The sum of the first thirteen terms of the geometric series is -7971615.
What is Geometric series?This is the sum of an infinite number of terms that has a constant ratio between successive terms.
To calculate the sum of the first thirteen terms of the geometric series, we use the formula below.
Formula:
S₁₃ = a(rⁿ-1)/(r-1).............. Equation 1Where:
S₁₃ = Sum of the first thirteen terms of the geometric series.a = First term of the seriesr = Common ratioGiven:
a = -10r = 3n = 13Substitute these values into equation 1
S₁₃ = -10(3¹³-1)/(3-1)S₁₃ = -7971615Hence, the sum of the first thirteen terms of the geometric series is -7971615.
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If the diameter of the circle is 14 units, calculate its area: then calculate its circumference
Answer:
Area: 153.86
Circumference: 43.96
Enter the number that belongs in the green box.
Answer:
The answer is x = 10.
Step-by-step explanation:
Two options:
1. Looking at the image it looks like a parallelogram. So, most side lengths are equal to each other or are the same.
2. We can use the Pythagorean Theorem to solve for x.
i need help finding the orignal price
Which polynomial function has a root of 1 with
multiplicity 2 and a root of 6 with multiplicity 1?
Of(x) = (x - 1)(x-6)
Of(x) = 2(x - 1)(x - 6)
Of(x) = (x - 1)(x - 1)(x-6)
O f(x) = (x - 1)(x-6)(x-6)
Answer:
C) f(x) = (x - 1)(x - 1)(x-6)
Explanation:
Multiplicity means number of times a factor appears in a particular equation.
For example, a root of 3 has multiplicity of 3 then = (x - 3)(x - 3)(x - 3)
Breakdown for this question:
If a polynomial where root of 1 has multiplicity of 2, then it means (x - 1)²
Where polynomial of root of 6 has multiplicity of 1, then it means (x - 6)
Joining them together:
(x - 1)²(x - 6) = (x -1)(x - 1)(x - 6) Hence option C is correct.
Bob walks dogs after school. He charges $43. 50 for 6 hours and $65.25.75 for 9 hours.
Enter an equation to represent the relationship. Let x represent the number of hours Bob works
and y represent the amount he charges.
The equation of the amount charged by Bob will be y = 7.25x.
What is an equation?
The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.
Given that:-
Bob walks dogs after school. He charges $43. 50 for 6 hours and $65.25.75 for 9 hours.The equation will be generated as follow:-
6 hours = $ 43.50
1 hours = $ 7.25
9 hours = $ 65.2575
1 hours = $ 7.25
Let x represent the number of hours Bob works and y represent the amount he charges. The equation will be:-
y = 7.25x dollars.
Therefore the equation of the amount charged by Bob will be y = 7.25x.
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Fred figured out the volume of the glass is 141.37cm. Show work
To solve this problem, we have to calculate the volume of a hemisphere and the volume of a cylinder and add them together. The volume of the glass can be only be calculated when we find the volume of the hemisphere and the volume of the cylinder and then add then up together.
Volume of a HemisphereThe volume of a hemisphere is given as
[tex]v = \frac{2}{3} * \pi * r^3[/tex]
Data
r = 3cmLet's substitute the values into the equation and solve.
[tex]v = \frac{2}{3} * \pi * r^3\\v = 56.556cm^3\\[/tex]
Volume of a CylinderThe formula of volume of a cylinder is
[tex]v = \pi r^2 h[/tex]
data given
h = 3cmr = 3cmLet's substitute the values into the equation and solve
[tex]v = \pi r^2 h\\v = 3.142 * 3^2 * 3\\v = 84.834cm^3[/tex]
Let's add both volumes together so we have the volume of the glass cup
[tex]56.556 + 84.834 = 141.39cm^3[/tex]
The volume of the glass can be only be calculated when we find the volume of the hemisphere and the volume of the cylinder and then add then up together.
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If you reflect point B(- 2, 5) over the y- axis, what is the reflected point ?
Answer:
(2,5)
Step-by-step explanation:
Since it is reflected across the y-axis only the x point will change and vise-versa
4/8 plus 2/4 find the common denomnator
Answer:
The common denominator is 4.
Step-by-step explanation:
4/8 simplified is 2/4.
Therefore, we can now add them together.
2/4 + 2/4 = 1.
Hope this helps:) Goodluck!
Select the correct answer.
What is the range of this absolute value function?
y
-10
-10.
-8
9
N-
N
A
-6
-8
-10
10
A lawn sprinkler sprays water 12 feet in every direction as it rotates. What is the area of the sprinkled lawn?
Find the product with the exponent in simplest
form. Then, identify the values of x and y.
X
1
3
6³.6
64 6
=
X ⇒7, y = 12/7
X ⇒12
x= 7/12
COMPLETE
7 , 12 are the answers
Answer:
x = 7
y = 12
Step-by-step explanation:
The key to solving this problem is understanding the properties of exponents:
If you are multiplying two powers with the same base (in this case the base is 6), the result is the base raised to the power of the two exponents added together.
6^1/3+1/4 = 6^x/y
6^7/12 = 6^x/y
So the product would be 6^7/12
Therefore, the answers are:
x = 7
y = 12
solving system of equations by graphing.
Answer:
see attached image
Step-by-step explanation:
1. What is the volume of this composite figure?
i6m
16 m
10 m
4 m
5 m
Answer:
560
Step-by-step explanation:
16 times 5 times 4=320
6 times 16 divide 2 then multiple 5
Solve this fraction, thanks!
[tex] \frac{10}{5} + \frac{ - 12}{5} [/tex]
Answer:
-2/5
Step-by-step explanation:
I actually didn't see the negative sign sorry and thanks for correcting my mistake!!!
Answer:
-2/5
Step-by-step explanation:
+ × - = -
10/5-12/5
apply the fraction rule a/c-b/c =a-b/c
10-12/5
substract 10-12 =-2
-2/5
A path in the park is 15 kilometers in. A trash bin is placed every 1/3 kilometers how many trash cans are along the path ?
Which one geos first to last 3/4 or 1/3 or 5/8
Need help on this one please
a line passes through the point (-9,1) and has a slope of 4/3. Write an equation in slope-intercept form for this line.
Answer: y=4/3x+1
Step-by-step explanation:
The formula is Y=mx+b
b is the y-intercept and MX is slope
What comes next in this pattern? 7/2, 6/3, 5/4, ... 4/9 4/7 4/5
Answer:4/3
4/3
Step-by-step explanation:
How many days would it take to breathe one billion times if you were
breathing at a rate of 12 times per minute?
Answer:
I think it would be 1,000,000.
Step-by-step explanation:
Let's begin with a correction: the verb in question is TO BREATHE; one instance of doing so is the noun BREATH.
12 times per minute; 60 minutes per hour; 24 hours per day; multiplying all of these gives some number of breaths per day. I'm going to call it B (you can calculate it).
Answer:
Step-by-step explanation:
12 / min
720 / hr
17,280 / day
6,307,200 / yr
Now divide 1,000,000,000 by 6,307,200 and you get 158 years
amusement on a particularly boring transatlanfic fight one of the authors am used himseft by counting the heads of the people in the seats in front of him. He noticed that all 37 of them either had black hair or had a whole row to themselves or both. Of this total 33 had black hair and 6 were fortunate enough to have a whole row of seats to themselves. How many black haired people had whole rows to themselves?
How many solution that following equation has? 2x +4= 2x-5 0 1 02 O infinitely many
Answer:
NO SOLUTIONStep-by-step explanation:
2x +4 = 2x - 5
4 + 5 = 2x - 2x
9 = 0
NO SOLUTION
Martin has a piece of purple yarn that is 3 1/2 inches long he has a piece of yellow yarn that is 3 5/6 inches Long how much longer is the yellow yarn?
Answer:
2 1/3 longer
Step-by-step explanation:
yw ;)
Answer:
⅓
Step-by-step explanation:
Expression : 3 ⅚ - 3 ½
3 ½ would become 3 3/6.
3 ⅚ - 3 3/6 = 2/6 = 1/3
A pedestrian walks 7.4 kilometers west
and then 9.2 kilometers south.
What is the magnitude of the
pedestrian's resultant vector?
Hint: Draw a vector diagram.
[ ? ] kilometers
Round your answer to the nearest tenth.
Answer: 11.8 km
Step-by-step explanation:
The resulting figure is a right angled triangle shown below
[tex]$$Apply the Pythagorean theorem to find out the magnitude of the resultant vector $A B$ in the triangle $A B C$ as follows -$$\begin{aligned}&A B^{2}=B C^{2}+C A^{2} \text { (Hypotenuse }{ }^{2}=\text { Base }^{2}+\text { Adjacent }^{2} \text { ) } \\&=7.4^{2}+9.2^{2} \\&=139.4 \\&A B=11.806777 \\&\quad A B \approx 11.8 \mathrm{~km} \text { (Rounded off to the nearest tenth) }\end{aligned}$$[/tex]
Mrs. Smith gave two classes the same quiz. She randomly selected 5 students from each class to compare the classes. The scores of the five students are shown below. Class A: 80, 82, 74, 92, 94 Class B: 82, 80, 88, 86, 82
What are the mean and range for each class ?
Class A- mean = 84.4 range = 14
Class B - mean = 83.6. range = 8
Using the information found in the question above which class mrs smith report had the more consistent performance on the unit test ?, explain what this means in terms of the situation
The mean and range for class A are 84.4 and 20 while the mean and range for class B are 83.6 and 8. Class B is more consistant then class A.
How to calculate the mean?We can see from the data that the consistency of class B is more becuase the repeatation of the same score is more in class B then class A and the range of class B is also less then the class A.
It should be noted that mean simply means average. It's the addition of the numbers divided by the total numbers.
In this case, the computation will be:
Class A: Mean = 422/5= 84.4.
Range: 94-74 = 20
Class B: Mean = 418/5 = 83.6.
Range= 88-80 = 8
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(x+3)^2+4=46
what is the solution of this equation
Answer:
x = -3 + √42
Step-by-step explanation:
1) Expand the square
2) Distribute
3) Distribute
4) Distribute
5) Combine like terms
6) Add the numbers
7) Move terms to the left side
8) Subtract the numbers
9) Use the quadratic formula
10) Simplify
11) Separate the equations
12) Solve
Therefore, the solution of this equation is x = -3 + √42
Step-by-step explanation:
(x + 3)² + 4 = 46
(x + 3)² = 42
x + 3 = ±sqrt(42)
x = ±sqrt(42) - 3
x1 = sqrt(42) - 3 = 3.480740698...
x2 = -sqrt(42) - 3 = -9.480740698...
HELP PLEASE 100 POINTS!!!
Given that triangle PHT is a right triangle and Line HY is an altitude, what is the missing justification in the proof that (PH)^2 + (HT)^2 = (PT)^2?
The missing reason is reflexive property.
Therefore, the correct option is D.
What is a triangle?A triangle is a type of polygon, which has three sides, and the two sides are joined end to end is called the vertex of the triangle.
Given that a triangle PHT is a right triangle and Line HY is an altitude.
According to the reflexive property, a side or an angle is congruent to itself.
If A is an angle of a triangle, then using reflexive property.
∠A ≅ ∠A
∠PHT ≅ ∠HYT (Both are right angles)
∠T ≅ ∠T (Reflexive property)
ΔPHT ~ ΔHYT (AA rule of similarity)
Other statements and reasons are already in the table.
Hence the correct option is D.
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This table represents a proportional relationship between x and y.
x 1.3 1.6 1.9 2.2
y 1.82 2.24 2.66 3.08
What is the constant of proportionality?
Enter your answer as a decimal in the box.
ill give brainliest this is for k12
The table is an illustration of a linear table, and the constant of proportionality is 1.4
How to determine the constant of proportionality?The table is given as:
x 1.3 1.6 1.9 2.2
y 1.82 2.24 2.66 3.08
The constant of proportionality (k) is calculated using:
k = y/x
Using the values on the table, we have:
k = 1.82/1.3
Divide
k = 1.4
Hence, the constant of proportionality is 1.4
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Choose ALL the numbers that round down when rounding to the nearest hundred! Is it!: 47,035, 3,140, 76,654, 1,298, 607,882, 8,560?
Answer:
The answer is:
the first one
second one
:D
Step-by-step explanation:
in this case, any number in the tens place less than five will make the number round down
Find the area of the Wrangle
The area of the triangle in square units 8 units 10 units
Answer:
The area is 40 units
Step-by-step explanation:
