Answer:
3025
Step-by-step explanation: Add the first five square numbers together then square that.
1²+2²+3²+4²+5² = 55
55² = 3025
Choose the correct simplification of the expression f4 • f8. f2 f4 f12 f32
Answer:
f^12
Step-by-step explanation:
f^4 * f^8
We that a^b * a^c = a^(b+c)
f^(4+8)
f^12
Hello!
We have the following expression:
[tex]\bf{f^4*f^8}[/tex]
Recall the Properties of Exponents:
[tex]\bold{a^ma^n=a^{m+n}}[/tex]
According to the property, if we have the same bases multiplied together, then we just add their exponents:
[tex]\bf{f^4f^8=f^{4+8}}[/tex]
Simplify:
[tex]\bf{f^{12}}[/tex]
Hope everything is clear.
Let me know if you have any questions!
[tex]\rule{2}{2}[/tex]Knowledge is Power!
Devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%. Its current value is $2,000. The equation mc025-1. Jpg represents the situation, where t is the age of the car in years and r is the rate of depreciation. About how old is Devon’s car? Use a calculator and round your answer to the nearest whole number. 1 year 2 years 5 years 8 years.
The age of the car that Devon purchased is given by: Option C: 5 years
How to calculate compound interest's amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:
[tex]CI = P(1 +\dfrac{R}{100})^T - P[/tex]
The final amount becomes:
[tex]A = CI + P\\A = P(1 +\dfrac{R}{100})^T[/tex]
We can use compound interest's formula (with a bit modification if necessary) whenever there is compounding on a base amount on some fixed rate for some time.
For this case, there is decrement happening, so rate can be taken negative. Thus, we take:
R = -35%
Let the car is T years old.
Then, as we have: Initial price of the car = P = $16000, and the final price of the car = A = $2000, thus, we get:
[tex]A = P(1 +\dfrac{R}{100})^T\\\\2000 = 16000(1 + (-35/100) )^T\\1/8 = (1-0.35)^T\\0.125 = 0.65^T\\\\T = log_{0.65}(0.125)\\T \approx 4.827 \approx 5 \text{ (in years) }[/tex]
Thus, the age of the car that Devon purchased is given by: Option C: 5 years
Learn more about compound interest here:
https://brainly.com/question/11897800
Answer:
C 5 years
Step-by-step explanation:
What is the resulting equation when the expression for y in the second equation is substituted into the first equation?
3x + y = 1
y=6 - 4x
Ox+6y=1
Ox+6=1
Ox -X + 6 = 1
7X+6=1
Hello!
Let's solve this question with the information given to us in the question.
We were given two equations:
3x + y = 1
y = 6 - 4x
The question asks us to plug in our 2nd equation into the "y" variable of the first equation.
Plug in and solve:
3x + y = 1
Substitute "6 - 4x" for y
3x + 6 - 4x = 1
Simplify
-x + 6 = 1
Therefore, your answer would be the -x + 6 = 1 choice in your answer box.
Answer: -x + 6 = 1
In the diagram below,EF is parallel to BC. IF BC is the twice length of ED,BD=36 and EF=14, find the length of ED. Figure are not necessary drawn to scale. State your answer in simplest ratio form if necessary.
Answer: sqrt(182)
Step-by-step explanation:
Math homework pls help!!!
Answer:
17.8
Step-by-step explanation:
The power ands the square root cancel out.
A circle has a radius of 5.4 m. what is the exact length of an arc formed by a central angle measuring 60°? enter your answer in the box. express your answer using π . m
The length of the arc of the circle with a radius of 5.4 m and the central angle measuring 60° is 5.655 meters.
What is the Length of an Arc?The length of an arc is given by the formula,
[tex]\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360}[/tex]
where
θ is the angle, which arc creates at the centre of the circle in degree.
The length of the arc of the circle with a radius of 5.4 m and the central angle measuring 60° can be written as
[tex]\text{Length of the Arc} = 2\pi r \dfrac{\theta}{360}[/tex]
[tex]= 2 \times \pi \times 5.4 \times \dfrac{60}{360}\\\\=5.655\rm\ m[/tex]
Hence, the length of the arc of the circle with a radius of 5.4 m and the central angle measuring 60° is 5.655 meters.
Learn more about Lenght of the Arc:
https://brainly.com/question/1577784
A flower pot is approximately in the shape off a cylinder. The diameter is 10 inches and the height is 6 inches. Find the surface area off the flower pot round to the nearest inch
The surface area of the cylindrical flower pot to the nearest inch is equal to [tex]346\;in^2[/tex]
Given the following data:
Diameter = 10 inches.
Height = 6 inches.
Radius = [tex]\frac{diameter}{2} =\frac{10}{2}[/tex] = 5 inches.
How to calculate surface area.Mathematically, the surface area (SA) of a cylinder is given by this formula:
[tex]S.A = 2\pi rh + 2\pi r^2[/tex]
Where:
h is the height.r is the radius.Substituting the given parameters into the formula, we have;
[tex]S.A = 2\pi (5)(6) + 2\pi (5)^2\\\\S.A =188.52+157.1 \\\\S.A = 345.62\\\\S.A=346\;in^2[/tex]
Read more on surface area here: brainly.com/question/21367171
Bill went on a very long run, so he ran kind of slowly. He ran 2 miles in 30 minutes. How many miles would he run in three hours?
Answer:
12 miles
Step-by-step explanation:
There are 3 hours = 180 minutes
180÷30=6
6×2=12
Hope that helps!
Answer:
12 miles
Step-by-step explanation:
A pharmaceutical company has developed a new drug for people with psoriasis, a skin condition. Researchers would like to estimate the proportion of users who saw improvement in their skin after using the drug. Let p represent the true proportion of users whose skin improved. Which of the following is the smallest number of users the researchers can survey to guarantee a margin of error of 0.05 or less at
the 99% confidence level? (Use p^ = 0.5)
a. 600
b. 650
c. 700
d. 750
======================================================
Explanation:
At 99% confidence, the z critical value is roughly z = 2.576 which is found using a Z table.
We're given that [tex]\hat{p} = 0.5[/tex] as the sample proportion and E = 0.05 is the desired error.
The min sample size n is:
[tex]n = \hat{p}*(1-\hat{p})\left(\frac{z}{E}\right)^2\\\\n \approx 0.5*(1-0.5)\left(\frac{2.576}{0.05}\right)^2\\\\n \approx 663.5776\\\\n \approx 664\\\\[/tex]
Always round up to the nearest integer.
Unfortunately n = 664 isn't one of the answer choices. The next closest value is 700. It appears that your teacher wants to know a valid sample size that is the smallest of the answer choices, not necessarily the smallest ever possible.
How much does it cost to buy 3 watering cans if each watering can costs $7.48?
Answer:
$22.44
Step-by-step explanation:
We can multiply the total number of watering cans being bought by the total cost of one watering can.
3 * 7.48 = 22.44
It will cost $22.44 to buy three watering cans.
Sketch the graph of the function y=3 sin(2x)-1
Function: y = 3sin(2x) - 1
Find y-intercept:
y = 3sin(2x) - 1y = 3sin(2(0)) - 1y = -1Formula for minimum: m = A ‐ |B|
Minimum:
-1 - |3|-4=========
When y = -4
3sin(2x) - 1 = -43sin(2x) = -3sin(2x) = -12x = sin⁻¹(-1)2x =-450°, -90°, 270°, 630°x = -225°, -45°, 135°, 315°Formula for maximum: M = A + |B|
Maximum:
-1 + |3|2=========
When y = 2
3sin(2x) - 1 = 2sin(2x) = 12x = sin⁻¹(1)2x = -630°, -270°, 90°, 450°x = -315°, -135°, 45°, 225°Now we can plot the graph for the equation in range of -360° < x < 360°
For more graphing problems: brainly.com/question/27117441
Answer:
[tex]y=A\sin(B(x+C))+D[/tex]
Amplitude = A
The height from the center line to the peak (or trough).
Period = (2π)/B
The horizontal distance from one peak to the next.
Phase shift = C
How far the function is shifted horizontally from its usual position.
(positive is to the left, negative is to the right).
Vertical shift = D
How far the function is shifted vertically from its usual position.
Parent function:
[tex]y=\sin(x)[/tex]
Therefore:
Amplitude = 1Period = 2πPhase shift = noneVertical shift = noneGiven function:
[tex]y=3\sin(2x)-1[/tex]
[tex]y=3\sin(2(x+0))-1[/tex]
Therefore:
Amplitude = 3Period = πPhase shift = noneVertical shift = -1**See attached images for how the parent function is transformed to the final function**
help pls
ty in advance
[tex]\bold{\huge{\underline{ Solution\: 2 }}}[/tex]
The name of the circle is IJKLThe name of central Angle[tex]\sf{\underline{= {\angle} IHJ }}[/tex]The name of the secant = KL[tex]{\bigstar}[/tex]Circle :- It is a round figures, which has no end points.
[tex]{\bigstar}[/tex] Central angle :- It the angle ,which lie in the middle of the circle.
Here, H is the mid point of the circle .So, Angle IHJ is the central angle.[tex]{\bigstar}[/tex] Secant :- A line drawn in circle in such a way that it intersect the circle from two distinct points. Then, It is called secant .
Here, KL is the line which acts as a secant because it intersect the circle from point K and point L.[tex]\bold{\huge{\underline{ Solution\: 3 }}}[/tex]
Semicircle = FGH and FIH Minor Arc :- FG or GH Major Arc :- FHG or GFH[tex]{\bigstar}[/tex] Semicircle :- Semicircle is nothing but the half of the circle.
Here, In second diagram
FGH and FIH are acting as two semicircles which simulatineously forming one circle.[tex]{\bigstar}[/tex] Minor Arc :- Minor Arc is nothing but the smaller arc of the circle and it is always smaller than the half of the circle that is semicircle.
Here,
FG or GH are the minor arc of the given circle.[tex]{\bigstar}[/tex] Major Arc :- Major Arc is nothing but the largest arc of the circle and it is always larger than the half of the circle that is semicircle.
Here,
FHG or GFH is the major arc as it is larger than the semicircle of the given circle .if f(x)=4x^2-3 and g9x)=x+1, find (f-g)(x)
Step-by-step explanation:
(f-g)(x) = f(x) - g(x)
the same applies to all other basic operations (like addition, multiplication, ...).
so,
(f-g)(x) = 4x² - 3 - (x + 1) = 4x² - 3 - x - 1 = 4x² - x - 4
A swimmer speeds up 1.9 m/s to 3.8 m/s during the last 11.0 seconds of the race. What is the acceleration of the swimmer?
Initial speed (v) = 1.9m/s
Final speed (u) = 3.8m/s
Time (t) = 11 s
Formula Used :-[tex]v = u + a×t [/tex](a = acceleration)
➾ [tex]a = {\frac{u-v}{t}}[/tex]
Solution:-[tex]a = {\frac{u-v}{t}}[/tex] (putting the value of v, u and t from above)
➾ [tex]a = {\frac{3.8-1.9}{11}}[/tex]
➾ [tex]a = {\frac{1.9}{11}}[/tex]
➾ [tex]a = 0.17 m/s (approx.)[/tex]
Therefore, the acceleration rate = 0.17m/s.
Maura is jogging on her treadmill. She runs 2.25 miles in
1
2
of an hour. At that speed, how many miles could Maura run in 1
1
2
hours?
Answer:
6.75 miles
Step-by-step explanation:
Since it is 2.25 per 1/2 hour to get to 1 1/2 hour you multiply by 3. Then you do 2.25 times 3 and it gives you 6.75 miles.
hope that helps
Answer:
6.75 miles
Step-by-step explanation:
How many 1/2 hours in 1 1/2 hour? 1.5 ÷ 0.5 = 3
2.25 x 3 = 6.75
OR
Find the unit rate = 2.25 x 2 = 4.50 (we multiply it by 2 because there 2 half hours in an hour)
4.50 x 1.50 = 6.75
what is (5.03x -8.03) - (3.5x +6.2)?
Answer:
1.53x−14.23
Step-by-step explanation:
simplify:
5.03x−8.03−(3.5x+6.2)
Distribute the Negative Sign:
=5.03x−8.03−1(3.5x+6.2)
=5.03x−8.03−1(3.5x)+(−1)(6.2)
=5.03x−8.03−3.5x−6.2
Combine Like Terms:
=5.03x−8.03+−3.5x−6.2
=(5.03x−3.5x)+(−8.03−6.2)
=1.53x−14.23
(5.03x -8.03) - (3.5x +6.2)=
Petra and jonhah are going on holiday to Poole
Petra buys 3 new shirts for her holiday
each shirt cost 9pound
how much does Petra pays in total
another one
Petra and Jonah has this information
home to the train station. 12 minutes
train to Poole 47 minutes
jonah says it will take less that 60 minutes in total to go from home to Poole.
Answer:
question one
one shirt cost=9pound
3 shirts=3*9=27pound
Im deseperate. Find x, y, and z such that x³+y³+z³=k, for each k from one to 100
Answer:
x = 1, y = -1, and z = 2
Please help 10 POINTS!!!
Step-by-step explanation:
[tex]y = 5x \\ y = 9x + 4 \\substitute \:y = 5x \: to \: the \: other \: equation \\ y = 9x + 4 \\5x = 9x + 4 \\ 5x - 9x = 4 \\ - 4x = 4 \\ x = \frac{4}{ - 4} \\ x = - 1[/tex]
PLS HELP ME 50 POINTS AND I WILL MARK THE BRAINLIEST
a kite is 50 m high when 200 m of sting is let out. what angle does the kite string make with the ground to the nearest tenth of a degree?
the angle between the kite string and the ground is ?
Check the picture below.
Make sure your calculator is in Degree mode.
How can you best describe a stop sign using polygons? The sign has sides, so it is. It appears to be because the sides and angles appear to be congruent.
The stop sign is an octagon or regular polygon.
It is given that a stop sign has 8 sides.
It is required to describe the sign using a polygon.
What is a polygon?It is defined as the flat planner geometry in two dimensions with a closed shape there are two types of polygon one is irregular in which the angle and sides are not equal and the second one is a regular polygon in which sides and angles are equal called regular polygon.
We have a stop sign that has 8 sides.
As we know the definition of a polygon they are planner geometry and in a regular polygon, the sides and angles are equal called regular polygon.
The stop sign has 8 if we assume they are all equal sides and angles then we can say that the stop sign is an octagon(in which the number of sides is 8) or a regular polygon.
Thus, the stop sign is an octagon or regular polygon.
Learn more about the polygon here:
https://brainly.com/question/17756657
Answer:
8, octagon, & regular
Step-by-step explanation:
I did it
Complete the description of what happens to a figure when the given sequence of transformations is applied to it: (x, y) + (-x,y); (x,y) → (0.4x, 0.4y);(x, y) + (x - 8, y + 8).
Reflection over the (x-axis/origin/y-axis); (transformation/translation/dilation/movement upwards) with a scale factor of 0.4; translation 8 units left and ___ units up.
Answer:
reflection over the y-axis; dilation with a scale factor of 0.4; translation 8 units left and 8 units upStep-by-step explanation:
ReflectionThe first transformation changes the sign of the x-coordinate. That means a point that was some number of units (3, for example) right of the y-axis will be transformed to a point 3 untis left of the y-axis. It is reflected across the y-axis.
__
DilationThe second transformation multiplies each coordinate value by 0.4. A point that was some number of units (3, for example) away from the origin, will be transformed to a point 3×0.4 = 1.2 units from the origin. It is dilated by a factor of 0.4.
__
TranslationThe third transformation subtracts 8 from the x-coordinate and adds 8 to the y-coordinate. The x-coordinate is a measure of the distance to the right of the y-axis, so subtracting 8 from the x-coordinate means the point is 8 fewer units to the right of the y-axis. It is translated left 8 units.
Similarly, the y-coordinate is a measure of the distance up from the x-axis. Adding 8 to the y-coordinate will move the point 8 more units up from the x-axis. It is translated up 8 units.
Please help! I am confused.
Answer:
z = 180°
Step-by-step explanation:
First, find the sum of the interior angles b using the following formula. S is sum and n is the number of sides.
S = (n-2)180
S = (6 - 2)180
S = (4)180
S = 720°
Next, make an equation adding all the interior angles and setting them equal to 720.
t + t + 2t + t + t + 2t = 720
8t = 720
8t/8 = 720/8
t = 90°
Finally, find the measure of angle z by substituting 90° for t.
z = 2t
z = 2(90)
z = 180°
8. Harper, Elie, and Raina are having a skateboard race. Harper began at the starting line and rode at a
constant rate of 3 feet per second. Elie got a five-foot head start and rode two feet every 3 seconds. Raina
rode 3 feet every five seconds and had a two-foot head start.
Answer:
Step-by-step explanation:
Clinton has a spinner labeled orange, blue, green and pink. He spins the spinner 100 times. He gets orange 33 times. What the experimental probability of him getting an orange? in fraction form
Explanation:
Divide the number of times orange shows up (33) over the number of total spins (100). Reduce the fraction if possible. In this case, 33/100 is fully reduced because 33 and 100 have no common factors other than 1.
Use PEMDAS to evaluate the expression 18 − 35 ÷ 5 + 4 x 8. ANSWERS: 37 40 43 46
PLSSS HELP IT WOULD MEAN A LOT TO ME
Answer:
43
Step-by-step explanation:
first we do 35/5=7 then 18-7=11. then 4*8=32. 32+11=43
Answer:
C. 43
Step-by-step explanation:
1. 35 ÷ 5 = 7
2. 4 x 8 = 32
3. 18 - 7 = 11
4. 11 + 32 = 43
Therefore the answer, is C. 43.
You're welcome! :)
What is the volume of the square pyramid?
Answer:
you can solve by using the formula
volume = length x width x height
(I'm also bad at math so sorry if this isn't very helpful)
Step-by-step explanation:
1 all the bases are the same which means your length and width should be 5m
2 just multiply 5 x 5 x 14.2 and that should give you the awnser
A cylinder has a base diameter of 16cm and a height of 20cm. What is its volume in cubic cm, to the nearest tenths place?
Answer:
4021.76
Step-by-step explanation:
v= πr^2h
3.142x8×8×20
HELPPPPPPPPPPPPPPPPPPPPPP
Answer:
(-3,8)
step by step explanation:
y=-4/3 +4
x=-3
put in x value in first Problem
y=-4/3(-3) +4
solve
y= 12/3+4
y=4+4
y=8
we already know what x is so
x= -3, y=8
(-3,8)
hope this helps