The sum of the first 75 terms of the sequence is -5.068*10^34
Given the following geometric sequence
[tex]a_1 = \frac{-1}{3} \\a_i = a_{i-1}*(-3)[/tex]
The sum of the nth term of the GP is expressed as;
[tex]S_n = \frac{a(1-r^n)}{1-r}[/tex]
a = -1/3
n = 75
r = a₂/a₁
a₂ = -3a₁
a₂ = -3(-1/3)
a2 = 1
r = 1/(-1/3)
r = -3
Substitute the given values in the formula;
[tex]S_n = \frac{-1/3(1-3^{75})}{1-(-3)}\\S_{75} = \frac{-1/3(3^{75}-1)}{1+3} \\S_{75} = \frac{-1/3(6.082 \times 10^{35}-1)}{4}\\S_{75} = \frac{-1/3(6.082 \times 10^{35})}{4}\\S_{75} = -0.5068 \times 10^{35}\\S_{75} = -5.068 \times 10^{34}\\[/tex]
Hence the sum of the first 75 terms is -5.068*10^34
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Give the most specific name for each quadrilateral.
Answer:
a. Parallelogram
b. Rectangle
C. Rhombus
D. Square
E. Kite
F. Parallelogram
Let me know if this helps!
Can someone answer this
Plss helppp
26
Mandy spent $287 on 7 pairs of shoes. She purchased some pairs of boots that cost $65 per pair and some pairs of workout shoes that cost
S23 per pair
Use a system of equations to help you identify how many pairs of boots (b) and workout shoes (w) Mandy bought
Enter the number of pairs of boots and workout shoes Mandy bought
Answer: Boots = 3
workout shoes = 4
Step-by-step explanation:
boots cost $65 so 65 x 3 = 195
and workout shoes cost $23 so 23 + 4 = 92 then 195 + 92 = 287
Which equation is true?
f(x) - 5 = g(x)
f(x) = g(x) - 5
Of(x) = g(x - 5)
Of(x - 5) = g(x)
PLZZZ HELPPP
Answer:
f(x)-5 = g(x)
Step-by-step explanation:
We translate the function g(x) down 5 units from the function f(x)
g(x) = f(x) -5
Rewriting
f(x)-5 = g(x)
Answer:
Option A
Step-by-step explanation:
f(x)-5=g(x)f(x) and g(x) are exponential functions
We can see that f(x) is shifted 5 units down
So change in y
hence 5 is to be subtracted
Please solve for the maximum value
f(x) = -2x^2 - 12x - 16
Answer:
-2(x+4)(x+2)
Step-by-step explanation:
thats the answerer
You roll a number cube two times in a row. What is the probability of rolling a 3 the first time and an even number the second time?
The probability of rolling a 3 the first time is 1/6.
The probability of rolling an even number is 1/2.
Jelena has a piece of fabric in the shape of a parallelogram the height is 10 feet and its base is 16 feet because the fabric into four equal parallelograms by current base and the height in half what is the
Complete question :
Jelena has a piece of fabric in the shape of a parallelogram the height is 10 feet and its base is 16 feet because the fabric into four equal parallelograms by current base and the height in half what is the area of each new parallelogram?
Answer:
40 ft²
Step-by-step explanation:
Given that:
Height = 10 feets
Base = 16 feets
Area of parallelogram = height * base
Area of parallelogram = 10 * 16 = 160 ft²
Area of each new parallelogram :
Area of parallelogram / number of divisions
= 160ft² / 4
= 40 ft²
Help please and thank you.
Twice the difference of a number and 2 is 7.
Answer:
9
Step-by-step explanation:
-Twice means muliply by 2
-The difference of a number and 7 means subtract a number/variable and 7.
-Is equal to 9 means =9
2(X - 7) = 9
An equation to model the number is: n - 7 x 2 = 2
To find the equation, break apart the question.
twice the difference of a number and 7 equals 2. - "Twice" means we are multiplying by 2, or x 2
twice the difference of a number and 7 equals 2. "The difference of a number and 7" means we are subtracting n - 7, and this is being multiplied by 2 so we have n - 7 x 2 so far.
twice the difference of a number and 7 equals 2. "Equals two" means the equation is equal to 2, or = 2, so our equation is n - 7 x 2 = 2.
Can you help me please! Hurry its due soon
Answer:
She earns $0.5 per hour
Step-by-step explanation:
mark brainliest
_____ earns $23.4 per hour, $.1 less than ___
Please help I will mark you as the brainiest, I sincerely am grateful if you answer~
Answer:
The amount of money they will spend at the restaurant is $35.16
Step-by-step explanation:
From the information given in the question, we have;
The amount Jessica, Genesis, and Violet received as bill at the restaurant, X = $29.30
The amount they wished to leave as tip, T = 20% (of the bill)
Therefore, the amount of money they will spend at the restaurant, 'A', is given as follows;
A = X + T
T = 20% of X = 20/100 × X = 0.2·X
∴ A = X + 0.2·X = 1.2·X
X = $29.30
A = 1.2·X = 1.2 × $29.30 = $35.16
The amount of money they will spend at the restaurant, A = $35.16
I need helppppppppp this is due ina hour
Answer:
Step-by-step explanation:
3. Area = pie r2
A = (22/7) (4)2
= 50.27
4. Circumference = pie d
C = (22/7) (13)
= 40.84
Riley let his friend borrow $12,750. He wants to be paid back in 4.75 years and is going to charge his friend 5.5% interest rate yearly.
Answer:
$16442.18
Step-by-step explanation:
12,750 x 1.055^4.75 = 16442.18
Hope this helps
Can someone please help me? thank you.
Answer:
Step-by-step explanation:
c(f) = [tex]\frac{5}{9}(f-32)[/tex]
[tex]-21 = \frac{5}{9}(f-32)[/tex]
Multiply both sides by 9
-21*9 = 5(f - 32)
-189 = 5*f - 5*32
-189 = 5f - 160
Add 160 to both sides
-189 + 160 = 5f
-29 = 5f
Divide both sides by 5
-29/5 = f
f = -5.8
f = -6 °C
How many ways can you write one whole as a fraction
Answer:
infinite
Step-by-step explanation:
you could say 1/1 or 4/4 or 146798245/146798245
any number over itself is a whole
Does that answer it? I feel like I'm missing something
Answer:
Any
Step-by-step explanation:
You can write one whole by making the numerator and denominator the same number. Examples: 2/2 3/3 4/4 5/5 6/6 7/7 8/8 9/9 10/10 100/100 20/20
Select all the correct measurement conversions.
A. 8 pints = 16 fluid ounces
B. 5 feet = 60 inches
C. 2 tons = 4,000 pounds
D. 5 meters = 5,000 centimeters
E. 2 days = 2,880 minutes
Find an equation of the line passing through the pair of points (4,5) and (6,9) . Write the equation in the form Ax+By=C .
Answer:
-2x + y = -3
Step-by-step explanation:
Find the slope:
9 - 5 / 6 - 4 = 4/2 = 2
Put it in point-slope form:
y - 5 = 2(x - 4)
rearrange:
y - 5 = 2x - 8
y - 2x = -3
-2x + y = -3
trapezoid DEFG is shown on this coordinate plane
Answer:
Hello, you forgot to attach an image. Please repost with a new image so I can respond.
A rectangle is a parallelogram. What is true of the diagonals of a rectangle
that is not true of the diagonals of a parallelogram, in general?
Answer:diagonals of rectangle are equal in length while diagonals of a parallelogram can be different lengths
Step-by-step explanation:
What is true of a rectangle that is not true of a parallelogram is that; the diagonals of a rectangle are equal but the diagonals of a parallelogram are not equal.
We are dealing with rectangles and parallelogram here.
Now, both rectangle and parallelogram have 4 sides respectively with 2 of the sides being equal.
Now, for a rectangle, the diagonals are always equal because all the internal angles are equal.
However, for a parallelogram, all the internal angles are not equal and as such the diagonals are also not equal.
In conclusion, what is true of a rectangle that is not true of a parallelogram is that the diagonals of a rectangle are equal but the diagonals of a parallelogram are not equal.
Read more about diagonals of Quadrilaterals at; https://brainly.com/question/25806235
what is -9 = -6r simplified
Answer:
Exact Form:
r = 3/2
Decimal Form:
r = 1.5
Mixed Number Form:
r =1 1/2
Step-by-step explanation:
PLEASE HELP DUE SOONNNNN SIMPLE ADVANCED MIDDLE SCHOOL MATH AKA FACTORING
Answer:
28. x(x+2)(x+5)
29. 2(2x+1)(x-2)
30. y(a+5)^2
Step-by-step explanation:
30. y(a+5)(a+5)
I'm so sorry be can you guys help me out here?
what is the value of 6n - 2 when n=3?
a.16
b.12
c. 6
d.7
Answer:
Step-by-step explanation:
value of 6n-2 when n=3 is 6(3)-2 = 18-2 = 16
Find the volume of the cone below. Use 3.14 for A. Round your answer to the nearest tenth.
3
r = 1.5
Answer:
D) 7.1 units³
Step-by-step explanation:
V = (3.14)(1.5)²(3/3)
= (3.14)2.25 = 7.1
Does anyone have “Geometry and Data Analysis” on edge? I really need help on the test if you are good at geometry..
POSSIBLE POINTS: 2
A tank that is 40% full contains 650 gallons of water. On a side sheet of paper, use a double number line to find the maximum capacity of the water tank.
What did you get?
gallons
Answer: max capacity is 1625 gallons.
Diagram is shown below.
=========================================================
Explanation:
We'll draw two horizontal number lines to help make a comparison or connection between percentages and tank capacity.
For the top number line, make 5 sections with the labels: 0%, 20%, 40%, 60%, 100%. The reason I'm picking 5 is because 40% = 40/100 = 2/5. So having 40% capacity means we're 2/5 full. That denominator 5 tells us how to subdivide each number line.
The bottom number line will also have 5 sections. We only know one label for this bottom portion right now. That label is 650. Place this directly under the "40%". This visually is one way to represent that 650 gallons is 40% filled. See the diagram below.
Cut the 650 in half to get 325. This corresponds to 40% cut in half to get 20%. Therefore, 325 will go under the 20%. Being 20% full means we have 325 gallons of water.
To figure out the 60% portion, we will multiply 325 by 3. This is because 3*20% = 60%, so 3*325 = 975. We'll write "975 gallons" under the "60%"
Then we have 1300 gallons under the 80% since 4*325 = 1300. Note how 4*20% = 80%, so that's where the '4' multiplier comes from.
Finally, we multiply 325 by 5 to get 1625 and that represents the full tank's capacity. Technically we could have just jumped to this directly without having to find the 60% or 80% capacity values, but it's good practice I think.
Again the diagram is shown below. The answer we're after is at the very bottom right corner. It's under the 100% to indicate the tank is completely full, or has reached max capacity.
-----------------------
Here's a way to find the answer without a double number line. This method involves setting up a proportion.
(40% full)/(650 gallons) = (100% full)/(x gallons)
40/650 = 100/x
40x = 650*100
40x = 65000
x = 65000/40
x = 1625
We confirm that the tank's max capacity is 1625 gallons.
Find the slope of the line.
Answer:
Rise -5 and Run 2
Slope of -5/2
Consider the two functions which statement is true
Answer:
I think it's C
Step-by-step explanation:
Because the line is straight up and it on -2
Hope this helps if it's wrong i'm sorry but i hope it's right.:)
The campus bookstore at a local university is interested in finding out whether the textbook preference and the class level (freshman, sophomore, junior, senior) of the student are associated. A random sample of 100 students is obtained, and each student in the sample is asked which textbook he or she prefers: new books, used books, or digital books. The students are also asked whether their class level is freshman, sophomore, junior, or senior.Which of the following is the appropriate test for the investigation?A. A one-sample tt-test for a population meanB. A two-sample tt-test for a difference between meansC. A chi-square goodness-of-fit testD. A chi-square test of homogeneityE. A chi-square test of independence
Answer:
The appropriate test for the investigation is;
E. A chi-square test of independence
Step-by-step explanation:
The chi-square test for independence is for the analysis of two categories from within a population to evaluate the existence of association among the different categories within the two variables
The chi-square test for independence is used for the analysis of contingency (frequency) table
Therefore, the appropriate test for the investigation in finding out (1) the textbook preference and (2) the class level of the associated student is the chi-square test of independence
Tickets for the CTA train cost $0.75 for students and $3.25 for
chaperones. If a school trip has a total of 50 people, how many students
and chaperones are on the trip? *
help i need this asap
HINT: Try graphing your equations or multiplying the cost equation by 4.
1.08 CREATE TRIGONOMETRIC MODELS
A cosine function has a period of 4, a maximum value of 20, and a minimum value of 0. The function is not a reflection of its parent function over the x-axis.
Which function could be the function described?
Answer:
○ [tex]\displaystyle f(x) = 10cos\:\frac{\pi}{2}x + 10[/tex]
Step-by-step explanation:
[tex]\displaystyle \boxed{f(x) = 10sin\:(\frac{\pi}{2}x + \frac{\pi}{2}) + 10} \\ \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 10 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-1} \hookrightarrow \frac{-\frac{\pi}{2}}{\frac{\pi}{2}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{4} \hookrightarrow \frac{2}{\frac{\pi}{2}}\pi \\ Amplitude \hookrightarrow 10[/tex]
OR
[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 10 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{4} \hookrightarrow \frac{2}{\frac{\pi}{2}}\pi \\ Amplitude \hookrightarrow 10[/tex]
The cosine graph in the photograph on the right is the OPPOCITE of the cosine graph in the photograph on the left, and the reason for this is because of the negative inserted in front of the amplitude value. Whenever you insert a negative in front of the amplitude value of any trigonometric equation, the whole graph reflects over the midline. Keep this in mind moving forward. Now, with all that being said, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
**Moreover, both graphs have the same maximum and minimum value, but we are looking for the equation that will not reflect over the midline of [tex]\displaystyle y = 10,[/tex]which means we do NOT want a negative in front of the amplitude value, therefore we have this equation:
[tex]\displaystyle f(x) = 10cos\:\frac{\pi}{2}x + 10[/tex]
If you are having trouble figuring out which graph is which, just remember that the parent function of [tex]\displaystyle y = cos\:x[/tex]never touches the origin unless it shifts one unit south or gets reflected from somewhere. In this case, the photograph on the left touches the origin because of a reflection [negative symbol], therefore the photograph on the right matches the equation selected.
I am delighted to assist you at any time.
The correct function is,
⇒ y = 10 cos (π/2x) + 10
What is Function?A relation between a set of inputs having one output each is called a function.
Given that;
A cosine function has a period of 4.
Since, The period is 4.
Hence, The relationship between period and b (the coefficient of the independent variable of the cosine function) is, (period) =(2π/b).
Hence, We get;
⇒ 4b = 2π
⇒ b = 2π/4
⇒ b = π/2
So, Now our equation y = a cos (bx) + c becomes as;
⇒ y = 10 cos (π/2x) + 10
Thus, The horizontal center line of this cosine curve is y = 10. The maximum value of the curve is 20, which is 10 + 10, and the minimum value is 0, which is 10 - 10.
Learn more about the function visit:
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