If the first term is [tex]a[/tex], then the second term is [tex]ar[/tex], the third is [tex]ar^2[/tex], the fourth is [tex]ar^3[/tex], and the fifth is [tex]ar^4[/tex].
We're given
[tex]\begin{cases}ar=6\\ar^4=48\end{cases}\implies\dfrac{ar^4}{ar}=r^3=8\implies r=2\implies a=3[/tex]
So the first five terms in the GP are
3, 6, 12, 24, 48
Adding up the first four gives a sum of 45.
If you were asked to find the sum of many, many more terms, having a formula for the n-th partial sum would convenient. Let [tex]S_n[/tex] denote the sum of the first n terms in the GP:
[tex]S_n=3+3\cdot2+3\cdot2^2+\cdots+3\cdot2^{n-2}+3\cdot2^{n-1}[/tex]
Multiply both sides by 2:
[tex]2S_n=3\cdot2+3\cdot2^2+3\cdot2^3+\cdots+3\cdot2^{n-1}+3\cdot2^n[/tex]
Subtract this from [tex]S_n[/tex], which eliminates all the middle terms:
[tex]S_n-2S_n=3-3\cdot2^n\implies -S_n=3(1-2^n)\implies S_n=3(2^n-1)[/tex]
Then the sum of the first four terms is again [tex]S_4=3(2^4-1)=45[/tex].
Write the following phrase as an expression. "7 more than n"
Answer:
7+n
Step-by-step explanation:
More indicates that we are adding an amount to n.
So since it is 7 more, we need to add 7 to n.
Note that an expression does not include an equal sign, so we are done.
Other commonly seen phrases are:
less than -> indicates subtraction
product of -> indicates multiplication
divided by -> division
Zane bought a pair of jeans that originally cost $56. He used a coupon for 25% off and paid 8% in sales tax. How much did he pay for his jeans?
Answer:
$38.64
Step-by-step explanation:
so the equation needed to solve is $56*0.25 and that number is 14. Since it is a coupon you subtract 14 from 56 and end up with 42. Now multiply 0.08*42 and you got your sales tax, $3.36. now subtract that from 42 and you have your answer! Don't forget the dollar sign!
hope this helped! : )
PLSSS HELP
Kenny and Michael have scored points during a basketball game. Kenny has scored 131313 points, and Michael has scored ppp points. Together they have scored a total of 272727 points. Select the equation that matches this situation. Choose 1 answer:
Choose 1 answer:
(Choice A)
A
13 + p = 2713+p=2713, plus, p, equals, 27
(Choice B)
B
13 = p + 2713=p+2713, equals, p, plus, 27
(Choice C)
C
13 - p = 2713−p=2713, minus, p, equals, 27
Answer:
A
Step-by-step explanation:
Kenny scored 13 points, and Micheal scored p points. They scored a total of 27 points. This means that 27 is the sum of their scores. The answer is A.
13 + p = 27
Answer:
It’s b or it’s 13+p=27
Step-by-step explanation:
Can anyone please help me with this?
Answer: 4
Step-by-step explanation:
Because there are two equal angles, this is an isoceles triangle. Line JP and HP are equal. To find the variable, write the equation which would be 3x-6=x+2. X is 4.
hope this helped:)
Answer: 4 AKA D
Step-by-step explanation:
Well to start off, we must first establish that line JP and line HP are equal because of the red ticks in the corner. So once we figured that out, then 3x-6 = x+2
»Next we add 6 to both side to make 3x = x+8
»Then we subtract x from both sides to equal 2x = 8
»Then we divide both sides by 2 which equals x=4
»So the final answer would be D. 4
Hope i helped
-lvr
Please answer it now in two minutes
Answer:
Area of the triangle WXY = 365.3 mm²
Step-by-step explanation:
By applying Sine rule in the given triangle XYW,
[tex]\frac{\text{SinY}}{\text{WX}}=\frac{\text{SinX}}{\text{YW}}[/tex]
[tex]\frac{\text{Sin70}}{\text{WX}}=\frac{\text{Sin43}}{\text{24}}[/tex]
WX = [tex]\frac{24.\text{Sin70}}{\text{Sin43}}[/tex]
= 33.068 mm
= 33.07 mm
Area of a triangle = [tex]\frac{1}{2}a.b.\text{Sin}\theta[/tex]
where a and b are the sides of the triangle and θ is the angle between the sides a and b.
Area = [tex]\frac{1}{2}(33.07)(24)\text{SinW}[/tex]
Since, m∠X + m∠Y + m∠W = 180°
m∠W = 180 - (43 + 70)
= 67°
Area of the triangle WXY = [tex]12\times (33.07)\text{Sin67}[/tex]
= 365.29 mm²
≈ 365.3mm²
If a test has 40 questions and you get 200 points for the whole test, how many points are each question worth?
Answer:
5
Step-by-step explanation:
To find the points for each question, you must divide the number of points (200) by the number of questions (40) to get the number of points for each question
[tex]\frac{200}{40}[/tex]
Divide 200 by 40 to get
[tex]\frac{5}{1}[/tex] or [tex]5[/tex]
Hope this helps. If you have any follow-up questions, feel free to ask.
Have a great day!
Answer:
5 points
Step-by-step explanation:
200points / 40 questions = 5points/1question
then:
1 questión worths 5 points
piece of wire 8 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle. (a) How much wire should be used for the square in order to maximize the total area
Answer:
piece of wire 8 m long
one piece is bent into square:
the square has four equal sides , so at least 4 m has to be cut from the wire to form a square with side=1 m.
the perimeter of the square =2L+2W=2(1)+2(1)=4 m
that is the max. amount can be cut from the wire, since the other part is bent into a circle.
( note if you cut more, the square will take the whole wire)
Perimeter=2L+2W=2(2)=2(2)=8 m and the area=2*2=4 m²)
Area and perimeter are two crucial characteristics of 2D shapes in mathematics.
The perimeter of the square exists 8 m and the area exists 4 m².
What is the perimeter and area of a square?Area and perimeter are two crucial characteristics of 2D shapes in mathematics. The area and perimeter both specify the shape's boundaries and the space they occupy, respectively. Area and perimeter are significant mathematical concepts that are used to daily life. All sizes and shapes, regular or unusual, are covered by this. Each shape's area and perimeter calculations are unique.
Piece of wire is 8 m long and one piece is bent into square:
The square has four equal sides , so at least 4 m has to be cut from the wire to form a square with side = 1 m.
The perimeter of the square = 2L + 2W = 2(1) + 2(1) = 4 m
Which exists the maximum amount that can be cut from the wire, since the other part is bent into a circle.
Perimeter = 2L + 2W =2(2) = 2(2) = 8 m and the area = 2 × 2= 4 m²
To learn more about perimeter and area, refer to:
brainly.com/question/19819849
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Carlos has 275% as much money as Mariame. Together they have $90. How much money does Mariame have?
Answer:
$24.
Step-by-step explanation:
Let's say Carlos has $c of money, and Mariame has $m of money.
c = 2.75m
c + m = 90
2.75m + m = 90
3.75m = 90
m = 24
c + 24 = 90
c = 66
So, Mariame has $24 and Carlos has $66.
Hope this helps!
You and your sister are selling cookies to help raise money for your field trip. You start out with $24 and sells each bag of cookies, c, for $3. Your sister doesn’t start out with any money but sells her bags of cookies for $5 each. How many bags of cookies must they sell in order for them to raise the same amount of money?
Answer:
12 bags of cookies.
Step-by-step explanation:
Since you already start out with $24, you will have a y-intercept of 24. Your slope will be 3, since each bag sells for $3.
Your equation will be y = 3c + 24.
Your sister does not start out with money, so she will have a y-intercept of 0. Her slope will be 5, as each bag sells for $5.
Her equation will be y = 5c.
Since y = y, you can set the two equations equal to each other.
3c + 24 = 5c
5c = 3c + 24
Subtract 3c from both sides
2c = 24
Divide both sides by 2
c = 12
So, they must sell 12 bags of cookies to raise the same amount of money, $60. Yum!
Hope this helps!
15. To save for retirement, Karla Harby put $625 each month into an ordinary annuity for 14 years. Interest was compounded monthly. At the end of the 14 years, the annuity was worth $156 comma 700. What annual interest rate did she receive? The interest rate she received was approximately _______%. (Round to two decimal places as needed.)
Answer:
40.08%
Step-by-step explanation:
From the given information;
the annual interest rate can be determined using the formula:
[tex]A =P \times( 1+ \dfrac{r}{n})^{nt}[/tex]
where;
A = amount
P is the installment per period = $625
r = interest rate
nt = number of installments= 14×(12) =168
i = rate of interest per year
[tex]156700 = 625 \times( 1+ \dfrac{r}{12})^{168}[/tex]
[tex]\dfrac{156700}{625} = {(1+ \dfrac{r}{12})^{168}[/tex]
[tex]250.72 = {(1+ \dfrac{r}{12})^{168}[/tex]
[tex]\sqrt[168]{250.72} = {(1+ \dfrac{r}{12})[/tex]
1.0334 = [tex]{(1+ \dfrac{r}{12})[/tex]
1.0334 -1 = r/12
0.0334 = r/12
r = 0.0334 × 12
r = 0.4008
r = 40.08%
Thus; Karla Harby received an interest rate of 40.08%
Please answer this in two minutes
Help please!!!thanks
Answer:
i believe it is c
Step-by-step explanation:
9. A solid rectangular block of copper 5 cm by 4 cm by 2 cm
is drawn out to make a cylindrical wire of diameter 2 mm.
Calculate the length of the wire.
Answer:
length = 1273.2 cm or 12.73 m
Step-by-step explanation:
Assume no loss.
diameter of wire, d = 2 mm
radius of wire, r = 1 mm = 0.1 cm
Volume of block, V = 5*4*2 = 40 cm^3
cross sectional area of wire, A = pi (r^2) = pi 0.1^2 = 0.01pi cm^2
Length of wire
= V/A
= 40 cm^3 / 0.01pi cm^2
= 4000/pi cm
= 1273.2 cm
= 12.73 m
suppose that f(x)=x^2 and g(x) = -2/3x^2 which statement best compares that graph of g(x) with the graph of f(x)?
Answer:
[tex] f(x) = x^2 , g(x)= -\frac{2}{3}x^2[/tex]
And we want to compare the two functions.
The minus signs is a reflection around the x axis and the value of 2/3 is a compression of the original function so then the best answer would be:
The graph of g(x) is the graph of f(x) compressed vertically and reflected over the x axis
Step-by-step explanation:
We have the following two function given:
[tex] f(x) = x^2 , g(x)= -\frac{2}{3}x^2[/tex]
And we want to compare the two functions.
The minus signs is a reflection around the x axis and the value of 2/3 is a compression of the original function so then the best answer would be:
d) The graph of g(x) is the graph of f(x) compressed vertically and reflected over the x axis
Answer:
C is the correct answer
Step-by-step explanation:
The radius of the base of the cone is an 5cm
and slant height is 9cm
Find out its total
surface area
area.
Answer:
The total surface area of cone is 70π cm² or 219.9 cm².
Step-by-step explanation:
Given that the formula of total surface area of cone is T.S.A = πr² + πrl where r represents radius and l is slant height. So you have to substitute the values :
[tex]t.s.a = \pi {r}^{2} + \pi{r}l[/tex]
[tex]let \: r = 5 \: , \: l = 9[/tex]
[tex]t.s.a = \pi {(5)}^{2} + \pi(5)(9)[/tex]
[tex]t.s.a = 25\pi + 45\pi[/tex]
[tex]t.s. a = 70\pi \: or \: 219.9 \: [/tex]
A candle burns at a constant rate of 2.5cm/h. The candle is 15cm tall when it is first lit. Let "t" represent the time is it burning in hours and let "h" represent the height of the candle in centimetres.
Answer:
The initial height of the candle is H = 15cm
The rate at which the candle burns is 2.5 cm per hour
Then after one hour, the height of the candle is:
h = 15cm - 2.5cm = 12.5cm
after two hours is:
h = 15cm - 2*2.5cm = 10cm
then, after t hours, the height of the candle is:
h = 15cm - (2.5cm/h)*t
now, the domain of h (or the range of the function) is:
h ∈ [0cm, 15cm]
when t = 0, h(0h) = 15cm
and the maximum value of t will be such that the candle is totally consumed:
h(t) = 0 = 15 - 2.5*t
t = 15/2.5 = 6
Then the domain of the function is:
t ∈ [0h, 6h]
On a map, the distance between two
cities is 5.25 inches. The map scale is
1 in.:25 mi To the nearest mile, what is
the actual distance between the two
cities?
Simplify: 3.59 x 106 : 9.5 x 10-6
Answer:
380.54:1007
Step-by-step explanation:
3.59✖️106=380.54
9.5✖️106=1007
380.54:1007
Answer:
[tex]\huge\boxed{3.779\times10^{11}}[/tex]
Step-by-step explanation:
[tex]\left(3.59\times10^6\right):\left(9.5\times10^{-6}\right)=\dfrac{3.59}{9.5}\times\dfrac{10^6}{10^{-6}}=\dfrac{359}{950}\times10^{6-(-6)}=\dfrac{359}{950}\times10^{6+6}\\\\=\dfrac{359}{950}\times10^{12}\approx0.3779\times10^{12}=3.779\times10^{11}\\\\\text{used}\ \dfrac{a^n}{a^m}=a^{n-m}[/tex]
which equation represents the line that is perpendicular yo y=3/2x+1 and passes through (-12,6)
Answer:
y = -2/3x - 2
Step-by-step explanation:
Step 1: Find slope m of perpendicular line
Simply take the negative reciprocal of the given line
m = -2/3
y = -2/3x + b
Step 2: Find b
6 = -2/3(-12) + b
6 = 8 + b
b = -2
Step 3: Rewrite perpendicular equation
y = -2/3x - 2
Simplify: 42x^7-(-11x^7)
Answer: 53x^7
Step-by-step explanation:
Subtracting a negative is like adding.
I would like to say that people need to work harder on writing good answers.
Answer:
Yes, it can.
Step-by-step explanation:
Looking at this table, we can see that each type of hat is ALWAYS next to the same type of flower.
Berets are ALWAYS next to Daffodils.
Panamas are ALWAYS next to Sunflowers.
Cloches are ALWAYS next to Violets.
Bowlers are ALWAYS next to Irises.
Fedoras are ALWAYS next to Narcissuses.
If we assume that every type of FLOWER is a number and every type of HAT is also a number, these will all match up.
So, they are consistent.
This means that the type of flower can be represented as a function of the type of hat.
Hope this helped!
Answer:
No
Step-by-step explanation:
There is not a known causation or correlation between the two variables.
What is the maximum value of the function
Answer:
[tex]10[/tex]
Step-by-step explanation:
[tex]f(x)=-x^2+6x+1[/tex]
x coordinate:
[tex]\frac{-b}{2a}[/tex]
[tex]a=-1\\b=6[/tex]
[tex]\frac{-6}{2(-1)} \\\frac{-6}{-2}\\ =3[/tex]
y-coordinate:
[tex]f(3)=-(3)^2+6(3)+1\\f(3)=-9+18+1\\f(3)=10[/tex]
Answer:
10
Step-by-step explanation:
Write the equation of a line that is perpendicular to x=3x=3x, equals, 3 and that passes through the point (0,-4)(0,−4)left parenthesis, 0, comma, minus, 4, right parenthesis.
Answer:
y= -4
Step-by-step explanation:
Khan Academy
The equation of a line that is perpendicular to x = 3 will be y = -4.
What is the equation of a perpendicular line?Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.
The equation is given below.
x = 3
The equation of the line that is perpendicular to the line x = 3 is given as,
y = d
The line is passing through (0, -4), then the equation of the line is given as,
y = -4
The equation of a line that is perpendicular to x = 3 will be y = -4.
More about the equation of a perpendicular line link is given below.
https://brainly.com/question/14200719
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YoIn a sale, the normal price of a book is reduced by 30%. The sale price of the book is £2.80 Work out the normal price of the book.
Answer: £4
Step-by-step explanation:
From the question, we are informed that when the normal price of a book is reduced by 30%, then the sale price of the book is £2.80.
Since the normal price of a book is reduced by 30%, that means the book is sold at (100% - 30%) = 70% of its normal price.
Let the normal price of the book be y.
70% of y = £2.80
70/100 × y = £2.80
0.7 × y = £2.80
0.7y = £2.80
y = £2.80/0.7
y = £4
The normal price of the book is £4.
A cylinder shaped can needs to be constructed to hold 400 cubic centimeters of soup. The material for the sides of the can costs 0.02 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.07 cents per square centimeter. Find the dimensions for the can that will minimize production cost.
Answer:
the dimensions for the can that will minimize production cost is 9.13 cents
Step-by-step explanation:
The volume of a cylinder V = π r²h
If we make the height h the subject of the formula; we have :
h = V/ π r²
Given that the volume of the cylinder = 400
Then
h = 400/ π r²
The total cost will be: 0.02 × 2πrh + 0.07 × 2πr²
= 0.04 (πrh) + 0.14 (πr²)
= 0.04 (πr[tex]\frac{400} {\pi r^2}[/tex]) + 0.14 (πr²)
= 16/r + 0.14 (πr²)
total cost(c)= 16/r + 0.14 (πr²)
(c') = -16/r² + 0.28 (πr)
Let differentiate (c') with respect to zero (0); then:
-16/r² = - 0.28 (πr)
r³ = 16/0.28 π
r³ = 18.19
r = 2.63 cm
Recall that:
h = 400/ π r²
h = 400/ π (2.63)²
h = 400/21.73
h = 18.41 cm
From; total cost = 0.04 (πrh) + 0.14 (πr²)
replacing the value of r and h ; we have:
= 0.04 (π×2.63×18.41) + 0.14 (π × 2.63²)
= 0.04 (152.11) + 0.14 ( 21.73)
= 6.0844 + 3.0422
= 9.1266
≅ 9.13 cents
Therefore; the dimensions for the can that will minimize production cost is 9.13 cents
These figures are similar. The area of one is give. Find the area of the other.
Answer:
64 in²
Step-by-step explanation:
Given that the two figures are similar, therefore, the ratio of the area areas of both figures is proportional to the ratio of the square of the corresponding side lengths of both figures. This means:
[tex] \frac{100}{x} = \frac{10^2}{8^2} [/tex]
Where x is the area of the other figure.
Solve for x
[tex] \frac{100}{x} = \frac{100}{64} [/tex]
Cross multiply
[tex] 100*64 = 100*x [/tex]
Divide both sides by 100
[tex] \frac{100*64}{100} = \frac{100*x}{100} [/tex]
[tex] 64 = x [/tex]
Area of the other figure = 64 in²
Hind Missing Angle
Instructions: Find the measure of the indicated angle to the
nearest degree.
54
?
31
?
Answer:
? = 35
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin ? = opp/ hyp
sin ? = 31/54
Taking the inverse sin of each side
sin ^-1 ( sin ? )= sin ^-1 (31/54)
? = 35.03481479
To the nearest degree
? = 35
WILL MARK BRAINLIEST!!!!
Answer:
See below.
Step-by-step explanation:
SQUARE:
The area of the square is:
[tex]9x^2-12x+4[/tex]
Factor it:
[tex]=9x^2-6x-6x+4\\=3x(3x-2)-2(3x-2)\\=(3x-2)(3x-2)\\=(3x-2)^2[/tex]
Remember that all four sides of a square is equal. The area is simply the side squared. Therefore, all four sides of the square measure (3x-2).
RECTANGLE:
[tex]25x^2-16y^2\\[/tex]
Factor it. This resembles the difference of two squares, where:
[tex](x-a)(x+a)=x^2-a^2[/tex]
[tex]25x^2-16y^2\\=(5x)^2-(4y)^2\\=(5x-4y)(5x+4y)[/tex]
This cannot be simplified further. Note that the sides of rectangles doesn't necessarily have to be the same.
The dimensions of the rectangle is:
(5x-4y) by (5x+4y)
Answer:
Step-by-step explanation:
1. the area of square is 9x^2-12x+4 square units
shortcut: (a-b)^2= a^2-2ab+b^2
then simplify 9x^2-12x+4 to (3x-2)^2
area of square = s^2
then side equals sqrt((3x-2)^2)
s = (3x-2) units
2. the area of rectangle is (25x^2-16y^2) square units
shortcut: (a^2-b^2) = (a-b)(a+b)
then simplify (25x^2-16y^2) to (5x-4y)(5x+4y) square units
one side is: (5x-4y) units
one side is (5x+4y) units
Amy invests $10,000 in an account that pays 1% compound interest annually. She uses the expression (1+) to find the total value of the account after years. What will be the total value of the account after 10 years?
====================================================
Work Shown:
P = amount deposited = 10000
r = interest rate in decimal form = 0.01
n = compounding frequency = 1 (annual compounding)
t = number of years = 10
--------
A = P*(1+r/n)^(n*t) ... compound interest formula
A = 10000*(1+0.01/1)^(1*10)
A = 11046.221254112
A = 11046.22 rounding to the nearest cent
What is x - 3y = -9 in function form??? Help!
This is basically in the form y = mx+b with m = 1/3 as the slope and b = 3 as the y intercept. I'm using f(x) in place of y to indicate function notation.
==========================================
Work Shown:
The goal is to solve for y.
x - 3y = -9
-3y = -9-x ... subtracting x from both sides
-3y = -x-9
y = (-x-9)/(-3) .... dividing both sides by -3
y = -x/(-3) - 9/(-3) ... break up the fraction
y = (1/3)x + 3 .... simplify
f(x) = (1/3)x + 3 .... replace y with f(x)