Recently, More Money 4U offered an annuity that pays 6.3% compounded monthly. If $1,986 is deposited into this annuity every month, how much is in the account after 8 years? How much of this is interest?
Answer:
[tex] A = 1986(1+ \frac{0.063}{12})^{12*8} =3283.153[/tex]
So then after 8 years we will have in the account 3283.153
And in order to find the interest we can do the following operation:
[tex] I = 3283.153 -1986 = 1297.153[/tex]
Step-by-step explanation:
For this case we can use the formula for the future value using compound interest given by:
[tex] A = P (1+ \frac{r}{n})^{nt}[/tex]
Where P= 1986 the initial amount invested. r = 0.063 represent the interest rate. n=12 represent the number of times that the rate is compounded in a year. And t =8 years . Replacing the info we got:
[tex] A = 1986(1+ \frac{0.063}{12})^{12*8} =3283.153[/tex]
So then after 8 years we will have in the account 3283.153
And in order to find the interest we can do the following operation:
[tex] I = 3283.153 -1986 = 1297.153[/tex]
help due timed !! help plss
Answer:
290 m
Step-by-step explanation:
3*6*5=90
5*5*8= 200
200+90=290
the base of a expoential function can be a negative number true or false
Answer:
This would be false
Step-by-step explanation:
Exponents can't be negative
Answer:
An exponential function can not be either 1, 0, or any negative number.
Asphere has a radius of 4 in. Which equation finds the volume of the sphere?
Answer:
[tex]V = \frac{4}{3} \pi r^{2}[/tex] - is the formula for the volume of a circle.
Step-by-step explanation:
Step 1:
- Insert your values:
- [tex]V = \frac{4}{3} \pi 4^{2}[/tex]
Step 2:
- Simplify using order of operations:
- Exponents First:
- [tex]V = \frac{4}{3} \pi 64[/tex]
- Division Second:
- [tex]V = 1.333 \pi 64[/tex]
- Multiplication Last:
- [tex]V = 268.01555[/tex]
- And Simplified:
- V = 268 (approx.)
Hope this helps! Good luck!
20% of US High School teens vape. A local High School has implemented campaigns to reduce vaping among students and believes that the percentage of students who vape at this High School is lower than the national average. School administration implements a survey of 300 randomly selected students. They find that 51 of the 300 vape.
If the true proportion of students who vape at this school is 20%, what is the approximate probability of observing 51 or fewer vapers in a random sample of 300?
Answer:
10.93% probability of observing 51 or fewer vapers in a random sample of 300
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 300, p = 0.2[/tex]
So
[tex]\mu = E(X) = np = 300*0.2 = 60[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{300*0.2*0.8} = 6.9282[/tex]
What is the approximate probability of observing 51 or fewer vapers in a random sample of 300?
Using continuity corrections, this is [tex]P(X \leq 51 + 0.5) = P(X \leq 51.5)[/tex], which is the pvalue of Z when X = 51.5 So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{51.5 - 60}{6.9282}[/tex]
[tex]Z = -1.23[/tex]
[tex]Z = -1.23[/tex] has a pvalue of 0.1093.
10.93% probability of observing 51 or fewer vapers in a random sample of 300
The main span of bridge A is 2500 is percent shorter than the main span of bridge B 4100
Answer:
16%
percentage is calculated by 100
A. 2500 × 1/100 = 25%
B. 4100 x 1/100 = 41%
41% - 25%
16%
therefore bridge A is 16% shorter than bridge B
which expression is equivalent p^6)2
So the right answer is p^12.
Look at the attached picture
Hope it will help you
Good luck on your assignment..
Answer:
[tex] {p}^{12} [/tex]
Step-by-step explanation:
[tex]( {p}^{6} ) ^{2} [/tex]
[tex]p ^{6 \times 2} [/tex]
[tex] {p}^{12} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
If MH = 18cm and HA = 29cm, what is MA?
Answer:
The leg MA measures 22.7 centimeters.Step-by-step explanation:
Assuming that's about a right triangle, the image attached shows a representation of this problem.
We use the Pythagorean Theorem to find the missing leg, which we are gonna call [tex]y[/tex]
[tex]29^{2} =18^{2}+y^{2}\\y^{2}=29^{2}-18^{2}\\y=\sqrt{841 - 324} \approx 22.7 \ cm[/tex]
Therefore, the leg MA measures 22.7 centimeters.
simplify the numerical expression
12-2³
Answer:
12-2³ = 12 - 8 = 4
Hope this helps!
:)
A file that is 278 megabytes is being downloaded. If the download is 19.9% complete, how many megabytes have been downloaded? Round your answer to the nearest tenth.
Answer:
55.3
Step-by-step explanation:
19.9% of 278 = 55.322
55.322 rounded to the nearest tenth = 55.3
Answer:55.3
Step-by-step explanation:
When Mustafa threw a beach ball to his friend, its horizontal velocity changed as it traveled through the air. The relationship between the elapsed time, tttt, in seconds, since Mustafa threw the ball, and its horizontal velocity, V(t)V(t)V(t)V, left parenthesis, t, right parenthesis, in cm/s\text{cm/s}cm/sstart text, c, m, slash, s, end text, is modeled by the following function: V(t)=4⋅(0.81)t Complete the following sentence about the percent change of the horizontal velocity of the ball. Every second, %\%%percent of horizontal velocity is the total horizontal velocity of the ball.
Answer:
The rate at which the horizontal velocity of the ball changes every second is, 19%.
Step-by-step explanation:
The exponential decay function is given by:
[tex]y=a(1-r)^{t}[/tex]
Here,
y = final value
a = initial value
r = decay rate
t = time
The relationship between the elapsed time, t, in seconds, since Mustafa threw the ball, and its horizontal velocity, V (t) is:
[tex]V(t)=4\cdot (0.81)^{t}[/tex]
The expression for the horizontal velocity of the ball represents the exponential decay function.
On comparing the two equations we get:
[tex]1-r=0.81\\r=1-0.81\\r=0.19[/tex]
Thus, the rate at which the horizontal velocity of the ball changes every second is, 19%.
Here is a Fill in the Gaps Question:
A prism is a three-______________ shape with the same _______________ all the way through.
Please help.
Jake :)
P.S you will get 40 pts :)
Answer:
A prism is a three-dimensional shape with the same cross-section all the way through.
Step-by-step explanation: Im not sure if i got the second right
A prism is a three-dimensional shape with the same cross-section all the way through.
A prism is a type of three-dimensional (3D) shape with flat sides. It has two ends that are the same shape and size (and look like a 2D shape).It has the same cross-section all along the shape from end to end; that means if you cut through it you would see the same 2D shape as on either end.
What is called prism?A prism has a solid shape consisting of two identical ends (such as triangle, square, rectangle, etc.), flat faces or surfaces and uniform cross-section across its length. The cross-section looks like a triangle hence called triangular prism. The shape of the prism does not have any curve.
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if a is a positive number then -a^6 is
Carl pays $45 per month for car insurance. How much does he spend on car insurance in 1 year?
Answer: 540
Step-by-step explanation: because if he pays 45 bucks a month and a year equals 12 then ya do 45x12 and ya get 540
Answer:
Carl spends $540 per year on car insurance
Step-by-step explanation:
Carl pays $45 per month. There are 12 months in 1 year.
All we need to do is multiply the rate per month by the number of months to get our answer.
[tex]45*12=540[/tex]
An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in fire control by the number of sprinklers that activate correctly. The researchers estimate the probability of a sprinkler to activate correctly to be 0.7. Suppose that you are an inspector hired to write a safety report for a large ballroom with 10 sprinklers. Assume the sprinklers activate correctly or not independently.
What is the probability that all of the sprinklers will operate correctly in a fire?
Answer:
2.82% probability that all of the sprinklers will operate correctly in a fire
Step-by-step explanation:
For each sprinkler, there are only two possible outcomes. Either they will operate correctly, or they will not. The probability of a sprinkler operating correctly is independent of other sprinklers. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The researchers estimate the probability of a sprinkler to activate correctly to be 0.7.
This means that [tex]p = 0.7[/tex]
10 sprinklers.
This means that [tex]n = 10[/tex]
What is the probability that all of the sprinklers will operate correctly in a fire?
This is P(X = 10).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{10,10}.(0.7)^{10}.(0.3)^{0} = 0.0282[/tex]
2.82% probability that all of the sprinklers will operate correctly in a fire
The probability that all sprinklers will operate correctly in a fire is 0.028
How to determine the probabilityThe given parameters are:
p = 0.7 ---- the probability that a sprinkler to activate correctly
n = 10 --- the number of sprinklers
The probability that all sprinklers activate correctly is calculated as:
[tex]P(10) = p^n[/tex]
So, we have:
[tex]P(10) = 0.7^{10[/tex]
Evaluate
[tex]P(10) = 0.028[/tex]
Hence, the probability that all sprinklers will operate correctly in a fire is 0.028
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In ΔIJK, the measure of ∠K=90°, KI = 3.8 feet, and JK = 6.7 feet. Find the measure of ∠I to the nearest degree.
Answer:
60
Step-by-step explanation:tanI=
adjacent
opposite
=
3.8
6.7
\tan I = \frac{6.7}{3.8}
tanI=
3.8
6.7
I=\tan^{-1}(\frac{6.7}{3.8})
I=tan
−1
(
3.8
6.7
)
I=60.44\approx 60^{\circ}
I=60.44≈60
∘
Where do you find your domain restrictions in a rational function?
Answer:
denominator zeros are excluded
Step-by-step explanation:
The domain is the set of values of the independent variable where the function is defined. A rational function is "undefined" where the denominator is zero.
The exclusions of interest are generally those values of the variable that make any denominator be zero.
__
Example:
f(x) = (2/(x-3)) / (4/(x -6))
has denominators of x-3 and x-6. These are zero for x=3 and x=6, so those two values are excluded from the domain of this function. We observe that the function can be simplified to ...
f(x) = (x -6)/(2(x -3))
but x=6 remains excluded from the domain because of its effect in the original function definition.
_____
Additional comment
If the rational function includes functions that have domain restrictions (such as square root, for example), then those restrictions apply as well.
Usually, but not always, the rational functions where you're asked about domain are the ratios of polynomials. So, you need to factor or otherwise find the zeros of any denominator polynomials in such functions.
Water is added to a cylindrical tank of radius 5 m and height of 10 m at a rate of 100 L/min. Find the rate of change of the water level when the water is 6 m deep. (1 L = 1000cm^3)
Answer:
[tex] V = \pi r^2 h[/tex]
For this case we know that [tex] r=5m[/tex] represent the radius, [tex] h = 10m[/tex] the height and the rate given is:
[tex] \frac{dV}{dt}= \frac{100 L}{min}[/tex]
[tex] Q = 100 \frac{L}{min} *\frac{1m^3}{1000L}= 0.1 \frac{m^3}{min}[/tex]
And replacing we got:
[tex] \frac{dh}{dt}=\frac{0.1 m^3/min}{\pi (5m)^2}= 0.0012732 \frac{m}{min}[/tex]
And that represent [tex] 0.127 \frac{cm}{min}[/tex]
Step-by-step explanation:
For a tank similar to a cylinder the volume is given by:
[tex] V = \pi r^2 h[/tex]
For this case we know that [tex] r=5m[/tex] represent the radius, [tex] h = 10m[/tex] the height and the rate given is:
[tex] \frac{dV}{dt}= \frac{100 L}{min}[/tex]
For this case we want to find the rate of change of the water level when h =6m so then we can derivate the formula for the volume and we got:
[tex] \frac{dV}{dt}= \pi r^2 \frac{dh}{dt}[/tex]
And solving for [tex]\frac{dh}{dt}[/tex] we got:
[tex] \frac{dh}{dt}= \frac{\frac{dV}{dt}}{\pi r^2}[/tex]
We need to convert the rate given into m^3/min and we got:
[tex] Q = 100 \frac{L}{min} *\frac{1m^3}{1000L}= 0.1 \frac{m^3}{min}[/tex]
And replacing we got:
[tex] \frac{dh}{dt}=\frac{0.1 m^3/min}{\pi (5m)^2}= 0.0012732 \frac{m}{min}[/tex]
And that represent [tex] 0.127 \frac{cm}{min}[/tex]
What is the distance between A(-8, 4) and B(4, -1)?
Answer:
10.908
Step-by-step explanation:
The diagram shows 2 different shapes ...................................................................................................................
Thanks in advance
Answer:
A) ?
B) Rhombus
Step-by-step explanation:
For A count the squares inside the shape. I am sorry I had to answer this quickly and did not have time time to count them, but that should be fairly straight forward.
B is Rhombus.
Answer:
P = 12
The height = 6
Base = 4
24*0.5 = 12
B = rhombus
At a costumer service call center for a large company, the number of calls received per hour is normally distributed with a mean of 150 calls and a standard deviation of 5 calls. What is the probability that during a given hour of the day there will be between 146 calls and 163 calls, to the nearest thousandth
We have been given that at a customer service call center for a large company, the number of calls received per hour is normally distributed with a mean of 150 calls and a standard deviation of 5 calls. We are asked to find the probability that during a given hour of the day there will be between 146 calls and 163 calls.
First of all, we will use z-score formula to find z-score corresponding to 146 and 163.
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]z=\frac{146-150}{5}[/tex]
[tex]z=\frac{-4}{5}[/tex]
[tex]z=-0.8[/tex]
[tex]z=\frac{163-150}{5}[/tex]
[tex]z=\frac{13}{5}[/tex]
[tex]z=2.6[/tex]
Our next step is to find percentage of data scores falls between both z-scores.
[tex]P(-0.8<z<2.6)=P(z<2.6)-P(z<-0.8)[/tex]
Using normal distribution table, we will get:
[tex]P(-0.8<z<2.6)=0.99534-0.21186[/tex]
[tex]P(-0.8<z<2.6)=0.78348[/tex]
Let us convert our answer into percentage.
[tex]0.78348\times 100\%=78.348\%[/tex]
Upon rounding our answer to nearest thousandths, we will get:
[tex]78.348\%\approx 78.35\%[/tex]
Therefore, the probability that during a given hour of the day there will be between 146 calls and 163 calls is approximately [tex]78.35\%[/tex].
Answer:
0.624
Step-by-step explanation:
DeltaMath
I have 25 pound bags of cat food . Each serving is 1.8 from the bag. How many servings can you get?
Answer:
10 servings
Step-by-step explanation:
try your best
Answer:
13.8 servings
Step-by-step explanation:
25 divided by 1.8
What’s the value of x?
Answer fast please
So the value of X is 15 degree.
Look at the attached picture
Hope it will help you
Good luck on your assignment
AC=180°
[tex]3x + 8x + 15 = 180 \\ 11x = 165 \\ x = 15[/tex]
Some nutritionists recommend that people eat 31,000 milligrams of fiber each day. The table shows the amount of fiber Jodi has eaten today. How many more grams of fiber does she need to get the recommended daily amount of fiber?
The amount of fiber Jodi needs to eat is 6000 milligrams or 6 grams if the nutritionists recommend that people eat 31,000 milligrams of fiber each day.
What is unit conversion?It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.
We have:
Some nutritionists recommend that people eat 31,000 milligrams of fiber each day.
The total amount of fiber Jodi took = 19 + 4 + 2(1) = 25 grams
1 gram = 1000 milligrams
25 grams = 25000 milligrams
The amount of fiber she needs to eat
= 31000 - 25000
= 6000 milligrams
or
= 6 grams
Thus, the amount of fiber Jodi needs to eat is 6000 milligrams or 6 grams if the nutritionists recommend that people eat 31,000 milligrams of fiber each day.
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what is the name of this 3D shape
Answer:
rectangular prism or cuboid
Step-by-step explanation:
The name of the given 3-D shape is rectangular prism or cuboid
In the NFL, a football field is 200 feet longer than it is wide, and the area of the field is 57,600ft^2
What is the width of the field?
(Before you mess this up, the field is not 100 yards long. You must include the lengths of the end Zones.) (And hey wait a second! Before you mess it up now, notice the problem is in
FEET.)
Answer
160ft
Step-by-step explanation:
Let the width be x.
Then the length is (x+200)
The area of the field=57600
Area=length*width
x(x+200)=57600
x^2+200x-57600=0
x=-360 or x=160
The width and length of the football field are 160 feet and 360 feet respectively.
Suppose the width of the field = x
So, the length of the field =x+200
What is the area of a rectangle?The area of a rectangle with length l and width b is lb.
So, the area of the football field =x(x+200)
Given that x(x+200)=57600
[tex]x^{2} +200x=57600[/tex]
[tex]x^{2} +200x-57600=0[/tex]
[tex]x=\frac{-200+\sqrt{200^2-4*1*(-57600)} }{2}[/tex]
x=160
So, the width of the field is 160 feet.
Hence, the width and length of the football field are 160 feet and 360 feet respectively.
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What is value of 3x2+4y2if x=2, y=1, and z=-3
Answer:
16
Step-by-step explanation:
3x² + 4y² where x = 2, y = 1, and z = -3
Here we just need to plug in the given values to their respective variables
3(2)² + 4(1)² There are no z variables in this equation so plugging in z = -3 is irrelevant Simplifying our equation we now have: 3(4) + 4(1) = 12 + 4 = 16Answer:
0 if the original expression is : 3x^2 + 4yz
Step-by-step explanation:
3x^2 + 4yz ; I guess this is the original expression.
When x=2, y = 1 z =-3
3x^2 + 4yz = 3(2)^2 + 4 × (1)×(-3)
= 3×4 + 4 × (-3) = 12 - 12 = 0
The jogging track is 5/9 of a mile long. If Ashley jogged around it four times how far did she run
Answer:
20/9 mile
Step-by-step explanation:
idk pretty self-explanatory
Two swimmers at opposite ends of a ninety-foot pool start to swim the length of the pool, one at 3 feet per second and the other at 2 feet per second. If they swim back and forth for twelve minutes, how many times do they pass each other?
Answer:
20 times
Step-by-step explanation:
The faster swimmer can swim twice the length of the pool in ...
(2·90 ft)/(3 ft/s) = 60 s
The slower swimmer can do it in ...
(2·90 ft)/(2 ft/s) = 90 s
The least common multiple of these times is 180 s = 3 minutes, after which time each swimmer will be back where they started.
A graph of position vs. time shows the swimmers pass 5 times in that 3-minute period. 4 of those are passes when they are going in opposite directions. A 5th pass occurs at one end of the pool, when the faster swimmer passes the slower one going in the same direction.
Since there are 5 passes in each 3-minute period, there are 20 passes in 12 minutes.
The swimmers pass each other 20 times in 12 minutes.
Three less than one-fourth of product of eight thirds and nine, write the expression
Answer:
1/4(8/3+9)-3
Step-by-step explanation:
1/4(8/3+9)-3