[tex]\qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\[-0.5em] \hrulefill\\ n=7\\ r=3 \end{cases} \\\\\\ S_7=a_1\left( \cfrac{1-r^7}{1-r} \right)\implies 5465=a_1\left( \cfrac{1-3^7}{1-3}\right)\implies 5465=a_1(1093) \\\\\\ \cfrac{5465}{1093}=a_1\implies \boxed{5=a_1}[/tex]
What is the end behavior of the function f of x equals negative 4 times the cube root of x?
A.)As x → –∞, f(x) → –∞, and as x → ∞, f(x) → ∞.
B.) As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞.
C.) As x → –∞, f(x) → 0, and as x → ∞, f(x) → 0.
D.) As x → 0, f(x) → –∞, and as x → ∞, f(x) → 0.
Answer:
B.) As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞.
Step-by-step explanation:
[tex]\lim_{x\rightarrow -\infty } f\left( x\right) =\lim_{x\rightarrow -\infty } -4\sqrt[3]{x} = (-4)\times(-\infty) = +\infty[/tex]
[tex]\lim_{x\rightarrow \infty } f\left( x\right) =\lim_{x\rightarrow \infty } -4\sqrt[3]{x} = (-4)\times(+\infty) = -\infty[/tex]
whats the volume formula?
PLEASE HELP ME ANSWER THIS
if the sum of 3.5 and .02 is subtracted from the product of 11 and .05 the result is
Answer:
7.53
3.5 + 0.02 = 3.52
11 + 0.05 = 11.05
11.05 - 3.52 = 7.53
Why couldn't you add the
feet, yards, and centimeters
together?
(BRAINLIEST) What is the slope of the line shown in the graph?
2
−1
−fraction 1 over 2
fraction 1 over 2
Answer: the slope is y=-1/2
Step-by-step explanation:
because the line is moving from left to right, it is a negative slope
Write 2.19 as the ratio of two integers in fraction form
Answer: [tex]\frac{219}{100}[/tex]
======================================================
Explanation:
Think of [tex]2.19[/tex] as [tex]\frac{2.19}{1}[/tex] or [tex]\frac{2.19}{1.00}[/tex]
This works because dividing anything over 1 does not change the original number.
Then we can move the decimal point two spots to the right for each number
2.19 becomes 2191.00 becomes 100Therefore, [tex]2.19 = \frac{219}{100}[/tex]
what is the n th term of this sequences 51,54,59,66,75,86,99
Question 6 of 10
Which of the following are not polynomials?
A,D and E are not polynomials.
Step-by-step explanation:
Well you see my friend, that's how things work.
A polynomial does not have the variable in the denominator.
a. What is the volume, in cubic feet, of the box in the diagram?
b. How many of these boxes can fit in the cargo hold of the truck?
Volume is a three-dimensional scalar quantity. The number of boxes that can fit in the cargo hold of the truck is 54.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of the box = Volume of the cube = a³ = (2.50)³ = 15.625 ft³
The volume of cargo hold = 7.50 × 7.50 × 15 = 843.75 ft³
Now, the number of boxes that can fit in the cargo hold of the truck will be,
Number of boxes = (Volume of truck container)/(Volume of box)
= 843.75/15.625
= 54
Hence, the number of boxes that can fit in the cargo hold of the truck is 54.
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What is volume of the box in diagram (in cubic ft.)
a = 2.5ft.Volume of cube = a³
putting the value of a
Volume = (2.5ft.)³
Volume = 15.625 ft³
To find how many such boxes can be fit into the truck , we need to first find the volume of cargo hold of the truck and then divide it by the volume of 1 box
Volume of Cargo hold of truck =
= 15ft. × 7.5ft. × 7.5ft
= 843.75 ft³
No. of boxes that can be fit into the truck =
Volume of truck/ Volume of one box
= 843.75ft.3³/15.625ft.³
= 54 boxes
The graphically and algebraically
What is the sum of all the angles that are labeled?
Answer:
61 + 142 + 44 = 247˚
Step-by-step explanation:
Just add haha
the person above is right
PLEASE HELP ITS EXTRA CREDIT AND I COULD REALLY USE IT !! BEING TIMED! for each of the following statements, determine if the statement is true or false and explain how you decided on your answers for the polynomial.
*equation and questions included in picture below*
A. True. We see this by taking the highest order term in each factor:
[tex]f(x) = -3x(x-5)^3(x+2)^2 = -3x (x^3 + \cdots) (x^2 + \cdots) = -3x^{\boxed{6}} + \cdots[/tex]
B. True. Again we look at the leading term's degree and coefficient. f(x) behaves like -3x⁶ when x gets large. The degree is even, so as x goes to either ± ∞, x⁶ will make it positive, but multiplying by -3 will make it negative. So on both sides f(x) approaches -∞.
C. False. f(x) = 0 only for x=0, x = 5, and x = -2.
D. False. Part of this we know from the end behavior discussed in part B. On any closed interval, every polynomial is bounded, so that for any x in [-2, 5], f(x) cannot attain every positive real number.
E. True. x = 0 is a root, so f(0) = 0 and the graph of f(x) passes through (0, 0).
F. False. (0, 2) corresponds to x = 0 and f(x) = 2. But f(0) = 0 ≠ 2.
|x|=x^2+x-15 solve absolute value equation and show steps please
Answer:
x=√15 or x = -5 or x=3
Step-by-step explanation:
Possibility one:
x=x^2+x-15
x-x^2=x^2+x-15-x^2 (subtract x^2 from both sides)
-x^2+x=x-15
-x^2+x-x=x-15-x (subtract x from both sides)
-x^2=-15
-x^2/-1=-15/-1 (divide both sides by -1)
x^2=15
square root both sides
x=√15 or x=-√15
Possibility two:
x=(-x^2+x-15)
x=-x^2-x+15 (simplify)
x-(-x^2-x+15)=-x^2-x+15-(-x^2-x+15) (subtract both sides by -x^2-x+15)
x^2+2x-15=0
(x-3)(x+5)=0 (factor left side of equation)
x-3=0 or x+5=0 (set factors equal to 0)
x=3 or x=-5
At a football game, 35% of people attending were supporting the home team, while 65% were supporting the visiting team. If 455 people attending the game supported the home team, what was the total number of people attending the game?
Answer:
1300 ppl
Step-by-step explanation:
35% = .35 in decimal
.35 x =455
x = 455/.35 = 1300 ppl
calculate the height of a cuboid with the following dimension a length is equal to 10 cm, height is equal to 5.5 cm, volume is equal to 385cm³
Volume is a three-dimensional scalar quantity. The height of the cuboid is 7 cm.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
Given the volume of the cuboid is 385cm³, the length of the cuboid is 10cm, while the width of the cuboid is 5.5 cm, therefore, the height of the cuboid is,
385cm³ = 10cm × 5.5cm × H
H = 385cm³/(10cm×5.5cm)
H = 7cm
Hence, the height of the cuboid is 7 cm.
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I need help finding the answer to this
Answer:
Step-by-step explanation:
Remark
If the figures are similar then this is a proportion question. A proportion is 2 equation ratios. The ratios can have at most 1 unknown.
Givens
DC = 7
ML = 4.9
AB = 4
JK = x
Equation
DC/ML = AB/x Substitute values into equation and solve
Solution
7/4.9 = 4/x Cross Multiply
7x = 4 * 4.9 Combine the right.
7x = 19.6 Divide by 7
7x/7 = 19.6/7
x = 2.8
Answer
x = 2.8
150 inches equals how many feet and inches?
Answer:
12 feet and 6inches ..................
Answer:
12 feet and 6 inches
Step-by-step explanation:
Round your answer to the nearest hundredth.
If two samples are drawn randomly from the same population and sample A has n=350 and sample B has n=500, which sample will have a larger standard error of the mean?
Group of answer choices
Sample B
Sample A
The standard errors will be the same
Reason:
The standard error of the mean has the formula [tex]\frac{\sigma}{\sqrt{n}}[/tex] where [tex]\sigma[/tex] (greek letter sigma) is the standard deviation and n is the sample size.
As n gets bigger, the standard error [tex]\frac{\sigma}{\sqrt{n}}[/tex] gets smaller, and vice versa. This assumes sigma is fixed. A larger sample indicates the error goes down to narrow in better on the population mean.
Based on what I mentioned, this tells us that sample A has the larger standard error since n = 350 is smaller than n = 500 for sample B.
Which expression is equal to 45 x 47 ÷4-²?
Where does the energy stored in coal originally come from?
A. The Earth's Core
B. Minerals
C. The Sun
D. Radioactive material in the crust
Answer:
C . The sun
plants absorb light which make carbohydrates which makes a part of bodies of animals and plants . When they die this compound in their bodies which later became coal
Find the indicated side of the
triangle.
Answer:
[tex]\huge \orange{b = \boxed{ 6} \sqrt{ \boxed{3}} }[/tex]
Step-by-step explanation:
[tex]a = 12 \sin 30 \degree \\ \\ \implies \: a = 12 \times \frac{1}{2} \\ \\ \implies \: \huge \red{ a = 6} \\ \\ b = 12 \cos 30 \degree \\ \\ \implies \: b = 12 \times \frac{ \sqrt{3} }{2} \\ \\ \implies \: b = 6 \times \sqrt{3} \\ \\ \implies \: \huge \orange{b = \boxed{ 6} \sqrt{ \boxed{3}} }[/tex]
Identify the equation of direct variation given that y varies directly with x. y is 75 when x is 5.
Answer:
y = 15x
Step-by-step explanation:
The equation for direct variation is ...
y = kx
where k is the constant of proportionality.
__
We can find k by dividing by x:
y/x = k
Using the given values, we find it to be ...
75/5 = k = 15
Using this value of k in the equation, we find the equation of direct variation is ...
y = 15x
The expression (cos 60°)(cos 30°) − (sin 60°)(sin 30°) can be rewritten as which of the following?
sin 30°
sin 90°
cos 30°
cos 90°
Answer:
cos 90°
Step-by-step explanation:
(cos 60°)(cos 30°) − (sin 60°)(sin 30°)
= cos ( 60° + 30°)
= cos 90°
The expression (cos 60°) (cos 30°) − (sin 60°) (sin 30°) is cos 30°.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = Perpendicular / Hypotenuse
Cosec = Hypotenuse / Perpendicular
Cos x = Base / Hypotenuse
Sec x = Hypotenuse / Base
Tan x = Perpendicular / Base
Cot x = Base / Perpendicular
We have,
(cos 60°)(cos 30°) − (sin 60°)(sin 30°)
We can use the trigonometric identity for the difference of angles between cosines.
cos(x - y) = cos(x)cos(y) - sin(x)sin(y)
By setting x = 60° and y = 30°.
So,
cos(60° - 30°) = (cos 60°)(cos 30°) − (sin 60°)(sin 30°)
cos 30° = (cos 60°) (cos 30°) − (sin 60°) (sin 30°)
Thus,
(cos 60°) (cos 30°) − (sin 60°) (sin 30°) is cos 30°.
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do a and b have the same value in the equations 2(a-1.1)=5.8 and 5/2b-2 3/4=7 1/4
Answer:
YesStep-by-step explanation:
Solve each equation and compare the solutions
1.
2(a - 1.1) = 5.8a - 1.1 = 5.8/2a - 1.1 = 2.9a = 2.9 + 1.1a = 42.
(5/2)b - 2 3/4 = 7 1/42.5b = 7 1/4 + 2 3/42.5b = 10b = 10/2.5b = 4Both a and b have same value
Answer:
Yes, a and b have the same value in the given equations.
Step-by-step explanation:
Equation 1
[tex]2(a-1.1)=5.8[/tex]
[tex]\implies 2a-2.2=5.8[/tex]
[tex]\implies 2a-2.2+2.2=5.8+2.2[/tex]
[tex]\implies 2a=8[/tex]
[tex]\implies \dfrac{2a}{2}=\dfrac{8}{2}[/tex]
[tex]\implies a=4[/tex]
Equation 2
[tex]\dfrac{5}{2}b-2\frac{3}{4}=7 \frac{1}{4}[/tex]
[tex]\implies \dfrac{5}{2}b-\dfrac{2 \times 4+3}{4}=\dfrac{7 \times 4+1}{4}[/tex]
[tex]\implies \dfrac{5}{2}b-\dfrac{11}{4}=\dfrac{29}{4}[/tex]
[tex]\implies \dfrac{5}{2}b-\dfrac{11}{4}+\dfrac{11}{4}=\dfrac{29}{4}+\dfrac{11}{4}[/tex]
[tex]\implies \dfrac{5}{2}b=\dfrac{40}{4}[/tex]
[tex]\implies \dfrac{5}{2}b=10[/tex]
[tex]\implies 2 \cdot \dfrac{5}{2}b=2 \cdot 10[/tex]
[tex]\implies 5b=20[/tex]
[tex]\implies \dfrac{5b}{5}=\dfrac{20}{5}[/tex]
[tex]\implies b=4[/tex]
Conclusion
As a = 4 and b = 4, the two variables have the same value in the given equations.
Which expression is equivalent to the expression shown?
7
71 7²
2
16
7
1'
712
7¹⁴÷7²
= 7¹⁴-²
=7¹²
hope this helps:)
Select the correct answer. Which expression is equivalent to the given expression? √150
Answer:
5√6
Step-by-step explanation:
√25 x 6
√25 x√6
5√6
hey can anyone help find the missing measurement pls
Answer:
? ≈ 6.5 yd
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here A = 13.3 and h = 4.1 , then
[tex]\frac{1}{2}[/tex] × 4.1b = 13.3 ( multiply both sides by 2 to clear the fraction )
4.1b = 26.6 ( divide both sides by 4.1 )
b = ? ≈ 6.5 yd ( to the nearest tenth )
Question 4 please, Thanks!
Answer:
the probability is 1.01
