Answer:
3x³ is a polynomial of degree
The degree of the polynomial 3x³ is 3
David invested $220 in an account paying an interest rate of 1. 7% compounded
continuously. Assuming no deposits or withdrawals are made, how much money, to
the nearest ten dollars, would be in the account after 10 years?
David's deposit of $220 compounded continuously at a rate of 1.7% will become $260 after 10 years.
Here we have been given that David invested $220.
The interest rate was 1.7%
Since the amount was compounded continuously, there is no fixed date of when it was compounded, the whole process is taken as an exponential distribution.
There were no withdrawals or additional deposits to this, so our Principal is constant. Hence we can write the formula
Amount = Principal X eᵃˣ
where a = rate of interest/100
x = time
Therefore, we can say that
Ampunt after 10 years = 220 X e¹⁰ ˣ ⁰°⁰¹⁷
= $260.76707
rounding off to the nearest 10 dollars we get
= $260
Hence David's deposit of $220 compounded continuously at a rate of 1.7% will become $260 after 10 years.
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How do you verify inverse?
To verify the inverse we can use Horizontal Line Test.
Suppose F is a function.
F does not have an inverse if any horizontal line crosses the graph of f more than once. If no horizontal line crosses the graph of F more than once, then F does have an inverse. In mathematics, having an inverse is a very significant quality, and it has a name.
If and only if a function f has an inverse, then it is one-to-one. The following definition, which is also the one that is most frequently used, is equivalent. If f(a) = f(b) implies a = b for all a and b in its domain, then a function f is one-to-one.
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Find the standard deviation for the set of data. {12,20,7,18,25,6,17,26,16}
A. 6.3
B. 6.65
C. 6.09
D. 8.22
Answer:
6.65
Step-by-step explanation:
That is approximately how far each number is from each other
A positive and negative Angel that is coterminal with 70 degrees
Scientists measure a bacteria population and find that it has 10,000 organisms. Five days later, they find that the population has doubled. Which function f could describe the bacteria population d days after scientists first measured it, assuming it grows exponentially?
Answer:
f(x)= 10,000(2)^x
Step-by-step explanation:
Exponential equations can be modeled by a(r)^x where a is the initial amount, r is the difference, and x is how many units the equation should be squared by.
A function that describes the bacteria population after d days would be,[tex]\bold{f(d) = 10000\times(1+0.15)^d}[/tex]
What is an exponential growth?An exponential growth function is a function that grows at a constant percent growth rate.
What is an exponential growth function?f(t) = a×(1 + r)^(t)
where f(t) = exponential growth function
a = initial amount
r = growth rate
t = number of time intervals
For given example,
initially a bacteria population (a) = 10,000
Five days later, they find that the population has doubled.
d = 5, f(5) = 20,000
Assuming it grows exponentially, we find the growth rate of a bacteria population by using the formula of exponential growth function.
[tex]\Rightarrow f(d) = a\times(1 + r)^{d}\\\\\Rightarrow f(5) = 10000\times (1+r)^5\\\\\Rightarrow 20000=10000\times (1+r)^5\\\\\Rightarrow 2=(1+5)^5\\\\\Rightarrow 1+r=\sqrt[5]{2}\\\\\Rightarrow 1+r = 1.15\\\\\Rightarrow r = 1.15-1\\\\\Rightarrow \bold{r = 0.15}\\\\\Rightarrow \bold{r=15\%}[/tex]
This means, the exponential growth function would be,
[tex]\bold{f(d) = 10000\times(1+0.15)^d}[/tex], where d represents number of days.
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A case holds 48 boxes of candy and costs $24. How much would 2 % cases of candy cost?
Answer:
48 cents
Step-by-step explanation:
There i a bag filled with 4 blue, 3 red and 5 green marble. A marble i taken at random from the bag, the colour i noted and then it i replaced. Another marble i taken at random. What i the probability of getting 2 blue?
The probability of getting 2 blue is 1/9.
You are choosing replacement marbles. The trials (marble selections) are independent from one another and follow the binomial distribution.
1/3 of the time, a blue marble will be the first one chosen.
(This is due to the fact that 4 out of 12 marbles are blue, therefore 4/12 equals 1/3.
A blue marble is 1/3 more likely to be chosen the second time.
The two probabilities can be multiplied to obtain the following results because the marble selections are independent:
The likelihood of receiving two blues is (1/3)2 =1/9.
Therefore, there is a 1/9 chance of obtaining two blues.
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
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Similar figures review - Question 1
For a house that have a height of 6 meters and length of 4.5 meters. On a scale drawing if the height of the house is 30 mm the length of the house will be 22.5 mm
What is proportions?In general, the term proportion refers to a part, share, or amount that is compared to a whole.
According to the definition of proportion, two ratios are in proportion when they are equal.
How to find the length of the houseThe length of the house on the map is calculated using equality in proportions as follows
The required proportion is
= height of the house / length of the house
= 6 / 4.5
= 4/3
Using this proportion, the length of the house in the drawing is
= 30 mm / 4/3
= 22.5
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Andre and diego were each trying to solve 2x 6=3x-8 describe the first step they each make to the equation
The final answer after solving the given equation could be 14.
What is Linear Equation ?
Linear Equation can be defined as the equation in which the highest degree of the variable is one. Linear equations are generally three types , they are standard form , slope intercept form , point slope form and linear equation is also called as the equation of straight line.
Given,
Given equation,
2x + 6 = 3x -8
separating the value into a similar term:
2x-3x = -8 - 6
subtracting the equation:
-x = -14
remove negative sign:
x = 14
Therefore , the final answer could be 14.
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does the point (2, 8) satisfy the equation y = 4x?
The point satisfies the equation ! 8 = 4 × (2)
Answer:
Yes
Step-by-step explanation:
If you plug in the numbers to the equation, you should get:
8 = 4(2)
Then,
8 = 8
therefore, (2,8) does satisfy the equation y = 4x.
How to solve 6×+8 = 12x-4
SHOW YOUR WORK 256 divided by 6400
Help please.
I've seen a bunch of different answers but none of them are the same.
The statement whether each data set is likely to be distributed nor not:
Number of minutes required to complete a marathon - Yes.
Number of miles in a marathon: - No.
Average age of a person who runs a marathon: No.
What is a distribution?The distribution of values in a field is described by a statistical distribution, often known as a probability distribution. In other words, the statistical distribution identifies the typical and unusual values. The bell-shaped normal distribution is one of many varieties of statistical distributions.
Let n miles in marathon.
To normally distribute, number of minutes required to complete a marathon:
The number of minutes required to complete a marathon is likely to be normally distributed with small amounts in tails (very slow, very fast) and large amount in middle.
So, yes.
To normally distribute, number of miles in a marathon:
The number of miles is a fixed number, not normally distributed.
So, no.
To normally distribute, average age of a person who runs a marathon:
The average age is a fixed number
Average age is not likely to be normally distributed.
So, no.
Therefore, the first one is yes, and the other two are no.
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Product sales by month (in thousands) Month Product 1 Product 2 Product 3 Product 4 Product 5 January 228 964 429 169 456 February 188 784 414 238 520 March 222 816 422 235 562 April 222 738 414 214 624 May 176 710 420 303 670 June 120 697 486 768 342 Popular products are often placed in the window to attract customers into the store. Based on this information, which product should be displayed in the window in July?
Based on the information provided, it seems that the product that should be displayed in the window in July is Product 5.
What is mean?A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the dataset's total number of values by the sum of all of those values yields this result. Both raw data and data that have been combined into frequency tables can be used for calculations. Average refers to a number's average. It is straightforward to calculate:
Divide by how many digits there are after adding up all the digits. the total divided by the count.
Based on the information provided, it seems that the product that should be displayed in the window in July is Product 5. This can be determined by looking at the sales data for each product over the months of January through June.
In every month, Product 5 has the highest sales figures among all the products. This suggests that Product 5 is the most popular among customers and would likely attract the most attention if it were to be placed in the window.
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13. Which situation can be represented bya true proportion?
A car used 3 gallons of gas to drive 72 miles on a highway and used 4 gallons of gas to drive 72 mileš town.
A store charged $20 for 2 shirts and charged $25 for 3 shirts.
A signal light flashed yellow 7 times in 28 seconds and flashed red 5 times in 35 seconds.
An alarm on a clock beeped 7 times in 6 seconds and beeped 14 times in 12 seconds.
The example of a proportion, is An alarm on a clock beeped 7 times in 6 seconds and beeped 14 times in 12 seconds.
What is a proportion?The term proportionality describes any relationship that is always in the same ratio.
Given are some statements,
a) A car used 3 gallons of gas to drive 72 miles on a highway and used 4 gallons of gas to drive 72 miles in a town.
Solution:- In this case, we see, a car is using 3 and 4 gallons of gas for driving in a highway and in a town for 72 miles respectively.
Since, the distance is same and quantity of gases is different therefore, this can not be represented as a proportion.
b) A store charged $20 for 2 shirts and charged $25 for 3 shirts.
Solution:- In this, let's first find the unit prices for each,
for $20 there are 2 shirts, therefore, for 1 shirt it will be $10, and for 3 shirts it costs $25, therefore, for 1 shirt it will cost $8.3
Since, unit price for both is not equal, therefore, this can not be represented as a proportion.
c) A signal light flashed yellow 7 times in 28 seconds and flashed red 5 times in 35 seconds.
Solution:- As in 2nd option, will here also find unit rate, since, yellow light is flashing 7 times in 28 seconds, therefore, in 4 seconds it will be flashed for 1 time, similarly, red light is flashing 5 times in 35 seconds, therefore, in 7 seconds it will be flashed for 1 time,
Since, both unit rates are not equal, therefore, this can not be represented as a proportion.
d) An alarm on a clock beeped 7 times in 6 seconds and beeped 14 times in 12 seconds.
Solution:- Again we will find unit rate, since, the alarm is beeping 7 times in 6 seconds, therefore, it will beep for 1 time in 6/7 seconds, similarly, it is beeping 14 times in 12 seconds, so for 1 time it will beep in 12/14 = 6/7 seconds.
Here, we see that, both the unit rates are equal, therefore, this is an example of a proportion.
Hence, the last option is the correct example.
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Suppose a, b, c, and d are constants such that a is not zero and the system below is consistent for all possible values of f and g . What can you say about the numbers a, b, c, and d?
Justify your answer. axı + bx2 = f cxı + dx2 = g
a and d are non-zero and ad = bc for the system to be consistent for all possible values of f and g.
By definition, a system is consistent if there exists a set of solutions that satisfy the equations. In this system, the constants a, b, c, and d are the coefficients of the two equations. Since the system is consistent for all possible values of f and g, then the coefficients must satisfy certain conditions. For example, a and d must both be non-zero in order for the equations to be solvable. Additionally, the coefficients of both equations must be in proportion to each other, meaning that ad must equal bc. This is necessary for the equations to have the same slope, which is necessary for them to be solvable. Thus, we can conclude that a and d are non-zero and ad = bc for the system to be consistent for all possible values of f and g.
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A box of highlighters originally cost
$
18
. It goes on sale at
10
%
off the original price.
Fill in the blanks:
Original percentage
=
%
Percentage off
=
%
Percentage left over
=
%
Complete the number sentence to show how to find the sale price of the box of highlighters:
Sale price
=_______% x $18
Answer:
hhhhjjff?ihd,uiufy?उग्फ्त्त्य्युउउउईईइय्त्ग्ग
When the inverse of a function is itself a function it is called?
When the inverse of a function is itself a function it is called self-inverse.
A mathematical phrase, rule, or law establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
This relationship is commonly symbolized as y = f(x)—which is said “f of x”—and y and x are related such that for every x, there is a unique value of y.
A self-inverse function ‘reverses itself’ to produce the original input.
A function f is self-inverse if it has the property that f(f(x))=x for every x in the domain of f. In other words, f(x)=f−1(x).
For example, 1x and 3−x are self-inverse.
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HELP DUE IN 10 MINS!
Determine which of the following quadrilaterals have the property below. Choose all that apply.
At least one pair of opposite sides are parallel??
Parallelogram
Rhombus
Rectangle
Square
Kite
Isosceles Trapezoid
Answer:
Parallelogram, rectangle, rhombus, square, and isosceles trapezoid.
c) The ratio between an exterior angle and an interior angle of a polygon is 1:5.
i) Find the magnitude of an exterior angle.
ii) How many sides are there in this polygon?
Answer:
30° and 12
Step-by-step explanation:
The sum of the exterior angle and the interior angle = 180°
sum the parts of the ratio, 1 + 5 = 6 parts
Divide 180° by 6 to find the value of one part of the ratio
180° ÷ 6 = 30° ← value of 1 part of the ratio
(i)
The exterior angle = 30°
(ii)
The sum of the exterior angles of a polygon is 360°
To find the number of sides n divide 360 by 30 , that is
n = 360 ÷ 30 = 12
NEED HELP ASAP, WILL GIVE BRAINLY TO BEST ANSWER
Answer:
58 degrees
Step-by-step explanation:
The answer is 58 degrees.
180 degrees in a triangle, subtract the angles of 65 and 57, you get 58 degrees.
180 - 57 -65 = 58
Maisie walked for 4 hours at an average speed of
1.6 miles per hour (mph).
How many miles did Maisie walk?
If your answer is a decimal, give it to 1 d.p.
Answer: Maisie walked 6.4 miles.
Step-by-step explanation:
Since Maisie is walking at a constant pace of 1.6 miles per hour we can set up the following equation:
y = 1.6(x)
In this equation, Y is the number of miles Maisie walked in total and X is the number of hours she walked. All we have to do is plug in 4 hours as x and solve.
y = 1.6(4)
y = 6.4 miles.
Consider the polynomial function ( x + 3 ) ( x + 9 ) ( x - 6 ) = 0 Which of the following are zeros of the function? Select all that apply.
What is the simplified form of this expression?
(-3x2 + 2x − 4) + (4x2 + 5x + 9)
7x2 + 7x + 5
x2 + 7x + 5
x2 + 7x + 13
x2 + 11x + 1
Answer:
x² + 7x + 5
Step-by-step explanation:
(- 3x² + 2x - 4) + (4x² + 5x + 9)
since both parenthesis are being multiplies by 1 , remove parenthesis
= - 3x² + 2x - 4 + 4x² + 5x + 9 ← collect like terms
= (- 3x² + 4x²) + (2x + 5x) + (- 4 + 9)
= x² + 7x + 5
Is y 4 a horizontal asymptote?
Yes, the horizontal asymptote is at y = 4.
The term asymptote in math is known as a straight line that constantly approaches a given curve but does not meet at any infinite distance.
Here we have given the expression y = 4.
In order to find whether it is an horizontal asymptote or not, we have to plot it on the graph,
The first process is to label the graph with x and y axis.
And then we have to defines the scale for the for the graph.
Now, we have to input the expression y = 4 on the graph then we get the graph like the following.
While we looking into the given graph we have identified that the expression y = 4 makes the horizontal asymptote on the graph.
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6th grade math help me please and thank you... IF YOU PUT A LINK DO EXPECT TO GET REPORTED anyways.. have a good day my luvs <3
What are the steps I need to solve this problem?
2x + 5 = 21
subtract 5 from each side, then divide by 2 on each side
divide by 2 on each side, then subtract 5 from each side
subtract 5 from each side, then subtract 2 from each side
subtract 21 from each side, then divide by 2 on each side
Which of the following could be the perimeter of a rectangle with an area of 16 square inches?
Answer:
16 inches
Step-by-step explanation:
Solve for x please I need help
Answer: picture wont seem to load, maybe try again
Step-by-step explanation:
Answer:
x = 7.9
Step-by-step explanation:
Sin = Opposite over Hypotenuse
Thus, [tex]sin(21)=\frac{x}{22}[/tex]
* multiply each side by 22 *
[tex]\frac{x}{22} *22=x\\22sin(21)=7.9[/tex]
we're left with x = 7.9 ( rounded )
MODELING REAL LIFE The volume of a sphere is given by the equation $V=\frac{1}{6\sqrt{\pi}}S^{3/2}$ , where $S$ is the surface area of the sphere. Find the volume of a water walking ball, to the nearest cubic meter, that has a surface area of 60 square meters. Use 3.14 for $\pi$ .
The volume of the water walking ball is 43.71 m³
What are the surface area and volume of a sphere?Surface Area of a Sphere. A = 4 π r2. The volume of a Sphere. V = (4 ⁄ 3) π r³. Where r is the radius of the circle
Given :
[tex]$V=\frac{1}{6\sqrt{\pi}}S^{3/2}$[/tex] and surface area of water walking ball is 60 m²
putting the values in the equation we get
V= 464.758/10.632
V=43.71
Hence, the volume of the water walking ball is 43.71 m³
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use a table to organize your guesses
A jar is filled with 100 coins, all of which are nickels and dimes. The change in the jar is worth $6.75. How many coins are nickels, and how many are dimes?
Answer:
35 dimes and 65 nickels
Step-by-step explanation:
We will need use a system of equations to find the total number of nickels and dimes.
Because there are 100 dimes and there are only nickels and dimes, one equation is N + D = 100, where N is the total number of nickels and D is the total number of dimes.
Because a dime is worth $0.10, a nickel is worth $0.05, and the total change in the jar is worth $6.75, the second equation is 0.05N + 0.1D = 6.75
Substitution will be the easiest method to solve:
[tex]0.05N+0.1D=6.75\\N+D=100\\\\N=-D+100\\\\0.05(-D+100)+0.1D=6.75\\-0.05D+5+0.1D=6.75\\0.05D+5=6.75\\0.05D=1.75\\D=35\\\\N+35=100\\N=65[/tex]