Answer:
19,531,248
Step-by-step explanation:
General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]
(where [tex]a[/tex] is the first term and [tex]r[/tex] is the common difference)
Given geometric series: 8 + 40 + 200 + ... + 15625000
[tex]\implies a_1=8[/tex]
[tex]\implies a_2=40[/tex]
[tex]\implies a_3=200[/tex]
To find the common ratio [tex]r[/tex], divide consecutive terms:
[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{40}{8}=5[/tex]
Therefore:
[tex]\implies a_n=8(5)^{n-1}[/tex]
To find n when [tex]a_n=15625000[/tex] :
[tex]\implies 8(5)^{n-1}=15625000[/tex]
[tex]\implies (5)^{n-1}=1953125[/tex]
[tex]\implies \ln (5)^{n-1}=\ln1953125[/tex]
[tex]\implies (n-1)\ln 5=\ln1953125[/tex]
[tex]\implies n=\dfrac{\ln1953125}{\ln5}+1[/tex]
[tex]\implies n=10[/tex]
Sum of the first n terms of a geometric series:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
Therefore, sum of the first 10 terms:
[tex]\implies S_{10}=\dfrac{8(1-5^{10})}{1-5}[/tex]
[tex]\implies S_{10}=19,531,248[/tex]
Drag the square to determine how the square and
rectangle intersect. Which statements are true? Check all
that apply.
They can intersect at a single point.
They can intersect at an infinite number of points,
forming a line segment.
They can intersect at an infinite number of points,
forming a ray.
They can intersect at an infinite number of points,
forming two line segments.
They can intersect at an infinite number of points,
forming four line segments.
Answer:
ABD
Step-by-step explanation:
10 points
e following numbers are placed on a number line. Which of the following best
sents point A?
B.D
to
-2
-1
7
H. 2.
7
G. -1-
1
№.
r
Answer:
G
Step-by-step explanation:
really look at the position of point A on the number line.
it is a little bit to the right of -2, but clearly to the left of -1 and especially 0.
so, A must be negative.
that eliminates already H and J.
remember, that e.g. -2 < -1.
so, seemingly "adding" something to the description of a value of a negative number makes that negative number even smaller.
-1 7/8 is for example NOT the same as -1 + 7/8.
it is the same as
-1 - 7/8 = -1 7/8
so, -1 7/8 is indeed smaller than -1.
but it is still larger than -2 (e.g -1 8/8 = -2).
therefore, only G makes sense.
Please help kind of urgent i only have 100 points so please help thanks:)
Answer:
√3
Step-by-step explanation:
To recall trigonometric ratios, there is a special acronym known as sohcahtoa which stands for
sin(x)=opposite/ hypotenusecos(x)=adjacent/hypotenuse tan(x)=opposite /hypotenuseFinding the angle [tex]\theta[/tex]
We are given that,
[tex] \displaystyle \sin( \theta) = \frac{ \sqrt{3} }{2} [/tex]
To find the angle [tex]\theta[/tex] , take inverse of sin of both sides,
[tex] \displaystyle { \sin}^{ - 1}( \sin( \theta) )= { \sin}^{ - 1} \bigg(\frac{ \sqrt{3} }{2} \bigg )[/tex]
with the help of unit circle,we acquire:
[tex] \displaystyle \boxed{\theta= {60}^{ \circ} }[/tex]
Finding [tex]\tan\theta[/tex]
simply plug in the value of theta:
[tex] \tan( {60}^{ \circ} ) [/tex]
using unit circle,we get:
[tex] \implies \tan( {60}^{ \circ} ) = \boxed{\sqrt{3} }[/tex]
and we're done!
Let's solve
[tex]\\ \rm\Rrightarrow sin\theta=\dfrac{\sqrt{3}}{2}[/tex]
[tex]\\ \rm\Rrightarrow \theta=sin^{-1}\left(\dfrac{\sqrt{3}}{2}\right)[/tex]
[tex]\\ \rm\Rrightarrow \theta=\dfrac{\pi}{3}[/tex]
Now
[tex]\\ \rm\Rrightarrow tan\theta=tan\dfrac{\pi}{3}[/tex]
[tex]\\ \rm\Rrightarrow tan\theta=\sqrt{3}[/tex]
PLEASE:
Tye has a square piece of yellow felt that has an area of 81 square inches. She wants to cut the largest circle possible from the material to create a sun for her art project. What is the area of the felt circle? Use 3.14 for π. Round to the nearest hundredth if necessary.
Answer:
63.59 in²
Step-by-step explanation:
The formula to find the area of a square: a², where a is the side.
The formula to find the area of a circle: πr², where r is the radius (diameter ÷ 2), and the pi is alterable (3.14 or 3.142 or 22/7).
1) Find the diameter of the circle. The side of a square is the diameter.
a²
a = √81
a = 9
2) Plug the values into the formula of the area of a circle. 9 ÷ 2 = 4.5 (radius).
= 3.14 x 4.5²
= 3.14 x 20.25
= 63.585
3) Round off the result to the nearest hundredth.
= 63.59
The largest circle possible from the square piece of yellow felt material to create a sun for her art project is of area 63.585 square inches.
What is area?Area is the quantity that expresses the extent of a region on the plane or on a curved surface
According to the question
Square piece of yellow felt that has an area = 81 square inches
Now ,
Area of square of yellow felt = 81 square inches
⇒ [tex]Side^{2} = 81[/tex]
⇒ Side = ± 9 (where -ve 9 cannot be side )
⇒ Side = 9
The largest circle possible from the material is
where, side of square = diameter of circle ( figure attached )
⇒ 9 = diameter of circle
⇒ 9 = 2r
⇒ [tex]\frac{9}{2}[/tex] = r or r = 4.5
Area of circle = [tex]\pi r^{2}[/tex]
= 3.14 * 4.5 * 4.5
= 63.585 square inches.
Hence, Area of the largest circle cut from the square piece is of 63.585 square inches.
To know more about Area here :
https://brainly.com/question/27683633
# SPJ2
What is the equation for the graph please help me ill give 20 pt
Answer:
y = 9x
Step-by-step explanation:
Answer:
4.5x OR 9/2x
Step-by-step explanation:
We know this is a lineasr equation isnce it is a straight line and goes by a slope factor.
We know that for every change in 9 on the y axis, there is a change of two on the x- axis. This slope is now 9/2
The equation can be 9/2x OR 4.5x depending on whether your teacher will accept decimal answers or fractional answers.
does anyone know where he got the 32pie from?
PLEASE HELP!!
BRAINLIEST TO CORRECT ANSWER!!!
The principal of Sycamore Middle School wants to know whether students are in favor of a new dress code.
She conducts a survey.
Which of these methods will produce the most representative sample of the student body at Sycamore Middle School?
O A. The principal surveys all eighth-grade students.
O B. The principal surveys the students in detention.
OC. The principal randomly selects homeroom classes and surveys each student in the chosen classes.
OD. The principal surveys all the students in the math club.
Answer:
C. The principal randomly selects homeroom classes and surveys each student in the chosen classes.
Step-by-step explanation:
Middle school is 6-8th. Surveying only the eighth-grade students won't give a representative sample of the whole school only the eighth-graders. Option A is incorrect.
Surveying only the students in detention represents a very small amount of students compared to the school, therefore it is not a representative sample. Option B is incorrect.
Yet again, the students in the math club is a small amount of students compared to the school. It does not represent the entire, or majority of the population. Option D is incorrect.
Picking students from homeroom classes and surveying each will give a wider variation of opinions from each grade and therefore a representative sample. Option C is the correct answer.
Answer:
C
Step-by-step explanation:
I just did the quiz and it was correct
what is 2x + y - 3z, x = 2/5 , y = 2/3, z = 1/6 what does it equal
femi went shopping for a new television. the television he wants to buy measures 32 inches diagonally. the length of the television is 24 inches. which measurement is the closest to the length of the height in inches?
Answer:
768
Step-by-step explanation:
I hope you mean this, if you don't say so
Frank lost 3 pounds per week for 19 consecutive weeks then 5 pounds in the 20th week which represent his total change in weight
Answer:
5 pounds
Step-by-step explanation:
Carry on learningLast week, Harry ran 5 laps around the lake. Sophia ran 1 5/6 times as many laps around the lake as Harry did. How many laps around the lake did Sophia run?
11
11) Terry earns $30 per hour walking
dogs. Terry pays $150 each month to a
grooming service for the dogs. Which
equation represents Terry's profit, y, for
walking x dogs?
a) y = 30 + 150x
b) y = 30x + 150
c) y = 30 - 150x
d) y = 30x - 150
So
here
rate of pay=30$ per hourIf hours be x
Question asked to plot a equation to calculate profit so all the expenses or loss should be deducted,here the constant loss is of 150 so 150 should be subtracted
The equation in slope intercept form
y=mx+by=30x-150Answer:
d) y = 30x - 150
Step-by-step explanation:
Let x = number of hours worked
Let y = profit earned
Profit is the amount left after expenses are deducted.
Given:
Terry earns $30 per hour walking dogs⇒ y = 30x
Given:
Terry pays $150 each month to a grooming serviceThis is Terry's expenses, so we must deduct this amount from the amount he earns walking the dogs to calculate the final profit:
⇒ y = 30x - 150
In a drawing, there are three circles, four stars, and three triangles. What is the ratio of stars to the total number of shapes? Simplify your answer.
Answer:
4:10
simplify = 2:5
pleaseeee I beg you helpppppp thank youuuuuu :)))
Answer: 1) 4%/40% 2)4%/40% 3)5%/50% 4)4%/40%
Step-by-step explanation:
i think those are the answers
Which equation represents the slope-intercept form of the line below!
5-
y-intercept = (0.-5)
slope = 1
O A. y=5x- *
O B. y=+*+5
O C. y=-x-5
O D. y = 5x + 1
pls answer this bc i need help with this
Answer:
A third degree or cubic polynomial with three terms. The constant term is -1/7, the leading term is -10x³ and the leading coefficient is -10
2x- 1 = 7
A= 2
B = 3
C=4
D=5
Answer:
4
Step-by-step explanation:
All you need to do is plug in each value for x & then solve the equation to see if it equals 7. When a number, like 2, is next to an x you multiply the two of them. So when you substitute a number for x, you multiply it by the 2.
2(3)-1= 5
2(4)-1= 7
2(5)-1=9
Sharon is jumping from an 18-foot diving board with an initial upward velocity of 4 ft/s. when sharon jumps, megan throws a beach ball up to sharon with an initial upward velocity of 16 ft/s from a height 5 feet off the ground. to the nearest hundredth of a second, how long after she jumps does the ball reach sharon? 0.65 seconds 0.92 seconds 1.08 seconds 1.15 seconds
It will take 1.08 seconds for the ball to reach Sharon after she jumps if the upward velocity of the ball is 16 ft/s from a height of 5 feet option third is correct.
What is the equation of motion?It is defined as the equation by which we can find the motion of a physical particle with respect to time. It is the representation of physical entity movement in a mathematical function.
We have:
The height of the Sharon from the diving board = 18 feet
The initial upward velocity of the Sharon = 4 ft/s
The height of the Megan from the ground = 5 feet
The initial upward velocity of the beach ball = 16 ft/s
We know the equation of motion is given by:
[tex]\rm h(t) = x + ut+\frac{1}{2} gt^2[/tex]
Put x = 18 feet and u = 4 ft/s in the above equation, we get:
[tex]\rm h(t) = 18 + 4t+\frac{1}{2} \times9.8t^2[/tex] ....(1) [g = 9.8 m/s²]
Put x = 5 feet and u = 16 ft/s in the equation of motion, we get:
[tex]\rm h(t) = 5 + 16t+\frac{1}{2} \times9.8t^2[/tex] ....(2)
Equate the equation (1) and equation (2), we get
[tex]\rm 18 + 4t+\frac{1}{2} \times9.8t^2= 5 + 16t+\frac{1}{2} \times9.8t^2\\[/tex]
18 + 4t = 5 + 16t
12t = 13
t = 1.08 seconds
Thus, it will take 1.08 seconds for the ball to reach Sharon after she jumps if the upward velocity of the ball is 16 ft/s from a height of 5 feet.
Learn more about the equation of the motion here:
https://brainly.com/question/13514745
Please help!! Will mark brainlyest.
The bottom figure, answer A
D has infinite lines of symmetry
B can be split from top left to bottom right, as well as from the top right corner to the bottom left corner
C can be split from left to right and top to bottom
A can only be split from left to right, as the sides aren’t equal to each other
Help will name Brainliest !
Answer:
2√5.
Step-by-step explanation:
Using the Pythagoras theorem
x^2 = (√10)^2 + (√10)^2
x^2 = 10 + 10
x^2 = 20
x = √20
= √4*√5
= 2√5
The triangles below are similar. Find x.
Answer:
1
Step-by-step explanation:
in this constellation the upper left vertex corresponds to the bottom right vertex. and the upper right vertex to the bottom left vertex.
so, the side x corresponds to the side x+2.
and, of course, the top side corresponds to the bottom side.
going from the small to the large triangle the scaling factor is 6/2 = 3/1 = 3.
therefore
3 × x = x + 2
3x = x + 2
2x = 2
x = 1
What is the volume of a sphere with a diameter of 7.9 ft
Answer:
V ≈ 258 ft³
Step-by-step explanation:
I given the diameter d= 7.9 ft so the radius is r = d/2 = 7.9/2 ft
Volume of a sphere is
V = (4/3) π·r³ = (4/3) · π · (7.9/2)³ = 258.1546167 ft³
Me pueden ayudar con el procedimiento?
24x+7=13
Answer: x = 1/4
Step-by-step explanation:
Lo primero que harías es restar 7 de ambos lados de la ecuación debido a tu propiedad de igualdad, que te permite hacer esto.
24x+7=13
-7 -7
24x=6
Ahora lo que harás es dividir ambos lados entre 24 para que puedas aislar x.
24x=6
/24 /24
x=6/24
Finalmente, puedes simplificar la fracción dividiendo el numerador y el denominador por 6.
x=6/6 / 24/6
x=1/4
Which equation represents a circle with a center at (–4, 9) and a diameter of 10 units? (x – 9)2 (y 4)2 = 25 (x 4)2 (y – 9)2 = 25 (x – 9)2 (y 4)2 = 100 (x 4)2 (y – 9)2 = 100
The circle can be illustrated by its equation, and the equation that represents the circle is (x + 4)² + (y - 9)² = 5²
How to determine the circle equation?The center of the circle is given as:
Center, (a,b) = (-4,9)
The diameter is given as:
d = 10
Calculate the radius (r)
r = 10/2 = 5
The circle equation is then calculated using:
(x - a)² + (y - b)² = r²
So, we have:
(x + 4)² + (y - 9)² = 5²
Hence, the equation that represents the circle is (x + 4)² + (y - 9)² = 5²
Read more about circle equations at:
https://brainly.com/question/1559324
Answer:
B on edge
Step-by-step explanation:
(x + 4)^2 + (y – 9)^2 = 25
help me please???????
Answer:
60.9 mi
Step-by-step explanation:
Circumference of circle:
diameter = 19.4 mi
Circumference of circle = πd
= 3.14 * 19.4
= 60.9 mi
The pyramid has a base that is a right triangle with side lengths 3 feet , 4 feef , 5 feet. It’s height is 6 feet. What
Answer:
12 ft ^3
Step-by-step explanation:
I assume you are looking ofr the volume of this pyramid
V = 1/3 base area * height
base area = area of 3-4-5 triangle = 1/2 * 3 * 4 = 6 ft^2
so Volume is :
1/3 * 6 * 6 = 12 ft^3
Calculate the circumference and area of this circle (6cm)
AREA Fomula: A = πr²
where:
R stands for radius.π stands for pi (value is 3.14)Find the Area of a 6 cm radius.
Solved:
A = πr²A = π (6 cm)²A = 3.14 (36 cm)²A = 113.04 cm²CIRCUMFERENCE Formula: 2πr
where:
C stands for circumferenceπ stands for pi (value is 3.14)R stands for radius.Find the Circumference of a 6 cm radius
Solved:
C = 2πr C = 2 (3.14)(6 cm) C = 2 (18.84 cm) C = 37.68cmTanelle is cutting out a paper banner as shown in the image. The entire piece of paper is 8 feet long and she is cutting a circle with a 1 foot diameter out of each of the 4 sections. (The circles are hemispheres, AKA half circles)
About how much paper will she need? Use 3.14 for pi and show your work.
Answer: 4.71
Step-by-step explanation:
Determine if the events are independent or dependent.
Answer: 1. Not dependent 2.2.Not dependent 3. Not dependent 4. Not dependent 5. Choosing marble without replacement is dependent
Step-by-step explanation: if you concert the decimals to fractions in each question, they are not related
What is the quotient of the following division problem? x 1 startlongdivisionsymbol x squared 3 x 2 endlongdivisionsymbol. minus x squared x to get a remainder of 0 ) 2 x 2. minus 2 x 2 to get a remainder of 0 and a quotient of x 2. x 2 x 1 x2 3x 2 0
The quotient of the provided division in which binomial is divided by a quadratic equation is x+2.
What is the quotient?Quotient is the resultant number which is obtained by dividing a number with another. Let a number a is divided by number b. Then the quotient of these two number will be,
[tex]q=\dfrac{a}{b}[/tex]
Here, (a, b) are the real numbers.
The given division expression is,
[tex]\dfrac{x^2+3x+2}{x+1}[/tex]
Let the quotient of this division problem is f(x). Thus,
[tex]f(x)=\dfrac{x^2+3x+2}{x+1}[/tex]
Factor the numerator expression as,
[tex]f(x)=\dfrac{x^2+2x+x+2}{x+1}\\f(x)=\dfrac{x(x+2)+1(x+2)}{x+1}\\f(x)=\dfrac{(x+2)(x+1)}{x+1}\\f(x)={x+2}[/tex]
Thus, the quotient of the provided division in which binomial is divided by a quadratic equation is x+2.
Learn more about the quotient here;
https://brainly.com/question/673545
Answer:
its A. on edge 2023
Step-by-step explanation: