StartFraction S minus pi r squared Over pi EndFraction. , where S is surface area of the cone. Use the formula to find the slant height, l, of a cone with a surface area of 500π ft2 and a radius of 15 ft.
Answer:
275 ft
Step-by-step explanation:
The formula given to use for the slant height l of the cone is ;
l = (s - πr^2)/π
Now substituting the parameters given in the question, 500 π for area and radius of 15, we have
l = {500π-15^(2)π}/π
l =( 500 π -225 π)/π
l = 275 π/π
l = 275 ft
Answer:
275
Step-by-step explanation:
^ and what they said
PLZ HELP ME W DIS!!!
Answer:
6^8
Step-by-step explanation:
When the equation looks like this, you can multiply the exponents to give you 6^8. I think that's the kind of answer you're looking for :)
Hope this helps you!
Mark created a flower bed that is semicircular in shape, as shown in the image. The diameter of the flower bed is 5m. What is the perimeter of the flower bed? (Approximate to be 3.14.) Round your answer to two decimal places.
Answer:
12.85
Step-by-step explanation:
P=1/2(3.14xd)+d
P=1/2x15.7+5
P=12.85
