Answer:
[tex]a_{n} = 5 * 3^{n-1}[/tex]
Step-by-step explanation:
To find the nth term of a geometric sequence, you have the general formula:
[tex]a_{1} *r^{n-1}[/tex]
where a1 is the first term and r is the common ratio. In order to find the 4th term, we can substitute what we have(n is 4 because we are looking for the fourth term):
135 = [tex]a_{1} * 3^{4 - 1}[/tex]
135 = [tex]a_{1} * 3^3[/tex]
135 = [tex]27a_{1}[/tex]
[tex]a_{1} = 5[/tex]
Now, we can substitute the first term back in:
[tex]a_{n} = 5 * 3^{n-1}[/tex]
7.
Reason The dot plot shows the numbers of pages students
in a class read during their dedicated reading time.
A. How many students are in the class?
B What percent of students read more than 6 pages?
Explain your reasoning
Pages Read During
Dedicated Reading Time
What fraction of the students read less than 5 pages?
D. How many total pages did all of the students read? Show your work
id speaker notes
Step-by-step explanation:
7equitacion h< y ⚽ de los siguientes dominios
What is 787,452 rounded to the nearest ten thousand?
Answer:
790000
Step-by-step explanation:
Answer:
790,000
Step-by-step explanation:
can someone please help I will do anything
Answer:
678.24 cubic centimeters
Step-by-step explanation:
7k-6,2k+14 solve for K
Answer:
0.8k +14
Step-by-step explanation:
See the steps below:)
You went to a bake sale and bought a whole bunch of
yummies!
Cookies were $1 and Brownies were $2. You spent
$13 total.
What are three combinations of cookies and brownies
that you could have gotten?
Write an equation that represents this situation.
Answer:
If cookies are for $1 and brownies are for $2, let number of cookies = x and number of brownies = y
∴ $1*(x*1) + $2*(y*1) = $13
Step-by-step explanation:
1) You can buy 4 brownies for $2 each = 2*4 = $8
The rest you can buy cookies = 5 cookies = $5
$8+$5=$13
2) You can buy 5 brownies and 3 cookies = $10+$3 = $13
3) You can buy 3 brownies and 7 cookies = $6+$7=$13
Equation: -
If cookies are for $1 and brownies are for $2, let number of cookies = x and number of brownies = y
∴ $1*(x*1) + $2*(y*1) = $13
Which fraction has the greatest value?
+
-1
0
Jh
1
O
Um
d
HELPPPPP!!!!
find the mean, median, mode, and range of the data 10, 13, 7, 6, 9, 4, 6, 3, 5
Which of the following are true statements about a 30-60-90 triangle?
Lan
Answer:
C and F
Step-by-step explanation:
Answer:
A, F
Step-by-step explanation:
ratio of sides in a 30-60-90 triangle is 1 : [tex]\sqrt{3}[/tex] : 2
just need a bit of help
Answer:
35A) arc AC = 360-(100+110+80)=
360-290 = 70°
35B) L D = ½× 70 = 35°
35C) L AEC = ½(100+70)=½×170= 85°
35D) L P = ½(100-70) = ½×30 = 15°
1 gold plate weight 30 mg if the weight of some plates is 450 ml mg find the number of plates
Answer:
15 plates
Step-by-step explanation:
450 divided by 30 = 15, meaning 30 x 15 would be 450 mg. This also means that if the weight of some plates was 450 mg, there would be 15 plates.
Answer:
15
Step-by-step explanation:
Your units are a little confused.
The mass (total ) is 450 mg
1 plate weighs 30 mg
1 plate / 30 mg = x plates / 450 mg Cross multiply
1 * 450 = 30x Divide by 30
450 / 30 = x
x = 15
There are 15 gold plates.
Integration of ∫(cos3x+3sinx)dx
Answer:
[tex]\boxed{\pink{\tt I = \dfrac{1}{3}sin(3x) - 3cos(x) + C}}[/tex]
Step-by-step explanation:
We need to integrate the given expression. Let I be the answer .
[tex]\implies\displaystyle\sf I = \int (cos(3x) + 3sin(x) )dx \\\\\implies\displaystyle I = \int cos(3x) + \int sin(x)\ dx [/tex]
Let u = 3x , then du = 3dx . Henceforth 1/3 du = dx . Now , Rewrite using du and u .[tex]\implies\displaystyle\sf I = \int cos\ u \dfrac{1}{3}du + \int 3sin \ x \ dx \\\\\implies\displaystyle \sf I = \int \dfrac{cos\ u}{3} du + \int 3sin\ x \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}\int \dfrac{cos(u)}{3} + \int 3sin(x) dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3} sin(u) + C +\int 3sin(x) dx \\\\\implies\displaystyle \sf I = \dfrac{1}{3}sin(u) + C + 3\int sin(x) \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}sin(u) + C + 3(-cos(x)+C) \\\\\implies \underset{\blue{\sf Required\ Answer }}{\underbrace{\boxed{\boxed{\displaystyle\red{\sf I = \dfrac{1}{3}sin(3x) - 3cos(x) + C }}}}}[/tex]
Which expression has a value of 7/12?
1. 2 1/12 + 5 1/12
2. 6/8 + 1/4
3. 1/3 + 1/4
4. 7/8 + 4
Answer: 3. 1/3 + 1/4
Step-by-step explanation:
1/3 = 4/12
1/4 = 3/12
4/12 + 3/12 = 7/12
URGENT... please help
can someone help me.?!
[tex]{\boxed{\mathcal{\red{h\:=\:9.5}}}}[/tex] ✅
Step-by-step explanation:-[tex]h + \frac{1}{2} = 10 \\ ⇢ h + 0.5 = 10 \\ ⇢ h \: = 10 - 0.5 \\ ⇢ h = 9.5[/tex]
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
Find the quotient for 5,600÷8
Answer:
700
Hope this helps!!
Answer:
700
Step-by-step explanation:
Choose a method you prefer to solve for a system of linear equations.
2x + 4y = -4
2x-y=6
Answer:
Elimination
x = 2
y = -2
Step-by-step explanation:
Elimination
2x + 4y = -4
2x - y = 6
Subtract the second equation from the first
5y = -10
Divide both sides by 5
y = -2
---------------------
Substitute for y = -2 in the second equation
2x - -2 = 6
2x + 2 = 6
subtract 2 from both sides
2x = 4
Divide both sides by 2
x = 2
What is the magnitude of -3 +4i?
Answer:
we have
-3+4i
let magnitude be |z|
|z|=[tex] \sqrt{( - 3) {}^{2} + 4 {}^{2} } [/tex]
|z|=5 unit
Answer:
The magnitude of -3 +4i is 5
Step-by-step explanation:
The table below shows the number of students in four schools with grade
point averages in various ranges. The grade point averages of the students in
which school represent a U-shaped distribution?
School A School B School C School D
Greater than 1.5 but less than 2.0 22 15 82 19
Greater than 2.0 but less than 2.5 39 43 46 57
Greater than 2.5 but less than 3.0 67 98 26
81
Greater than 3.0 but less than 3.5 41 45 59 50
Greater than 3.5 but less than 4.0 27 12 78 17
A. School B
O
B. School C
C. School D
Ο Ο
D. School A
Answer:
b
Step-by-step explanation:
Step-by-step explanation:
school c so B would be correct
Which polynomial function has a leading coefficient of 2, root-5 with multiplicity 3, and root 12 with multiplicity 1?
Of(x) = 2(x - 5)(x - 5)(x - 5)(x + 12)
Of(x) = 2(x + 5)(x + 5)(x + 5)(x - 12)
O f(x) = 3(x - 5)(x - 5)(x + 12)
Of(x) = 3(x + 5)(x + 5)(x - 12)
Answer:
Of(x) = 2(x + 5)(x + 5)(x + 5)(x - 12) or Choice 2
Step-by-step explanation:
The last two answers get eliminated because their leading coefficients aren't 2. The first option is wrong because if you plug in -5 and +12 into x the function won't equal 0. So the correct answer is the Second answer: Of(x) = 2(x + 5)(x + 5)(x + 5)(x - 12)
Answer:
The polynomial function that has a leading coefficient of 2, a root of 5 with a multiplicity of 3, and a root of 12 with a multiplicity of 1 is choice 2.
Step-by-step explanation:
A leading coefficient of 2 means that the number multiplying all the binomial would be 2, so you know it is not choices 3 and 4. A root of -5 with a multiplicity of 3 means that when you replace x with -5, three binomials will result in 0, which helps eliminate the first choice. A root of 12 with a multiplicity of 1 means that when you replace x with 12, you will have a binomial that results in 0. Using all of this information, you'll get that the polynomial that has a leading coefficient of 2, a root of -5 with a multiplicity of 3, and a root of 12 with a multiplicity of 1 is [tex]f(x)=2(x+5)(x+5)(x+5)(x-12)[/tex].
If 2x + 5 = 82, then 12x = ?
A 5
B
10
C 15
D 20
Answer:
2x= 38.5
Step-by-step explanation:
I'm not sure where u got 12x but 2 x = 38.5:
2x + 5 =82
subtract 5 for 82
2x = 77
77 divided by 2 is 38.5
x = 38.5
hope this helps :)
A dilation has center at the origin. Which of the following is the image of the point P(1.- for a scale
factor of
A
D: (P) = P(x3)
B
D}(P) = P',
C
D:(P) = P1C-
D
D}(P) = PG-)
Answer:
C. [tex]D_\frac{1}{7} (P)=P'(\frac{1}{4},-\frac{5}{14} )[/tex]
Step-by-step explanation:
[tex]\frac{7}{4}*\frac{1}{7}=\frac{7}{28} =\frac{1}{4}[/tex]
[tex]-\frac{5}{2} *\frac{1}{7} =-\frac{5}{14}[/tex]
A flood lamp is installed on the ground 200 feet from a vertical wall. A six-foot-tallman is walking towards the wall at the rate of 30 feet per second. How fast is the tip of his shadow moving down the wall when he is 50 feet from the wall
Answer:
The rate at which the tip of his shadow is moving down is [tex]\frac{24}{15} ft/sec[/tex]
Step-by-step explanation:
Given - A flood lamp is installed on the ground 200 feet from a vertical wall. A six-foot-tall man is walking towards the wall at the rate of 30 feet per second.
To find - How fast is the tip of his shadow moving down the wall when he is 50 feet from the wall ?
Proof -
From the given information, the figure becomes
Triangle ABC and Triangle DBE are similar triangle
AC/DE = BC/BE
⇒h/6 = 200/(200-x)
⇒h = 1200/(200 -x)
Now,
Differentiate h with respect to t, we get
[tex]\frac{dh}{dt} = 1200(-\frac{1}{(200-x)^{2} } )(-1)\frac{dx}{dt}[/tex]
⇒[tex]\frac{dh}{dt} = (\frac{1200}{(200-x)^{2} } )\frac{dx}{dt}[/tex]
Now,
If the rate of the tip is moving down the wall
At x = 50 feet, dx/dt = 30 feet per second
So,
⇒[tex]\frac{dh}{dt} = (\frac{1200}{(200-50)^{2} } )(30)[/tex]
⇒[tex]\frac{dh}{dt} = \frac{1200}{(150)^{2} } (30)[/tex]
⇒[tex]\frac{dh}{dt} = \frac{1200}{(150)(150) } (30)[/tex]
⇒[tex]\frac{dh}{dt} = \frac{24}{15 }[/tex]
So, we get
The rate at which the tip of his shadow is moving down is [tex]\frac{24}{15} ft/sec[/tex]
A rectangular room is 11 feet by 14 feet. The ceilings are 9 feet high. If a gallon of paint covers 250 square feet. How many gallons of paint are needed to paint the room?
Answer:
3 gallons or 3.032
Step-by-step explanation:
find the total surface area (758)
divide by 250 or subtract 250 till it is under that number
Help me out please???
If G is the incenter of ∆ABC, then GD = GF = GE.
Given, GD is 3x + 5 and GF is 6x - 4.
According to the above statement,
GD = GF
or, 3x + 5 = 6x - 4
or, 5 + 4 = 6x - 3x
or, 9 = 3x
or, 9/3 = x
or, 3 = x
The value of x is 3.
By putting the value of x in GD or GF, we get
GD = 3(3) + 5 = 9 + 5 = 14
GF = 6(3) - 4 = 18 - 4 = 14
Therefore, GE = 14.
You pick a card at random, put it back, and then pick another card at random. 3 4 5 6 What is the probability of picking a 5 and then picking a 3?
Answer:
1/16
Explanation:
You have a 1/4 chance both times but in probability you multiply when in a sequence of events. 1/4*1/4= 1/16
The point (-8,0) reflected in the x-axis is
Answer:
That would be (8,0) my good sir ( ma'am )
Step-by-step explanation:
Have a nice day
If using the method of completing the square to solve the quadratic equation x2+14x-14=0, which number would have to be added to "complete the square"?
Answer:
49
Step-by-step explanation:
the number would simply be
14÷2=7
7²=49
Which binomial is a factor of 3x^2 + 2x − 5 ?
3x-1
3x-5
x-1
x-5
Answer:
3x-1
Step-by-step explanation:
3x^2+2x-5=3x-1 x1-25
Red Blue Yellow Green What is the probability of a player spinning the color blue and then rolling a 4?
A: 1/4
B: 1/24
C: 1/6
D: 1/16
Answer:
(1/4)×4=1/16
Step-by-step explanation:
Blue is 1 out of the 4 colours, it rolls for 4 times
Please help me solve this problem
Answer:
72 in²
Step-by-step explanation:
lateral area: the surface area of a 3D figure, but excluding the area of any bases
the lateral area of this prism is the sum of the three rectangular sides.
calculate the third side of the triangle first because it's also the side of one of the rectangle:
√(5² - 4²) = 3
4 × 6 + 5 × 6 + 3 × 6 = 72