Answer:
Number of terms: n=6
Step-by-step explanation:
We are given:
a₁ = 0.75
r = 4
Sₙ = 1023.75
We need to find number of terms i.e n
The formula used will be:[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]
Putting values and fining n
[tex]S_n=\frac{a(r^n-1)}{r-1}\\1023.75=\frac{0.75(4^n-1)}{4-1}\\ 1023.75=\frac{0.75(4^n-1)}{3}\\3\times 1023.75=0.75(4^n-1)\\3071.25=0.75(4^n-1)\\4^n-1=\frac{3071.25}{0.75}\\4^n-1=4095\\4^n=4095+1\\4^n=4096[/tex]
We know that [tex]4^6= 4096[/tex]
[tex]4^n=4^6[/tex]
Using Exponent rule: [tex]a^n=a^b => n=b[/tex]
[tex]n=6[/tex]
So, Number of terms: n=6
Find all values of $x$ such that $\sqrt{4x^2} - \sqrt{x^2} = 6$.
9514 1404 393
Answer:
x = -6 or 6
Step-by-step explanation:
The square root is always positive, so the equation simplifies to ...
[tex]\sqrt{4x^2}-\sqrt{x^2}=6\\\\2|x|-|x|=6\\\\|x|=6\\\\x=\{-6,\ 6\}[/tex]
_____
The graph shows the solutions to f(x) = 0, where f(x) = √(4x²) -√(x²) -6.
can someone help me plz
Answer: The answer is 1 and 2/3
Hope this helps you bye
Find the explicit formula for the given sequence 1/4, 3/4, 5/4, 7/4
Step-by-step explanation:
d=(3/4)-(1/4)=(5/4)-(3/4)=(7/4)-(5/4)=1/2
then it is an arithmetic sequence
by using this equation :
a(n) = a1 +(n-1)d
and we have : a1=(1/4), d=(1/2)
So:
Explicit formula: a(n) = (1/4) +(n-1)*(1/2)
hope this helps
Answer:
Step-by-step explanation:
d=(3/4)-(1/4)=(5/4)-(3/4)=(7/4)-(5/4)=1/2
then it is an arithmetic sequence
by using this equation :
a(n) = a1 +(n-1)d
and we have: a1=(1/4), d=(1/2)
So:
Explicit formula: a(n) = (1/4) +(n-1)*(1/2)
Scientists released 6 rabbits into a new habitat in year 0. Each year, there were four times as many rabbits as the year before. How many rabbits were there after x years?
Answer: 6 × 4^x
Step-by-step explanation:
From the question, we are told that scientists released 6 rabbits into a new habitat in year 0 and that each year, there were four times as many rabbits as the year before.
The number of rabbits there after x years will be:
= 6 × 4^x
For example, let us say we want to calculate the number of rabbits after 2 years.
= 6 × 4^x
= 6 × 4²
= 6 × 16
= 96 rabbits
Calculate the square root of 1/2
Answer:
I looked it up and it said 0.5
your aunt and uncle have been visiting at your home. five minutes after they drive away, you realize that they forgot their luggages you happen to know the drive slowly, so you get in your car and drive to catch up with them. Your average speed is 10 miles and hour faster that their average speed, and you catch up with them in 25 minutes. How fast did you drive.
When you catch up, the distance traveled is the same
Distance = rate x time
r = uncle's rate
30 min = 30/60 hr = uncle's time
25 min = 25/60 hr = your time
Uncle's distance = Your distance
(r)(30/60) = (r + 10)(25/60)
(r)(1/2) = (r + 10)(5/12)
r/2 = 5r/12 + 50/12
6r = 5r + 50
r = 50
Uncle's rate = 50 mph
Your rate = 50 + 10 = 60 mph
Jon went to a restaurant and gave a 20% gratuity of $15 on the meal. How much was the original amount of the bill?
Answer:
$75
Step-by-step explanation:
$15 divided by 0.2 = $75
0.2 = 20%
If you can answer that would be nice, thank you.
What type of angle is shown here?
Answer:
I would say Acute. The angle is definitely less than a right angle. Reflex angles are angles more than 180 degrees, but less than 360 degrees.
What is an adjective that starts with t and means sweet? Okay, here's context, I'm making a u s e r n a m e, and one of the adjectives is "taro" If not, what are just some good u s e r n a m e s
Treat
The question confuses me but treat starts with t, is an adjective, and rhymes with sweet
which could describe the graph of a nonproportional relationship
A- the Y - intercept is positive
B- the y-intercept is 0
C- the line intersects the origin
D- the y- intercept is negative
Luis wants to buy a skateboard that usually sells for $80. All merchandise is discounted 20%.
What is the total cost of the skateboard if Luis has to pay a state sales take of 6%?
Answer: $68.80
Step-by-step explanation: the discount is 14% because it is subtracted from 20% and 0.14 x 80 is 68.80 hope this helps
please help meee i dont know what i have to do
please help it is due today
Answer:
4 2/5 tons
Step-by-step explanation:
2/5 = 4/10 = .40
4.40 tons > 4.3 tons
.........answer this for me plz ill give brainliest
Answer:
I think I donot say it is correct only peridect 4cm*4cm*3cm*8cm=384cm
Answer:
18
Step-by-step explanation:
area of the square-->12
area of the triangle--->6
area of the square + area of the triangle = area of the trapezoid
12+6=area of the trapezoid
18 = area of the trapezoid
What is the approximate circumference of the circle shown below?
A. 48.7 cm
B. 24.3 cm
C. 97.3 cm
D. 39.5 cm
Answer:
The answer is A. 48.7
Step-by-step explanation:
The approximate circumference of the circle is,
⇒ C = 48.7 cm
What is mean by Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
We have to given that;
A circle is shown in image.
And, Diameter of circle = 15.5 cm
Since, WE know that;
Circumference of circle is,
C = πd
Where, d is diameter of circle
Hence, The approximate circumference of the circle is,
⇒ C = 3.14 × 15.5
⇒ C = 48.7 cm
Thus, the circumference of the circle is,
⇒ C = 48.7 cm
Learn more about the circle visit:
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Bentley took a ride on Rudolph’s back. At 8:00 pm, he counted 68 stars. At 10:00 pm, he counted twice as many stars. At 12:00 am, he counted five times more stars than his first count.
A. How many stars did Bentley count at 10:00 pm?
B. How many stars did Bentley count at 12:00 am?
Answer:
A. 136 stars
B. 340 stars
Answer:
At 10 pm he counted 136 stars and at 12 pm he counted 340
Step-by-step explanation:
for 10 pm:
68 x 2
for 12 pm:
68 x 5
Cho is making a rectangular garden, where the length is x feet and the width is 6x + 6 feet. He wants to add garden stones around the perimeter of the garden once he is done. If the garden is 6 feet long, how many feet will Cho need to cover with garden stones? Cho will need to cover _______ feet with garden stones.
Solve the system of equations using substitution.
y = −2x + 1
4x + 2y = −2
No solution
Infinitely many solutions
(0, −4)
(−4, 0)
Answer:
no solution
Step-by-step explanation:
x cancel out each other
Answer:
no solution
Step-by-step explanation:
A plane is flying at an elevation of 1000 feet, directly above a straight highway. Two cars on the highway are on different sides of the plane. The angle of depression to one car is 10 degrees and to the other car is 8 degrees. How far apart are the cars, to the nearest foot
Answer:
Step-by-step explanation:
A study by Great Southern Home Insurance revealed that none of the stolen goods were recovered by the homeowners in 80 percent of reported thefts: [ 6 marks] a. During a period in which 200 thefts occurred, what is the probability that no stolen goods were recovered in 170 or more of the robberies? b. During a period in which 299 thefts occurred, what is the probability that no stolen goods were recovered in 150 or more robberies?
Solution :
Given :
n = 200, p = 80% = 0.8, q = 1 - p = 0.2
[tex]$\mu = np$[/tex]
[tex]$= 200 \times 0.8 = 160$[/tex]
[tex]$\sigma= \sqrt{npq}$[/tex]
[tex]$\sigma= \sqrt{200 \times 0.8 \times 0.2}$[/tex]
= 5.6569
a). x = 169.5
∴ [tex]$z = \frac{x- \mu}{\sigma}$[/tex]
[tex]$z = \frac{169.5- 160}{5.6569}$[/tex]
= 1.6794
[tex]$P(x \geq 170) = P(z>1.6794) = 0.0465$[/tex]
Therefore, probability that the stolen goods were not recovered in 170 robberies or more is = 0.0465
b). x= 149.5
[tex]$z = \frac{x- \mu}{\sigma}$[/tex]
[tex]$z = \frac{149.5- 160}{5.6569} = -1.8561$[/tex]
[tex]$P(x \geq 150) = P(z>-1.8561) = 0.9683$[/tex]
Therefore the probability that the stolen goods were not recovered in the 150 or in more robberies is = 0.9683
Gas mileage is the number of miles you can drive on a gallon of gasoline. A test of a new car shows it can drive 370 miles on 20 gallons of gas. How far could you drive on 65 gallons of gas?
Answer:
1202.5 miles
Step-by-step explanation:
It is given that.
A test of a new car shows it can drive 370 miles on 20 gallons of gas.
We need to find how far you could drive on 65 gallons of gas.
20 gallons of gas = 370 miles
1 gallon = 18.5 miles
For 65 gallons of gas, multiply 65 and 18.5.
65 gallons = 18.5 × 65 miles
= 1202.5 miles
Hence, 1202.5 miles you could drive on 65 gallons of the gas.
If a snowman has 3 old felt hats and 4 scarves from which to choose, how many different hat/scarf outfits can he wear?
Answer:
12 hat/scarf outfits
Step-by-step explanation:
If a snowman has 3 old felt hats and 4 scarves from which to choose, how many different hat/scarf outfits can he wear?
We solve this question using the fundamental counting principle.
This states that:
When we have two events, a and bthe number of ways both events can happen is a × b
From the above question, our two events is
a = 3 old felt hats
b = 4 scarves
Hence, the different hat/scarf outfits can he wear is given as
3 × 4 = 12 hat/scarf outfits
On mercury, the distance d (in feet) that an object falls in time t(in seconds) can be modeled by the function f(t)=6t^2. how long would it take an object to fall 54 feet on Mercury. ( plz show the work on how u got the answer)
Answer: t=3.75
Step-by-step explanation:45=6t×2
6t=22.5
t=3.75
The object will take 3 seconds to fall 54 feet on Mercury according to the given function f(t) = 6t².
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
A function can be regarded as a computer, which is helpful.
Given the function,
f(t) = 6t² where t is time in seconds while f(t) is the distance in feet.
At f(t) = 54 feet
6t² = 54
t² = 54/6 = 9
t = 3 seconds
Hence "The object will take 3 seconds to fall 54 feet on Mercury according to the given function f(t) = 6t²".
For more about the function,
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Question #3: Complete the statement below to show the correct value of 100%. Part A: The expression 100 3 = 10 because 100 = 102 and = 101 = 10. Po Part B: When simplified, the answer is rational irrational
Answer:
Step-by-step explanation:
Part A.
Expression [tex](100)^{\frac{1}{2}}[/tex] = 10
Because 100 = [tex](10)^{2}[/tex] and [tex][(10)^2]^{\frac{1}{2}}=10^1=10[/tex]
[Since, [tex](a^{2})^{\frac{1}{2}}=a^{2\times \frac{1}{2}}=a^1[/tex]]
Part B.
When simplified, the answer is RATIONAL.
[Since, 10 can be written as [tex]\frac{10}{1}[/tex]]
16x2 + 4x2 – 2x – 12x2 + 4x
Answer:
8x^2 + 2x
Step-by-step explanation:
Here are the prices of some items and the amount of sales tax charged on each in Nevada. row 1 cost of item ($) sales tax ($) row 2 10 0.46 row 3 50 2.30 row 4 5 0.23 What is the sales tax rate in Nevada
Answer:
4.6%
Step-by-step explanation:
Cost of item __ sales tax
10 ___________0.46
50 __________ 2.30
5 ___________ 0.23
To obtain the sales tax % :
Sales tax % * cost of item = amount of sales tax
Let sales tax % = x
Using any of the rows in the table :
x * 10 = 0.46
x = 0.46 / 10
x = 0.046
x = (0.046) * 100% = 4.6%
Which point on the graph represents they-intercept
Answer:
Where's the graph kid sir?
Step-by-step explanation:
Answer:
The y-intercept on a sloped line is where the line crosses the y-axis. Taking a look at your graph, Find a point where the line crosses the y-axis.
PLS HELP DUE AT 11:59 AND I MISSED THE LESSON ON THIS
Answer:
try -14!
Step-by-step explanation:
4x+188=6x+216
x=-14
Answer:
x = -14
Step-by-step explanation:
To start since the angles are congruent then they must be equal to each other, so we start by setting them equal to each other. The equation will be 4x + 188 = 6x + 216
Next we solve for x, subtracting 188 and 6x from each side. The new equation will be
-2x = 28
Then divide both sides by negative 2 to get x = -14.
5.5.5.5.5.5. in expanded form
Answer:
You can't even do that I'm pretty sure
Step-by-step explanation: Too many decimals points
Classify the special quadrilateral.
Answer: Rhombus
=====================================================
Explanation:
The tickmarks show that all four sides are the same length. Therefore, this figure is a rhombus. It is not a square because the angle would need to be 90 degrees. We can say it is a non-square rhombus, or a rhombus that isn't a square. It is also not a rectangle either because all rectangles have each angle at 90 degrees.