The sum of the geometric series is 1328600
How to determine the sum?The given parameters are:
a1 = 5
r = 3
n = 12
The sum of the terms is:
[tex]S_n = \frac{a(1 - r^n)}{1 - r}[/tex]
This gives
[tex]S_n = \frac{5 * (1 - 3^{12})}{1 - 3}[/tex]
Evaluate the difference
[tex]S_n = \frac{5 * (1 - 531441)}{-2}[/tex]
This gives
[tex]S_n = \frac{5 * - 531440}{-2}[/tex]
Evaluate
[tex]S_n = 1328600[/tex]
Hence, the sum of the geometric series is 1328600
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PLEASE HELP! And thank you so much! I will mark you brainliest. I just need an urgent response! Thank you for your time
Answer:
A)
x + y = 80
y = x + 20
B) x = 30 minutes
C) No. If Pam dances for 60 minutes, and dances for 20 minutes longer than she does math, then she does math for 40 minutes. This means she spends 100 minutes total. 100 minutes is not 80 minutes, thus this is not possible.
Step-by-step explanation:
A)
x + y = 80
y = x + 20
B) x = 30 minutes
Replacing y with x + 20 in the first equation ->
x + x + 20 = 80
2x + 20 = 80
2x = 60
x = 30
C) No. If Pam dances for 60 minutes, and dances for 20 minutes longer than she does math, then she does math for 40 minutes. This means she spends 100 minutes total. 100 minutes is not 80 minutes, thus this is not possible.
find the value of x
a) 2:5=8:x
Step-by-step explanation:
solution:
given,
or, 2:5 = 8:x
or, 2/5 = 8/x [ changing into fraction form ]
or, 2x = 40 [ doing cross-multiplication ]
or, x = 20 [ dividing both sides with 2]
Please help me with this math quickly
The area of the shaded part is 52 sq. inches. The correct option is b. 52 sq. inches
Calculating AreaFrom the question, we are to determine the area of the shaded part
In the given diagram, the shaded part is a rectangle
Area of a rectangle = Length × Width
Length of the shaded part = 18 inches - 4 inches - 1 inch = 13 inches
Width of the shaded part = 6 inches - 2inches = 4 inches
Then,
Area of the shaded part = 13 inches × 4 inches
Area of the shaded part = 52 sq. inches
Hence, the area of the shaded part is 52 sq. inches. The correct option is b. 52 sq. inches
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Beginning with the graph of f(x) x2, what transformations are needed to form g(x) = 3(x + 2)2 - 1?
O The graph of g(x) is narrower than f(x) and S shifted to the right 2 units and down 1 unit.
O The
graph of g(x) is narrower than f(x) and is shifted to the left 2 units and down 1 unit.
• The graph of g(x) is wider than f(x) and is shifted to the left 2 units and down 1 unit.
• The graph of g(x) is wider than f(x) and is shifted to the right 2 units and down 1 unit.
Answer: The graph of g(x) is narrower than f(x) and is shifted to the left 2 units and down 1 unit.
Step-by-step explanation:
See attached image.
The function f(x) = x² is transformed and became g(x) = 3(x+2)² -1 has the graph of g(x) is wider than f(x) and is shifted to the left 2 units and down 1 unit.
What are graph transformations ?By applying suitable graph transformation we can shift, stretch, shrink, a given graph along x and y axis.
According to the given question given a graph f(x) = x² and g(x) is 3(x+2)² - 1.
Let us break transformations of g(x) one by one.
g(x) = 3f(x) which implies it's amplitude or vertical stretch is increased by a factor of 3.
Now, g(x) = 3(x+2)² implies the graph is shifted towards left by 2 units as x + 2 = 0 is x = -2.
Now, g(x) = 3(x+2)² - 1 implies that the whole graph has been shifted 1 units down along the y axis.
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n an element’s square on the periodic table, the number with the greatest numerical value represents the
Question 10 (2.5 points) ✓ Saved
Write the comparison below as a ratio in simplest form using a fraction, a colon (:), and the word to.
15 dollars to 27 dollars
Molly wants to buy a dress that costs $20. She has a coupon for 40% off, and there is a 10% sales tax. how much will she pay all together
1. after using the coupon what is the sale price of the dress Show Your Work
2.how much is th 10% tax on the sale price Explain how you found your answer
Answer:
$13.50
Step-by-step explanation:
If I am taking off 40%, that means that the dress now cost 60% of the original cost. .6 x 20 is 12.
You could also calculate the 20% off and subtract that from the original cost. .4 x 20 =8. Now 20 - 8 is also 12.
Now, we have to calculate the tax. 10% of 12 is .1 x 12 or $1.20. We add the tax to the 12 to get 13.50.
For Exercises 11–16, use inductive reasoning to draw the next shape in each
picture pattern.
The ways to illustrate the shapes are given.
How to depict the shape?11. In each new figure, one vertex is introduced, and each vertex is joined to each other vertex.
12. In each new figure, 2 rows and 1 column are introduced, and the shading at the corner moves 90 degrees clockwise.
13. In each new figure, one row and one column are introduced, and exactly half of the rectangles are shaded.
14. In each new figure, except at the bottom vertex, two perpendicular lines are introduced at the remaining vertices.
15. In each new figure, one inverted white triangle is inscribed in the orange triangle.
16. The number of squares increases in the pattern. There are blue circles inscribed in one diagonal square and there are yellow circles inscribed in the remaining squares. Also, the blue circles in the diagonal alternate.
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What is the length of the apothem of the regular pentagon shown below? Round to one decimal place
Answer:
A
Step-by-step explanation:
Draw a diagonal line connecting the centre to a vertex at the bottom. This makes a triangle. It is a regular pentagon so the base of that triangle is 7.6 / 2, which is 3.8. You also know that the angle from the apothem to the base is 90 degrees. You also know that you could split the centre angle into 5 triangles. 360 / 5 = 72 and we have half of it so it is 36 degrees.
Let's see what we have so far:
The base of the triangle is 3.8
The angle at the bottom is 90
The angle at the top is 36
We now have the tan and the opposite and we need the adjacent so rearrange for adjacent.
This gives you adjacent = opposite / tan(angle)
adjacent = 3.8 / tan(36)
adjacent = 5.2m
Lighthouse B is 10 miles west of lighthouse A. A boat leaves A and sails 6miles. At this time, it is sighted from B. If the bearing of the boat from B is N63E, how far from B is the boat?
The boat is either _ miles or _ miles from lighthouse B, to the nearest tenth of a mile.
The boat in discuss is 9.03 miles from lighthouse B.
What is the distance of the boat from lighthouse B?The distance of the boat from lighthouse B as required can be determined by means of the cosine law in which case we have;
c² = 10² + 6² - (2×6×10Cos 63)
c = 81.52
c = 9.03miles.
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A solution of ibuprofen contains 150g in 800ml. What is the percent strength of this solution?
Answer:
18.75 percent
Step-by-step explanation:
150 / 800 x 100 = 18.75
cual es el coeficiente de variacion de los resultados de 30,60,90,45?
based on the given results, the coefficient of variation can be found to be 45.54.
what is the coefficient of variation?first, find the mean:
= (30 + 60 + 90 + 45) / 4
= 56.25
find the standard deviation using a spreadsheet:
= 25.61737691
the coefficient of variation is therefore:
= standard deviation / mean x 100
= 25.61737691 / 56.25 x 100
= 45.54
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A theater sells 2 types of fixed-price tickets - orchestra and balcony. Peter pays $50 for 1 orchestra and 4 balcony tickets. Justine pays $150 for 3 orchestra and 12 balcony tickets. А B The cost of 1 balcony ticket. The cost of 1 orchestra ticket. The quantity under A is greater than the quantity under B. The quantity under B is greater than the quantity under A. The quantities under A and B are equal. The information given is insufficient to make the comparison.
Using a system of equations, it is found that:
The cost of an orchestra ticket is of $10.The cost of a balcony ticket is of $10.The quantities are equal.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable a: Cost of an orchestra ticket.Variable b: Cost of a balcony ticket.Peter pays $50 for 1 orchestra and 4 balcony tickets, hence:
a + 4b = 50 -> a = 50 - 4b.
Justine pays $150 for 3 orchestra and 12 balcony tickets, hence:
3a + 12b = 150.
a + 4b = 50 -> a = 50 - 4b.
The equations are equal, hence we suppose that the costs are equal, that is:
a + 4b = 50 -> 5a = 50 -> a = 10.
Hence:
The cost of an orchestra ticket is of $10.The cost of a balcony ticket is of $10.The quantities are equal.More can be learned about a system of equations at https://brainly.com/question/24342899
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Need help on these trig homework
8. The length of the support is 7. 9 m
9. The length of the conveyer is 12m
3. a = 59m
A = 44°
B = 52°
4. c = 88. 6 mm
b = 49. 1 m
B = 34°
How to solve the trigonometry
8. We have the angle to be 20 degrees
Opposite side = x
hypotenuse = 23m
Using the sine ratio
sin θ = opposite/ hypotenuse
[tex]sin 20 = \frac{x}{23}[/tex]
Cross multiply
[tex]sin 20[/tex] × [tex]23 = x[/tex]
[tex]x = 0. 3420[/tex] × [tex]23[/tex]
x = 7. 9 m
The length of the support is 7. 9 m
9. The angle of elevation is 37. 3 degrees
Hypotenuse = 19 . 0m
Opposite = x
Using the sine ratio
sin θ = opposite/ hypotenuse
[tex]sin 37. 3 = \frac{x}{19}[/tex]
cross multiply
[tex]x = 0. 6059[/tex] × [tex]19[/tex]
x = 11.5
x = 12 m in 2 significant figures
The length of the conveyer is 12m
3. To determine the sides and angles, we use the sine rule;
[tex]\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}[/tex]
For side a, we use the Pythagorean theorem
[tex]c^2 = a^2 + b^2[/tex]
[tex]85^2 = a^2 + 67^2[/tex]
[tex]a = \sqrt{89^2-67^2}[/tex]
[tex]a = \sqrt{3432}[/tex]
a = 58. 58, a = 59m
To find angle A and B, use the sine rule
[tex]\frac{59}{sin A } = \frac{85}{sin 90}[/tex]
cross multiply
[tex]sin A[/tex] × [tex]85[/tex] = [tex]sin 90[/tex] × [tex]59[/tex]
make sin A subject of formula
[tex]sin A = \frac{59}{85}[/tex]
[tex]sin A = 0. 6941[/tex]
A = [tex]sin^-^1(0. 6941)[/tex]
A = 44°
[tex]\frac{67}{sin B} = \frac{85}{sin 90}[/tex]
cross multiply
[tex]sin B[/tex] × [tex]85[/tex] = [tex]sin 90[/tex] × [tex]67[/tex]
make sin b subject of formula
[tex]sin B = \frac{67}{85}[/tex]
[tex]sin B = 0. 7882[/tex]
B = [tex]sin^-^1( 0. 7882)[/tex]
B = 52°
4. To find the sides, we use the sine rule;
[tex]\frac{74. 0}{sin 56. 6} = \frac{c}{sin 90}[/tex]
Cross multiply
[tex]sin 56. 6[/tex] × [tex]c = sin 90[/tex] × [tex]74[/tex]
make 'c' subject of formula
[tex]c = \frac{74}{0. 8348}[/tex]
c = 88. 6 mm
To find length b, we use the Pythagorean theorem
[tex]c^2 = a^2 + b^2[/tex]
[tex]b^2 = c^2 - a^2[/tex]
[tex]b^2 = 88. 8^2 - 74^2[/tex]
[tex]b = \sqrt{7885. 44 - 5476}\\\\ b = \sqrt{2409. 44}[/tex]
b = 49. 1 m
[tex]\frac{74. 0}{sin 56. 6} = \frac{49. 1}{sin B}[/tex]
cross multiply
[tex]sin B = \frac{40. 99}{74. 0}[/tex]
B = [tex]sin^-^1(0. 5539)[/tex]
B = 34°
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A sales agent gets 15%commission for each motivational book he sells. if he sold books worth #284000,how much commission will he get?
Answer:
$42,600
Step-by-step explanation:
284000 x .15
the function f(t) = 5 cos(pi/4*t) + 11 represents the tide in dark sea. it has a maximum of 16 feet when time (t) is 0 and a minimum of 6 feet. the sea repeats this cycle every 8 hours. after six hours, how high is the tide?
The height of the tide after eight hours is 16 feet.
How to illustrate the function?From the information given, the function is given as 5cos (π/4)t + 11.
In this case, the time is given as eight hours. This will be:
f(8) = 5 × cos (π/4) × 8 + 11
f(8) = 5 × cos(2π) + 11
= (5 × 0.999) + 11
= 16 feet
The height is 16 feet.
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A student is taking an exam with 40 questions on it.To pass the exam she needs to answer 70% of the questions correctly. Unfortunately she answered only 40% of the 15 questions correctly. What percent of the remaining 25 questions does she have to answer correctly to pass the exam?
The first step is to find out how question in total she is able to miss, while still passing.
We know that there are [tex]40\\[/tex] questions on the test and she must get [tex]70[/tex]% of the questions correct.
Let's calculate how many questions that is:
40 x 0.70
= 28.
Subtract
40 - 28
= 12.
She is able to get 12 answers incorrect.
Now we must find out how many questions she got wrong when she got 40% of the first 15 correct.
If she got 40% correct; She got 60% incorrect.
Let's do the math:
Multiply:
15 x 0.40
= 6
Subtract:
15 - 6
= 9
This means that she got 6 questions correct, and 9 questions incorrect.
With the total allotment of 12 incorrect answers allowed, she can only get 3 more questions wrong.
Now we must find the percentage of the remaining 25 questions she can get wrong.
She can only get 3 wrong and she must get 22 correct.
Multiply:
22 x 4
= 88.
This means that she has to get 88% of the remaining 25 questions correct.
Can anyone help me find all the calculations to these cups?
The volume of the glasses is as follows;
glass 1 = 170 cm³glass 2 = 141 cm³glass 3 = 60 cm³How to find volume ?The volume of cylinder glass 1 = πr²h
The volume of cylinder glass 1 = 3.14 × 3² × 6
The volume of cylinder glass 1 = 3.14 × 9 × 6
The volume of cylinder glass 1 = 169.56 cm³ = 170 cm³
The volume of the glass 2 = 2 / 3 π r³ + πr²h
The volume of the glass 2 = 2 / 3 × 3.14 × 3³ + 3.14 × 3² × 3
The volume of the glass 2 = 56.52 + 84.78
The volume of the glass 2 = 141.3 cm³ = 141 cm³
The volume of conical glass 3 = 1 / 3 πr²h
The volume of conical glass 3 = 1 / 3 × 3.14 × 3² × (√7² - 3² = √40)
The volume of conical glass 3 = 9.42 × √40
The volume of conical glass 3 = 59.5773111176
The volume of conical glass 3 = 60 cm³
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Help again please. 10 points for help!! Thanks
Answer: 23 inches by 7 inches
Step-by-step explanation:
161 = 7 x 23 (or 1 x 161 but that doesn't help...)
And to check:
7 x 3 + 2 = 23
Answer:
23inches by 7inches
Step-by-step explanation:
7 ×3+2=23
An insurance company wants to conduct a customer satisfaction survey. Because the company suspects the type of coverage might influence customers' opinions, it
divides the list of customers based on what type of insurance they have (auto, homeowner, rental, life, disability, or a combination of these). If five customers are randomly selected from each group, what sampling method would this represent?
A) Simple Random Sample (SRS)
B) Systematic
C) Stratified
D) Cluster
QUICK I need help on what the answer is and an explanation would be much appreciated too thank you
The nonreal solutions to the polynomial equation are: (2 + i√11, 2 - i√11).
How to determine the nonreal solutions?By critically observing the graph given, we can logically deduce that the real solutions of the polynomial are -1 and 4. This ultimately implies that, the given polynomial expression can be evaluated as follows:
(x + 1)(x - 4) = x² - 3x - 4.
x⁴ - 7x³ + 23x² - 29x - 60 = x² - 3x - 4.
Also, the nonreal solutions can be determined by dividing the polynomial expression by the real solutions as follows:
Nonreal solutions = (x⁴ - 7x³ + 23x² - 29x - 60)/(x² - 3x - 4)
Nonreal solutions = (2 + i√11, 2 - i√11).
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Lines a and b are parallel and lines e and f are parallel what is the value of x
The value of x using the alternate exterior angle theorem is 82°
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An angle is formed from the intersection of two or more lines. Types of angles are acute, obtuse and scalene.
From the diagram:
x = 82° (alternate exterior angles)
The value of x using the alternate exterior angle theorem is 82°
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w^14+w^16
what will be the answer pls help
Answer:
there shouldnt be an answer, they are not like terms, for a proper answer it would have to be like terms, for example:
x^2+x^2=2x^2
or
w^12+w^12=2w^12
they need to have the same exponent for addition to happen
−6 + 3 = −21 pls can uhelp me with this
Answer:
No Solution
Step-by-step explanation:
1) Simplify -6 - 3 to -3.
-3 = -21
2) Since -3 = -21 is false, there is no solution.
No solution
A couple deposits $20,000 into an account earning 5% annual interest for 30 years. Calculate the future value of the investment if the interest is compounded monthly. Round your answer to the nearest cent.
The future value of the investment if the interest is compounded monthly is $89,354.89.
What is the future value of the investment?Given that;
Principal P = $20,000Annual interest rate r = 5% = 5/100 = 0.05Time t = 30 yearsCompound monthly = 12Future value = A = ?Using the compound interest formula;
A = P( 1 + r/n )^(nt)
We plug in our values.
A = 20000( 1 + 0.05/12 )^(12 × 30)
A = 20000( 1 + 0.0041666666666667)^(360)
A = 20000( 1.0041666666666667)^(360)
A = 20000( 4.46774965 )
A = 89354.89
Therefore, the future value of the investment if the interest is compounded monthly is $89,354.89.
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You expect to receive $10,000 at graduation in two years. You plan on investing it at 11% until you have $75,000. How long will you wait from now?
Answer:
about 19.31 years
Step-by-step explanation:
[tex]10000( {1.11}^{x} ) = 75000[/tex]
[tex] {1.11}^{x} = 7.5[/tex]
[tex]x ln(1.11) = ln(7.5) [/tex]
[tex]x = \frac{ ln(7.5) }{ ln(1.11) } = 19.31[/tex]
Find DE
3x - 28
3x - 30
D
G
E
F
33
Answer:
11
Step-by-step explanation:
(3x-28) + (3x-30) + x = 33
7x - 58 = 33
7x = 91
x = 13
DE = 3x - 28 = 3*13 - 28 = 11
Which is the statement is true about f(x)=-2/3|x+4|-6
Answer: The graph of f(x) is horizontally stretched
Maria plots the following points on a coordinate grid. Then, she connects each plotted point to the previous one in the order shown to form a figure. What is the area, in square units, of the enclosed figure?
The area of the enclosed figure is 4 square units.
What is the area?The area is the amount of area occupied by an object's flat (2-D) surface or shape.
The triangle's area can be described as,
Area = 1/2 x base x height.
To find the area of the enclosed figure, we need to first plot the given points and then determine the shape of the figure.
Plotting the points A, B, and C on a coordinate grid, we get:
The image is given below.
Connecting points A, B, and C, we can see that the figure formed is a right triangle with legs of lengths 4 and 2.
Therefore, the area of the enclosed figure is:
Area = (1/2) x base x height
= (1/2) x 4 x 2
= 4 square units
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The complete question:
Maria plots the following points on a coordinate grid. Then, she connects each plotted point to the previous one in the order shown to form a figure. What is the area, in square units, of the enclosed figure?
Point A (1, 3)
Point B (5, 7)
Point C(5, 3)
Point A (1, 3)
Calculate the distance between the points C = (0,-2) and L= (-4, 1) in the coordinate plane. Give an exact answer. (not a decimal approximation)
Answer: 5
Step-by-step explanation:
[tex]\sqrt{(-4-0)^2 + (1-(-2))^2}=5[/tex]