Explanation:
[tex]\boxed{\sf \sum _{n=1}^{32}\left(2n+8\right)}[/tex]
Formula Required:
[tex]\sf sum \ of \ arithmetic \ series = \dfrac{n}{2} (2a \ + \ (n-1) \ d)[/tex]
Identify the following's:
First Term (a) = (2(1) + 8) = 10Common Difference (d) = 2nd term - first term = (2(2) + 8) - (2(1) + 8) = 2Total Terms (n) = 32Insert variables:
[tex]\rightarrow \ \sf S_{32} = \dfrac{32}{2} (2(10) + (32-1) 2) \quad \xrightarrow{\text{Simplify} } \quad 1312[/tex]
Question:
A circular frame has a diameter of 10 inches. Identify the area of the mirror that the frame
can hold. Use 3.14 for TT.
The frame can hold a mirror with an area of 78.5 in².
How to find the area?
The area for a circle of diameter D is given by the formula:
[tex]A = pi*(D/2)^2[/tex]
Where pi = 3.14
Here we know that the diameter is 10 inches, replacing that in the area equation we can get:
[tex]A = 3.14*(10in/2)^2 = 3.14(5in)^2 = 78.5 in^2[/tex]
So the frame can hold a mirror with an area of 78.5 in².
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Part a
describe the process you could use to find the probability that jake will earn at least 30 points on a throw, given that he hits the target? note: assume that it is equally likely that he will hit any region in the target.
The probability that Jake will earn at least 30 points on a throw is 0.335
How to describe the process?The attached image represents the missing part of the question.
From the attached image, we can see that:
For Jake to earn at least point, he must hit the three circles (starting from the inner circle)
The radius of the yellow circle is:
Radius = 3
While the width of the other circles is:
Width = 4
The total area of the sections that give a point of at least 30 is:
A₁ = π * (3 + 4 + 4)² = 121π
The total area of all the sections is:
A₂ = π * (3 + 4 + 4 + 4 + 4)² = 361π
The probability of getting at least 30 points is:
P(At least 30) = 121π/361π
Evaluate
P(At least 30) = 0.335
Hence, the probability that Jake will earn at least 30 points on a throw is 0.335
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Indicate the most appropriate if-then statement that the english sentence represents: people 18 or older can vote in a federal election
The most appropriate if-then statement that the english sentence represents is: B. If a person is 18 years old or older, then the person can vote in Federal elections.
What is Federal Election?
Federal election can be defined as the way in which a person vote for a preferred.
For a person to be eligible to vote during election, such person must be 18 years old or older.
The if -then statement is: If a person is 18 years old or older, then the person can vote in Federal elections.
Therefore the correct option is B.
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someone help me.............asap
Answer:
14 rides
Step-by-step explanation:
if she wants to spend less than 35 then we can subtract the initial 6$ fee wich gives her 29$ left and the most 2 can go into 29 is 14 because 14x2 is 28 leaving her with 1 dolar left which means she didnt spend 35$!!
Mathematics
height=1cm,base=√5cm.what is the area of isosceles triangle?
Step-by-step explanation:
what is the formula for the area of a triangle ? hmm ?
area = baseline × height / 2
in our case (it does not matter for this question, if it is an isoceles triangle or not, the formula applies to all)
area = sqrt(5) × 1 / 2 = sqrt(5)/2 cm² = 1.118033989... cm²
Answer:
[tex]\huge\boxed{\sf Area = 1.12 \ cm^2}[/tex]
Step-by-step explanation:
Given data:Height = h = 1 cm
Base = b = √5 cm
Required:Area = A = ?
Formula:[tex]\displaystyle Area = \frac{1}{2}(b)(h)[/tex]
Solution:[tex]\displaystyle Area = \frac{1}{2} (\sqrt{5} )(1)\\\\Area = \frac{\sqrt{5} }{2} \\\\Area = 1.12 \ cm^2\\\\\rule[225]{225}{2}[/tex]
If triangle ABC has vertices A(1, 2), B(-1, -1), and C(0, -2), which of the following coordinates is B’ of the dilation using the scale factor 4?
Answer: B'(-4, -4)
Given : A(1, 2), B(-1, -1), C(0, -2)
"Focusing on B coordinates"
If the points are dilated with a scale factor of 4
Then new coordinates : (-1, -1) × 4 = B'(-4, -4)
Answer:
B' = (-4, -4)
Step-by-step explanation:
Dilation: A type of transformation that makes the pre-image larger or smaller without changing its shape.
Center of a dilation: a fixed point about which all points are dilated.
Given:
A = (1, 2)B = (-1, -1)C = (0, -2)Scale factor = 4For dilation when the center of dilation is the origin (0, 0), simply multiply the coordinates of the vertices of the pre-image by the given scale factor to find the image under dilation:
Therefore:
A' = (1 x 4, 2 x 4) = (4, 8)
B' = (-1 x 4, -1 x 4) = (-4, -4)
C' = (0 x 4, -2 x 4) = (0, -8)
5x-7≥8
This is a 2-step inequality: solve for x
your work by listing each step of the
process.
Answer:
x≥3
Step-by-step explanation:
Let's solve your inequality step-by-step. 5x−7≥8
Step 1: Add 7 to both sides.
5x−7+7≥8+7
= 5x≥15
Step 2: Divide both sides by 5.
5x/5≥15/5
= x≥3
100 points and brainlyest !!! ONLY ANSWER IF U KNOW THE ANSWER !!!
Answer:
Step-by-step explanation:
A” (-2,2)
B” (-1,-2)
C” (-4,-4)
Answer:
A''(-1,5)
B''(0,1)
C''(-3,7)
Which equation is represented by the graph below?
Answer:
1
Step-by-step explanation:
this is becasue the slope is positive
if 7544644555- x is 45000 whats the value of x
Answer:
Step-by-step explanation:
45000+7544644555=x
x=7544689555
Answer:
x = 7544599555
Step-by-step explanation:
First let's make an equation :
7544644555 - x = 45000
Now to make x the subject and positive :
We add x to both sides :
7544644555 = 45000 + x
Now we subtract 45000 from both sides :
7544644555 - 45000 = x
x = 7544599555
Hope this helped and brainliest please
Determine the marginal distribution of Gender. In paragraph form, how you calculated the marginal distribution. Include your calculations in your explanation.
The marginal distribution for gender tells you the probability that a randomly selected person taken from this sample is either male or female, regardless of their blood type.
In this case, we have total sample size of 714 people. Of these, 379 are male and 335 are female. Then the marginal probability mass function would be
[tex]\mathrm{Pr}[G = g] = \begin{cases} \dfrac{379}{714} \approx 0.5308 & \text{if }g = \text{male} \\\\ \dfrac{335}{714} \approx 0.4692 & \text{if } g = \text{female} \\\\ 0 & \text{otherwise} \end{cases}[/tex]
where G is a random variable taking on one of two values (male or female).
I'm not good at time questions can someone help me?
Randy should begin his homework by 07:10 in order to sleep by 10:00
How to determine the time to start the homework?The given parameters are:
Social studies = 45 minutesScience = 40 minutesMath = 1 hour and 15 minutesBed preparation = 10 minutesIf the above activities are done, the time spent would be:
Time = 45 minutes + 40 minutes + 1 hour and 15 minutes + 10 minutes
Add the time
Time = 2 hour and 50 minutes
He wants to go to bed by 10:00.
So, the time to begin his homework is:
Begin = 10:00 - 2 hour and 50 minutes
Evaluate the difference
Begin = 07:10
Hence, Randy should begin his homework by 07:10
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Anton is drawing a flag of switzerland, which has a square shape, for a school project. if he wants the flag to have sides that are 16 inches long, what will be the area of the completed flag? 64 inches squared 128 inches squared 256 inches squared 512 inches squared
Considering the side length, the area of the complete square flag will be of 256 inches squared.
What is the area of a square?The area of a square of side length l is given by l squared, that is:
A(l) = l².
In this problem, we have that l = 16 inches, hence the area in square inches is given by:
A(16) = 16² = 256.
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O is the center of the regular octagon below. Find its area. Round to the nearest tenth
if necessary.
Answer:229.1
Step-by-step explanation: to much work I thought to hard that’s the answer your welcome buddy
A cylinder has a height of 4 meters and a radius of 1.5 meters. What is the approximate radius of a sphere that has the same surface area
as the cylinder?
OA. 2.0m
OB. 4.1 m
O c. 1.7m
OD. 2.9 m
If the surface area of the cylinder is 12π square meters. Then the radius of the sphere will be 1.7 meters.
What is a cylinder?A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.
A cylinder has a height of 4 meters and a radius of 1.5 meters.
Then the approximate radius of a sphere that has the same surface area as the cylinder.
We know that the Surface area of the cylinder will be is given as
Surface area = 2πrh
Surface area = 2 x π x 1.5 x 4
Surface area = 12π square meters
Then we have
Surface area of sphere = surface area of cylinder
4πr² = 12π
r² = 3
r = 1.7 meters
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Answer:
2.0 m
Step-by-step explanation:
A. 2.0 m
Which statement best describes the polynomial?
-24x7-12x²-9x+6
OIt is in standard form because the exponents are in order from highest to lowest.
OIt is in standard form because the coefficients are in order from highest to lowest.
OIt is not in standard form because the constant should be the first term.
OIt is not in standard form because it can be further simplified.
It is in standard form because the exponents are in order from highest to lowest.
The given polynomial is [tex]-24x^{7} -12x^{2} -9x+6[/tex].
We need to determine from the given statements, which statement best describes the given polynomial.
What is the standard form of the polynomial?The highest degree of terms is written first, followed by the next degree, and so on, to represent a polynomial in standard form. The standard form of the polynomial is [tex]f(x)=a_{n} x^{n} +a_{n-1} x^{n-1}+a_{n-2} x^{n-2} +........a_{1}x+a_{0}[/tex].
So, in the given polynomial [tex]-24x^{7} -12x^{2} -9x+6[/tex], the exponents of the variable are in decreasing order.
Therefore, it is in standard form because the exponents are in order from highest to lowest.
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Which angle in the figure is a right angle?
A. ∠STU
B. ∠TSR
C. ∠TUS
D. I don't know.
Answer:
∠TUS I'm pretty sure because t and u make a right angle
Which function has the following characteristics?
D
A vertical asymptote at x = 3
●
A horizontal asymptote at y = -1/2
Using the asymptote concept, the function with a vertical asymptote at x = 3 and an horizontal asymptote at [tex]y = -\frac{1}{2}[/tex] is given by:
[tex]f(x) = -\frac{x}{2(x - 3)}[/tex]
What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.The vertical asymptote at x = 3 means that x = 3 is a root of the denominator, hence:
[tex]f(x) = \frac{g(x)}{x - 3}[/tex]
The horizontal asymptote at y = -1/2 means that:
[tex]\lim_{x \rightarrow \infty} f(x) = -\frac{1}{2}[/tex]
Which happens if [tex]g(x) = -\frac{x}{2}[/tex], hence the function is:
[tex]f(x) = -\frac{x}{2(x - 3)}[/tex]
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A family purchases a Light sphere to be used out on their patio. The diameter of the sphere is 20 inches. What is the volume of the light sphere? Use 3.14 for pi. Enter your answer as a decimal and round only your final answer to the nearest hundredth.
Two people had different answers but had 5 stars. So can someone explain how to solve this question correctly. Thank you in advance
Answer:
The answer is 4188.79 ft^3.
Step-by-step explanation:
The formula is V=4/3πr^3. The radius is 10, turning that into V=4/3π10^3. 10^3 is 1000, and 1000 times 4/3 is 1333.33. 1333.33 times 3.14 (or π) is equal to 4188.79 ft ^3 rounded to the nearest 100th. I hope this helps! :)
what is the surface area of a sphere that has a volume of 3000cm
The surface area of the sphere given its volume is 1006.06 cm².
What is the surface area?The first step is to determine the radius of the sphere from its volume.
Volume of a sphere = (4/3) x (n) x (r^3)
n = 22/7r = radius∛(3000 x 3/4 x 7/22) = 8.95
Surface area of a sphere = 4πr²
4 x 8.95² x 22/7 = 1006.06 cm²
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A figure is contained completely in Quadrant III of the coordinate plane. After applying the composition Ro.-90° ry to the figure, in which quadrant does the image lie?
The transformation can be defined as the introduction of a new set of mathematical coordinates that are declared to be different functions of the original coordinates. The correct option is C.
What is transformation?The transformation can be defined as the introduction of a new set of mathematical coordinates that are declared to be different functions of the original coordinates.
The meaning of Ro.-90° ry, is that the figure is reflected across the y-axis, and then rotated about the origin by 90° in the clockwise direction, therefore, the figure will again lie in the third quadrant.
Hence, the correct option is C.
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If a is real and the product of (a+6i)(5-3i) is a real number, the find a.
PLS HELP ASAP WILL MARK BRAINLIEST
Answer:
5a−3ai+30i+18
Step-by-step explanation:
i just did this
Pls help I literally have no clue what this means
Find the missing number based on the description
below:
“12 less than 7 times a number is the same as 32 less than the product of -3 and the number”
A.-5
B.10
C.-2
D.-1
Answer:
I think the answer is c -2
Step-by-step explanation:
but don't quote me on that and if it's wrong i truly am sorry
Answer:
Step-by-step explanation:
A rental car company charges $77.50 per day to rent a car and $0.10 for every mile driven. Sydney wants to rent a car, knowing that:
She plans to drive 275 miles.
She has at most $260 to spend.
Write and solve an inequality which can be used to determine xx, the number of days Sydney can afford to rent while staying within her budget.
The number of days that Sydney can afford to rent while staying within her budget is 3 days.
How many days can Sydney afford to rent?Total budget ≤ (total number of days x cost per day) + (cost per mile x total mile)
$260 ≤ $77.50xx + ($0.10 x 275)
$260 ≤ $77.50xx + 27.50
$260 - 27.50 ≤ $77.50xx
232.50 ≤ $77.50xx
xx ≤ 232.50 / $77.50
xx ≤ 3
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2/3 - 5/4 + 7/3 whats the4 answer pls
Answer:
7/4Step-by-step explanation:
2/3 - 5/4 + 7/3
=8/12 - 15/12 + 28/12 (LCM=12)
(8 - 15 + 28)/12
=21/12
=7/4
pls answer asap, thanks!!
Since the amount is compounded monthly, the amount would triple after 26 months
Since the money is compounded monthly, we use the compound interest formula
How to calculate compound interestThe amount obtained on compound interest is given by A = P(1 + r)ⁿ where
P = present value, r = interest rate and n = timeNow, since you deposit an amount of $1000 at an interest rate of 3.15 % per year compounded monthly and an extra $75 added monthly after n month, the amount is A = A' the amount compounded monthly + the extra amount monthly A"
Amount compounded monthly
Since A' = P(1 + r)ⁿ where
P = initial amount = $1000, r = interest rate = 3.15 %/12 (since it is compounded monthly) = 0.002625 and n = number of monthsSo, A' = P(1 + r)ⁿ
= 1000(1 + 0.002625)ⁿ
= 1000(1.002625)ⁿ
Extra amount added monthly
Also, since $75 is added monthly, after n months, A" = 75n
Total amount after n months
So, the total amount added is A = A' + A"
= 1000(1.002625)ⁿ + 75n
Time for amount to tripleSince we require the time when the initial amount would triple, so, A = 3A'
= 3 × 1000
= 3000.
So,
A = 1000(1.002625)ⁿ + 75n
3000 = 1000(1.002625)ⁿ + 75n
3000 - 75n = 1000(1.002625)ⁿ
The solution of the above equation is obtained graphically. Find the graph in the attachment. They intersect at (25.736, 1069.797)
So, n = 25.736
≅ 26 months
So, the amount would triple after 26 months
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Select all the correct answers.
Which expressions represent a quadratic expression in factored form?
x²-x-72
(x+3)(x-7)
-8(x + 56)
(x + 1)(x - 2)
(x-2) + (x + 3)
Answer:
(x + 3)(x - 7)
(x + 1)(x - 2)
Step-by-step explanation:
The general form of factored equations :
y = (x + a)(x + b) [it can be ±, so don't worry about that part]
===============================================================
Hence, the expressions which are in factored form :
⇒ (x + 3)(x - 7)
⇒ (x + 1)(x - 2)
a) At what percent rate of compound interest per annum will the compound interest on Rs 1,25,000 be Rs 91,000 in 3 years?
The rate of compounding on the investment is 20%.
What is the rate of compounding?
When an amount compounds annually, it means that both the amount invested and the interest accrued increases in value once a year.
The formula that can be used to determine the rate of compounding is: (FV / PV)^(1 /n)
Where:
FV = future value = 125,000 + 91,000 = 216,000PV = present value = 125000n = number of years - 3(216,000 / 125000)^ (1 / 3) - 1 = 20%
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Write an equation for the function whose graph is the shape of f(x) = x2, but shifted three units to the lef
9₁(x) =
Write an equation for the function whose graph is in the shape of g₁(x), but shifted five units up.
9₂(x) =
Write an equation for the function whose graph is in the shape of g₂(x), but reflected in the x-axis.
93(x)
The equation for the functions g₁(x), g₂(x), and g₃(x) are (x + 3)², (x + 3)² + 5, and -[(x + 3)² + 5] respectively.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = x²
We have:
g₁(x) which is a transformed function of f(x)
f(x) shifted three units to the left.
Plug x → (x + 3)
g₁(x) = (x + 3)²
Similarly,
Equation for the function whose graph is in the shape of g₁(x), but shifted five units up.
g₂(x) = (x + 3)² + 5
Equation for the function whose graph is in the shape of g₂(x), but reflected in the x-axis.
g₃(x) = -[(x + 3)² + 5]
Thus, the equation for the functions g₁(x), g₂(x), and g₃(x) are (x + 3)², (x + 3)² + 5, and -[(x + 3)² + 5] respectively.
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If f(x) = 16x – 30 and g(x) = 14x – 6, for which value of x does (f – g)(x) = 0?
The value of the x will be 12. The value of the x is obtained from the condition,(f – g)(x) = 0
What exactly is a function?A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.
Given function;
f(x) = 16x – 30
g(x) = 14x – 6
⇒(f – g)(x) = 0
⇒(16x – 30)-(14x – 6)=0
⇒16x-30-14x+6=0
⇒2x-24=0
⇒x=24/2
⇒x=12
Hence, the value of the x will be 12.
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