The given sequence represents the sales of a product over time. The sum of the first 6 terms is 693.75, which is calculated by multiplying each term in the sequence by its respective exponent.
The sum of the first 6 terms of the geometric sequence is calculated as follows:
[tex]a_1 = 125 \left(\frac{1}{5}\right)^{1-1} = 125 \\[/tex]
[tex]a_2 = 125 \left(\frac{1}{5}\right)^{2-1} = 25 \\[/tex]
[tex]a_3 = 125 \left(\frac{1}{5}\right)^{3-1} = 5 \\a_4 = 125 \left(\frac{1}{5}\right)^{4-1} = 1 \\a_5 = 125 \left(\frac{1}{5}\right)^{5-1} = \frac{1}{5} \\a_6 = 125 \left(\frac{1}{5}\right)^{6-1} = \frac{1}{25} \\[/tex]
Total sum = 125 + 25 + 5 + 1 +[tex]\frac{1}{5} + \frac{1}{25}[/tex] = 693.75
The geometric sequence a_n=12[tex]5\left(\frac{1}{5}\right)^{n-1}[/tex]represents the sales of a product over time, where n is the number of years after its release. The sum of the first 6 terms is calculated by multiplying each term in the sequence by its respective exponent. This gives us the following 6 terms: a_1 = 125, a_2 = 25, a_3 = 5, a_4 = 1, a_5 = 1/5, and a_6 = 1/25. The sum of these 6 terms is 693.75.
Learn more about sequence here
https://brainly.com/question/21961097
#SPJ4
Bonami High School has 82 juniors at its school. There are 29 students enrolled in Spanish class and 31 enrolled in history. There are 15 students enrolled in both Spanish and history. If a junior is selected at random to say the morning announcement at the beginning of the school day, what is the probability that it will be a student enrolled in Spanish or history?
Answer:
73%
Step-by-step explanation:
Haan' hitory cla i taking a field trip to the tate capitol building. The capitol building i 50 mile from Haan' chool. The cla plan to top after 45 minute, or 0. 75 hour, to view a local monument. The bu driver plan to drive at an average peed of 40 mile per hour
The class has a 45-minute, or 0.75-hour, climb to the summit planned to observe a nearby monument. The bus driver intended to travel at a steady 40 mph. Accordingly, the average speed is 0.888.
How long does it take to drive 60 miles at 40 miles per hour?The time required to travel 20 miles at 40 mph is 30 minutes, and the time required to go 40 miles is 60 minutes. The journey of 60 miles will therefore take 90 minutes. In most cases, an hour's worth of time, this will tell you the average speed.
As a result, Ben's average speed was 50 miles per hour when he covered 150 miles in 3 hours. 40m in an hour. 12 hour to cover 20 miles. In fifteen minutes, ten miles. It is determined by dividing something's total travel distance by its total journey time. Take the earlier automobile, for instance. The average speed of the vehicle would be 70 / 2 = 35 miles per hour if it covered 70 miles in two hours.
To learn more about average speed refer to :
brainly.com/question/553636
#SPJ4
Complete question is: Hassan's history class is taking a field trip to the state capitol building. The capitol building is 50 miles from Hassan's school. The class plans to stop after 45 minutes, or 0.75 hours, to view a local monument. The bus driver plans to drive at an average speed of 40 miles per hour. Which equation can you use to find how many hours, x, the second part of the trip will take?
40 % ply tennis 24% plays baseball 58% plays neither. If you pick a student at random what will be the probably plays both sports.
Answer:
The probability is 0.22
Step-by-step explanation:
We know that:
40% of the students play tennis
24% of the students play baseball
58% of the students play neither.
If we add these numbers, we get:
40% + 24% + 58% = 122%
Here we should get exactly 100%, but we get more because we are counting some of the students twice, and that happens because some of the students play both sports, so these students are counted in both percentages.
And we can conclude that exactly 122% - 100% = 22% of the students play both sports:
Now, the probability that a randomly picked student plays both sports, is equal to the quotient between the percentage of students that play both sports and the 100%, this is:
p = 22%/100% = 0.22
The probability is 0.22
all real number w that are less than 0 and greater than 19
Answer:
all negative numbers
Step-by-step explanation:
Find the value of p and q for which the system of equations represent coincident lines:
2x + 3y = 7
(p + q + 1)x + (p + 2q + 2)y = 4(p + q) +1
Answer: The value of p and q for which the system of equations represent coincident lines is p = 2 and q = 1.
Step-by-step explanation: To represent coincident lines, the two lines must be proportional. Therefore, the slope of the second line must be equal to the slope of the first line.
The slope of the first line is 3/2. The slope of the second line is p + 2q + 2/p + q + 1. Therefore, we set these two equal:
3/2 = p + 2q + 2/p + q + 1.
Cross multiplying, we get:
3(p + q + 1) = 2(p + 2q + 2).
Simplifying, we get:
3p + 3q + 3 = 2p + 4q + 4.
Combining like terms, we get:
p - q = 1.
Therefore, the value of p and q for which the system of equations represents coincident lines is p = 2 and q = 1.
Find the volume of the cylinder as pictured below with a = 5 cm and b = 10
cm. Use 3.14 for rand round your answer to the nearest hundredth. Do not
include units in your answer.
b
a
Answer:
[tex]\huge\boxed{\mathfrak{\underline{Answer...}}}[/tex]
[tex]\small\mathfrak\red{volume \: of \: cylinder =\pi \: r {}^{2} h } \\ \\ \small\mathfrak\red{ r =5cm \: | height = 10cm } \\ \\ \small\mathfrak\red{volume \: of \: cylinder =3.14 \times 5 {}^{2} \times 10 } \\ \\ \small\mathfrak\red{volume \: of \: cylinder = 785 \: cm.cube} \\ \\ \small\mathfrak\green{hope \: it \: helps .... }[/tex]
Answer:
Step-by-step explanation:
Whats fifty-six thousandths in decimal form
Answer:
0.056
Step-by-step explanation:
56/1000
56 divided by 1000 = 0.056
Answer:
0.056.
Step-by-step explanation:
Find the orthocenter& circumcenter of a triangle when their vertices are A(1, 2), B(2, 6), C(3,-4).
=> Please don't spam or answer Irrelevantly.
Note:
Ortho centre :a point of intersection of altitudes of a triangle meets the opposite angle.
Given:
For Orthocentre:.
A(1, 2), B(2, 6), C(3,-4). are vertices of a triangle:
Slope of AB[m1]=[tex] \frac{6-2}{2-1} [/tex]=4
Since it is perpendicular to CX.
slope of CX=m2
we have for slope of perpendicular
m1m2=-1
m2=-¼
It passes through the point C(3,-4)
equation of line CX becomes;
(y-y1)=m(x-x1)
y+4=-¼(x-3)
4y+16=-x+3
x+4y+16-3=0
x+4y+13=0........[1]
again:
Slope of AC[m1]=[tex] \frac{-4-2}{3-1} [/tex]=-3
Since it is perpendicular to BY
slope of BY=m2
we have for slope of perpendicular
m1m2=-1
m2=⅓
It passes through the point B(2,6)
equation of line BY becomes;
(y-y1)=m(x-x1)
y-6=⅓(x-2)
3y-18=x-2
x-3y+18-2=0
x-3y+16=0.........[2]
Subtracting equation 1&2.
x+4y+13=0
x-3y+16=0
-__________
7y-3=0
y=[tex] \frac{3}{7} [/tex]
again
Substituting value of y in equation 1.
x+4*[tex] \frac{3}{7} [/tex]+13=0
x=-13-[tex] \frac{12}{7} [/tex]
x=[tex] \frac{-103}{7} [/tex]=-14[tex] \frac{5}{7} [/tex]
So
orthocenter is (-14[tex] \frac{5}{7} [/tex],[tex] \frac{3}{7}[/tex])
And for circumcenter.Circumcentre: a point of intersection of perpendicular bisector of the triangle.
Now
X,Y and Z are the midpoint of AB,AC and BC respectively.
X(a,b)=([tex] \frac{2+1}{2} [/tex],[tex] \frac{2+6}{2} [/tex])=
([tex] \frac{3}{2} [/tex],4)
Slope of AB=4
Slope of OX=-¼
Equation of line OX passes through ([tex] \frac{3}{2} [/tex],4)is
y-4=-¼(x-[tex] \frac{3}{2} [/tex])
4y-16=-x+[tex] \frac{3}{2} [/tex]
8y-16*2=-2x+3
2x+8y=3+32
2x+8y=35
x+4y=[tex] \frac{35}{2} [/tex]........[1]
again
Y(c,d)=([tex] \frac{3+1}{2} [/tex],[tex] \frac{-4+2}{2} [/tex]=(2,-1)
Slope of AC:-3
Slope of OY=⅓
Equation of line OY passes through (2,-1) is
y+1=⅓(x-2)
3y+3=x-2
x-3y=3+2
x-3y=5......[2]
Multiplying equation 2 by 3 and
Subtracting equation 1&2.
x+4y=35/2
x-3y=5
-_______
7y=[tex] \frac{25}{2} [/tex]
y=[tex] \frac{25}{14} [/tex]
Substituting value of y in equation 2.
x-3*[tex] \frac{25}{14} [/tex]=5
x=5+[tex] \frac{75}{14} [/tex]
x=[tex] \frac{145}{14} [/tex]
x=10[tex] \frac{5}{14} [/tex]
circumcenter of a triangle: (10[tex] \frac{5}{14} [/tex],1[tex] \frac{11}{14} [/tex])
Find the output, y, when the input, z, is -4.
y=
-8-6 -4
8
6
a f
Y
4-
2-
do
-2-
-4-
-6+
4
6/ 8
Answer:
y = 1
Step-by-step explanation:
locate x = - 4 on the x- axis, go vertically up to meet the graph at (- 4, 1 ), so
when input x = - 4 the output is y = 1
The ratio of the number of report cards Ms. Wickham folded to the number that Ms. Cho folded was 2:3. At the end of the day, Ms. Leiva and Mr. Gamory folded 300 report cards. Who folded more report cards and by how many
Ms. Wickham folded 200 report cards and Ms. Cho folded 300 report cards, giving Ms. Cho an average of 100 report cards.
Ms. Wickham and Ms. Cho together folded 500 report cards.
Ms. Wickham folded 200 report cards
(200/500 = 2/5)
Ms. Cho folded 300 report cards
(300/500 = 3/5)
Mr. Leiva and Mr. Gamory folded 300 report cards.
Ms. Cho folded more report cards than Ms. Wickham, by
100 (300 - 200 = 100).
Ms. Wickham and Ms. Cho together folded 500 report cards, with the ratio of Ms. Wickham's report cards to Ms. Cho's being 2:3. Ms. Wickham folded 200 report cards, while Ms. Cho folded 300. At the end of the day, Mr. Leiva and Mr. Gamory folded an average 300 report cards. This meant that Ms. Cho folded more report cards than Ms. Wickham, by 100. Therefore, Ms. Cho folded 400 report cards in total, while Ms. Wickham only folded 300.
Learn more about average here
https://brainly.com/question/24057012
#SPJ4
help
x^2 + 4x - 3 = 0
Answer:
x = − 2 + √ 7 , − 2 − √ 7
Step-by-step explanation:
Answer:
x = +/- 2 +/- √7
Step-by-step explanation:
What is the best approximation for the area of this figure?
21+14. 5π units²
21+7. 25π units²
10. 5+7. 25π units²
10. 5+14. 5π units²
Coordinate plane with axes labeled x and y. A closed figure is formed by two segments and a semicircle. A segment extends from negative 5 comma negative 2 to negative 5 comma 1. Another segment extends from negative 5 comma 1 to 2 comma 1. A semicircle extends from 2 comma 1 to negative 5 comma negative 2. What is the area of this polygon?
28. 5 units²
34. 5 units²
37. 5 units²
40. 5 units²
6 sided polygon on a coordinate plane with vertices at (negative 6, negative 2), (negative 5, 1), (negative 1, 4), (1, 1), (5, 3), and (1, negative 2)
1) The best approximation for the area of this figure is 21+14. 5π units².
2) The total area of the closed figure is 10.5 + 19.63 = 30.13 square units.
3) This is a hexagon with vertices at the specified coordinates on a coordinate plane.
FIGURE AND POLYGON1) The best approximation for the area of this figure is 21 + 14.5π units². The area of a semicircle with a radius of 7 is 14.5π units², and the two segments form a rectangle with an area of 21 units². Adding these two values together gives 21 + 14.5π units².
2) This closed figure can be divided into two parts: a triangle and a quarter of a circle. The area of the triangle can be found using the formula for the area of a triangle (base times height divided by 2). The base of the triangle is the length of the segment from negative 5 comma negative 2 to negative 5 comma 1, which is 3 units. The height of the triangle is the length of the segment from negative 5 comma negative 2 to 2 comma 1, which is 7 units. So the area of the triangle is (3*7)/2 = 10.5 square units.
The area of the quarter of a circle can be found using the formula for the area of a circle (pi times the radius squared). The radius of the semicircle is the length of the segment from 2 comma 1 to negative 5 comma negative 2, which is 5 units. So the area of the quarter of the circle is (pi*5²)/4 = 19.63 square units.
So the total area of the closed figure is 10.5 + 19.63 = 30.13 square units.
3) A hexagon is a polygon with six sides and six angles. In this case, the hexagon is placed on a coordinate plane, with each of its vertices (or corners) located at specific x and y coordinates.
The coordinates provided are: (negative 6, negative 2), (negative 5, 1), (negative 1, 4), (1, 1), (5, 3), and (1, negative 2). These coordinates correspond to six points on the plane, and the hexagon is formed by connecting these points in the specified order.
Learn more about polygon here:
https://brainly.com/question/24464711
#SPJ4
HELPPPPppPPppPpP MeEEEeEEEE PLEASEEEEeEeeEEe
helppppp plss i dont understand
I need help asap deadline 1600
Lara says that she can use this picture to show that two pairs of congruent angles and one pair of corresponding congruent sides is enough information to prove that two triangles are congruent. Is Lara correct
Yes, the information provided regarding the two pairs of congruent angles so one pair with corresponding congruent sides is sufficient to demonstrate the congruence of two triangles.
Define the term congruent triangles?Congruent refers to things that are exactly the same size and shape.
When a triangle has precisely the same sides and precisely the same three angles, it is said to be congruent.These triangles are congruent if two pairs of comparable angles and the pairs of included sides are also congruent. The triangles are congruent if two pairs with corresponding angles and just a pair of non-included sides also are congruent.For the stated question-
The following are the steps:
Due to a sequence of stiff motions, the triangles will line up precisely.Additionally, Lara is right only if the matching congruent side is situated halfway between the two angles.Angle Side Angle Congruceny, or "ASA" triangle congruceny, would be the case here.Thus, the information provided regarding the two pairs of congruent angles so one pair with corresponding congruent sides is sufficient to demonstrate the congruence of two triangles.
To know more about the congruent triangles, here
https://brainly.com/question/3999145
#SPJ4
The vertices of a trangular plot of land are A(1,5), B(7,5), and C(8,0)
The area of the triangular plot of land from the vertices is 20 square units
How to determine the area of the triangular plot?From the question, we have the following parameters that can be used in our computation:
A(1,5), B(7,5), and C(8,0)
Represent the vertices properly
So, we have the following representation
A = (1,5)
B = (7,5)
C = (8,0)
The area of the triangle is calculated from the vertices using the following equation
Area = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)|
Substitute the known values in the above equation, so, we have the following representation
Area = 0.5 * |1 * (5 - 0) + 7 * (5 + 0) + 8 * (5 - 5)|
Evaluate the sum of products
Area = 0.5 * |40|
Remove the absolute bracket
Area = 0.5 * 40
Evaluate
Area = 20
Hence, the area of ABC with vertices is 20 square units
Read more about areas at:
brainly.com/question/22972014
#SPJ1
Complete question
The vertices of a trangular plot of land are A(1,5), B(7,5), and C(8,0)
Calculate the area.
What information is missing in order to prove the following triangles are
congruent by SAS?*
Answer:
Two triangles are congruent if they meet one of the following criteria. : All three pairs of corresponding sides are equal. : Two pairs of corresponding sides and the corresponding angles between them are equal. ... and another pair of corresponding sides are equal in two right triangles.
Please help quickly this is for a big test.
ES=____ units.
Round your answer to the nearest tenth.
That would be [tex] \sqrt{113} [/tex]
Instructions: Find the missing length indicated.
PLEASE HELP, NO LINKS PLEASE
Answer:
PLEASE DONT DELETE
Step-by-step explanation:
I am sorry that I cant answer your problem. However, I am only answering so I can get answers to my own problems. Good luck on that problem!
Pls help me I am so sad for my l kid
Answer:
Do you have a ruler?
Step-by-step explanation:
The front row in a movie theatre has 23 seats. If you were asked to sit in the seat that occupied the median position, in which seat would you have to sit?
Answer:
12
Step-by-step explanation:
The median is the one in the middle. For an odd number of seats, average the first and last seat numbers.
(1 + 23) / 2 = 24 / 2 = 12. That means there will be 11 people on your left and 11 people on your right.
For an even number of seats, the same method doesn't work as well! If there are 14 seats, for example, (1 + 14) / 2 = 15 / 2 = 7.5, and if you sit in "seat" 7 and a half, it will be awkward!
Figure ABCD is a parallelogram if point C lies on the line y=-1 what is the x vale of point C
The value of x of point C is 4. The coordinate of C is (4,-1).
What is the coordinate of a point?
The coordinates represent the location of a point in the 2D coordinate plane with respect to the origin. A point's x-coordinate is its perpendicular distance from the y-axis as measured along the x-axis. A point's y-coordinate is the perpendicular distance from the x-axis measured along the y-axis.
The distance between points A and B is 4 units.
The opposite sides of a parallelogram are equal and parallel.
To make parallelogram, the point C lies on the left side of point D.
The distance between point C and D must be 4 unit.
The coordinates of C is (4,-1).
The x value of point C is 4.
To learn more about parallelogram, click on the below link:
https://brainly.com/question/14539570
#SPJ1
f(x)=x2+3 & g(x)=2x−7
1) (f−g)(x)=
2) (f⋅g)(x)=
3) (f°g)(5)=
4) (g°f)(x)=
Step-by-step explanation:
1)
f-g(x)x²+3-2x+7x²-2x+102)
f×g(x)(x²+3)(2x-7)2x³-7x²+6x-213)
fog(5)f(g(5))f(2×5-7)f(3)3²+39+3124)
gof(x)g(f(x))g(x²+3)(2x-7)²+32x²-2×2x×7+7²2x²-28x+49stay safe healthy and happy.
Solve for x.
please help w this problem, will give thanks !
Answer:
[tex]x = 1[/tex]
Step-by-step explanation:
[tex] \frac{141x - 1}{2} = 70[/tex]
[tex]141x - 1 = 140[/tex]
[tex]141x = 141[/tex]
[tex]x = 1[/tex]
A blueprint was using a scale of 3cm=4.5m. Find
the actual length if it is 5cm on the drawing.
A 1.5 m
B. 13.5 m
C. 1.5 m
D. 1.7 m
Answer:
7.5
Step-by-step explanation:
You didn't list the right answer choices. But I think 7.5 is the answer.
The CEO of a large company claims that 85% of customers are repeat customers. They define a repeat customer as someone who makes more than one purchase per month. A random sample of 200 customers shows that 162 are repeat customers. Do these data provide convincing evidence at the 5% significance level that less than 85% of customers of this company are repeat customers?
The P-value of this test is 0.0571. What conclusion should be made?
Because the P-value of 0.0571 < α = 0.05, we reject H0. We have convincing evidence that less than 85% of customers of this company are repeat customers.
Because the P-value of 0.0571 > α = 0.05, we fail to reject H0. We do not have convincing evidence that less than 85% of customers of this company are repeat customers.
Because the P-value of 0.0571 > α = 0.05, we fail to reject H0. We have convincing evidence that less than 85% of customers of this company are repeat customers.
Because the P-value of 0.0571 < α = 0.05, we reject H0. We do not have convincing evidence that less than 85% of customers of this company are repeat customers.
Answer:
b. Because the P-value of 0.0571 > α = 0.05, we fail to reject H0. We do not have convincing evidence that less than 85% of customers of this company are repeat customers.
Step-by-step explanation:
EDGE 2021
I hope this helps!
Answer: Because the P-value of 0.0571 > α = 0.05, we fail to reject H0. We do not have convincing evidence that less than 85% of customers of this company are repeat customers.
Step-by-step explanation: EDGE 2022
Expand.
This question is worth 50 points!
Answer:
the answer is (a) x² - 2hx + h²
Step-by-step explanation:
(x-h)² = (x-h)(x-h) = x(x-h)-h(x-h)
x² - hx -hx + h²
= x² - 2hx + h²
Answer:
A) x² - 2hx + h²-----------------------------
Use the identity:
(a - b)² = a² - 2ab + b²Substitute a = x, b = h to get:
(x - h)² = x² - 2hx + h²This is the option A.
Find the area. Round to the nearest tenth if necessary.
Answer:
575.4 sq inches
Step-by-step explanation:
you can divide this shape into:
13 x 13 square
trapezoid with bases of 13 and 30 with a height of 20
semi-circle with radius of 15
A(square) = 169
A(trapezoid) = 53
A(semi-circle) = 353.4
HELP ASAP! I WILL GIVE BRAINLEST! I HAVENT TURNED THIS IN AND ITS DUE TOMORROW.
Find the area of the polygon.
Answer:
332m²
Step-by-step explanation:
the formatting for finding the area of the triangle is base x height x 1/2
so we need to find 8.3 x 10
8.3 x 10 = 83
83/2 = 41.5
there are 8 triangles in this shape so...
41.5 x 8 = 332
so the area of the polygon is 332m²
hope this helped!
- cheesetoasty
Answer:
Hello! answer: 332
Step-by-step explanation:
What they did was give you the height and base of a triangle in the polygon so you can find the rest because each would be equivalent to that one triangle if that makes sense...
Triangle area = base × height ÷ by 2
8.3 × 10 = 83 83 ÷ 2 = 41.5 I will multiply by 8 cause there will be 8 of those same triangles if you dont understand I advise to look at the picture I put here and 41.5 × 8 = 332 therefore the area is 332 HOPE THAT HELPS!