Use long division or a calculator to write 4/99 as a decimal. Then tell whether the decimal is terminating or repeating
Answers
0.0404
Repeating decimal (periodic)
1) Let's proceed with the long division of 4 by 99:
1.1) Since 4 is way smaller than 99 let's add one zero to the dividend and another for the quotient followed by a dot.
But 40 is still lesser than 99, so let's add another zero after the dot to make it 400. Now we can divide 400 by 99
1.2) Again to proceed with that division we'll need to write a zero at that 4 and another one in the quotient.
As and we can see already this a repeating decimal or periodic. This division will yield 0.0404040404.....
2) Hence, the answer is 0.0404
Related Questions
Chain rule in calculus
Answers
In the given example:
[tex]\begin{gathered} u=4x^3-5 \\ f(u)=u^4 \\ \text{If we do a function composition then they will be the same} \\ f(x)=\big(4x^3-5\big)^4\rightarrow f(u)=u^4,\text{ note that }u=4x^3-5 \end{gathered}[/tex]Solve for each derivative of dy/du and du/dx
[tex]\begin{gathered} \frac{du}{dx}=3\cdot4x^{3-1}-0 \\ \frac{du}{dx}=12x^2 \\ \\ \frac{dy}{du}=4\cdot u^{4-1} \\ \frac{dy}{du}=4u^3,\text{ then substitute }u \\ \frac{dy}{du}=4(4x^3-5)^3 \\ \\ \text{Complete the chain rule} \\ \frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx} \\ \frac{dy}{dx}=\big(4(4x^3-5)^3\big)\big(12x^2\big)\text{ or }\frac{dy}{dx}=48x^2(4x^3-5)^3 \\ \end{gathered}[/tex]Valentina earned some money doing odd jobs last summer and put it in a savings account that earns 7% interest compounded quarterly after 5 years there is 500.00 in the account how much did valentina earn doing odd jobs
Answers
two factor of 2=2²two factor of 3=3²
Answers
Exponents indicate how many times a number is multiplied by itself
Two factor two= 2*2= 2²=4
Two factor of three is 3*3=3²=9
18)Betsy is collecting data on the amount of time shoppers spend inside of a particular large department store. She stands outside the department store and surveys every 10th shopper who exits. What type of sampling is used? Explain your answer.
Answers
Consider the 5 main types of sampling: Random, Systematic, Convenience, Cluster, and Stratified.
In the case of systematic sampling, every kth element of the data set is taken.
In our case, consider all the shoppers and imagine that they can be ordered in a line; then, Betsy selected the 10th shopper in the line, the 20th one, and so on.
This is analogous to systematic sampling; the answer is systematic sampling.A beach ball rolls off a cliff and onto the beach. The height, in feet, of the beach ball can be modeled by the function h(t)=64−16t2, where t represents time, in seconds.What is the average rate of change in the height, in feet per second, during the first 1.25 seconds that the beach ball is in the air?Enter your answer as a number, like this: 42
Answers
STEP - BY - STEP EXPLANATION
What to find?
The average rate of change in the height, in feet per second, during the first 1.25 seconds that the beach ball is in the air.
Given:
[tex]h(t)=64-16t^2[/tex]Step 1
Differentiate the heigh with reospect to t.
The rate of change of height is the differentiation of the height.
[tex]\frac{dh(t)}{dt}=-32t[/tex]Step 2
Substitute t= 1.25
[tex]h^{\prime}(t)=-32(1.25)[/tex][tex]=-40ft\text{ /s}[/tex]ANSWER
Average rate = -40 ft / s
Solve the exponential equation. Express irrational solutions as decimals correct to the nearest thousandth.5x -5.e-2x = 2eSelect the correct choice below and, if necessary, fill in the answer box to complete your choice.A. The solution set is(Round to the nearest thousandth as needed. Use a comma to separate answers as needed.)OB. The solution is the empty set.
Answers
We are asked to solve the exponential equation given below:
e^5x - 5 * e^-2x = 2e
First let's apply the exponent rules:
5x - 5 - 2x = In(2e)
Solving 5x - 5 - 2x = In(2e)
3x - 5 = In(2e)
Add 5 to both sides:
3x = In(2e) + 5
Divide both sides by 3
x = In(2e) + 5
3
x = 2.23104
x = 2.231 (To the nearest thousand)
Therefore, the correct option is A, which is The solution set is 2.231 (Round to the nearest thousand).
A plane intersects both bases of a cylinder, passing through the center of each baseof the cylinder. What geometric figure will be formed from this intersection?
Answers
When a plane intersects both bases of a cylinder, passing through the center of each base of the cylinder, the cross section formed is a rectangle.
Fowler has a collection of marbles of different sizes and colors. Big Small Red 9 9 Green 14 9 Purple 9 6 Blue 0 10 What is the probability that a randomly selected marble is not red or is not small? Simplify any fractions.
Answers
From the given table, the following are observed:
No. of marbles that are not red and not small = No. of Big Green and Big Purple
= 14 + 9
= 23 Marbles
Total number of marbles = 9 + 14 + 9 + 9 + 9 + 6 + 10 = 66 Marbles
We get,
[tex]\text{ Probability of getting a marble that is not red or not small = }\frac{\text{ 23 Marbles}}{66\text{ Marbles}}[/tex][tex]\text{ = }\frac{23}{66}[/tex]We can no longer simplify 23/66. Therefore, 23/66 is the answer.
If we use 3.14 for pi, describe the ratio between the circumference and the diameter of a circle.
Answers
Solution
The ratio of the circumference of any circle to the diameter of that circle.
[tex]\begin{gathered} \text{circumference of a circle=}\pi d \\ \text{where d is the diameter} \\ \\ \text{circumference of a circle=3.14}d \end{gathered}[/tex]The ratio of the circumference of any circle to the diameter of that circle. Regardless of the circle's size, this ratio will always equal pi.
If f(x) = -3 and g(x) = 4x + 2x - 4, find (* + )(x).O A. 4x2 + x +1OB. 432 + x ->C.X2-12OD. 4x2+2x-7
Answers
You have the following functions:
[tex]\begin{gathered} f(x)=\frac{x}{4}-3 \\ g(x)=4x^2+2x-4 \end{gathered}[/tex]In order to find (g + f)(x) add like terms of each function. Remind that like terms are those terms with the same variable and same exponent.
Then, you have:
[tex]\begin{gathered} (f+g)(x)=4x^2+2x+\frac{x}{4}-3-4 \\ (f+g)(x)=4x^2+\frac{9}{4}x-7 \end{gathered}[/tex]Hence, the answer is
4x^2 + 9/4 x - 7
A class had a quiz where scores ranged from 0 to 10.N(s) models the number of students whose score on the quiz was s.What does the statement N(8) > N(5) mean?Group of answer choicesA score of 8 is greater than a score of 5.There are more students who scored 8 than students who scored 5.There are 8 students who scored higher than 5.
Answers
The expression N(s) models the number of students that got a score "s" on the quiz.
Then the expression N(8) represents the number of students that scored 8 on the quiz.
And N(5) represents the number of students that scored 5 on the quiz.
[tex]N(8)>N(5)[/tex]Can be read as: "The number of students whose score on the quiz was 8 is greater than the number of students whose score on the quiz was 5"
Therefore, you can conclude that there were more students who scored 8 than students who scored 5. (option 2)
Given the following function, find f(-3), f(0), and f (2) f(x)=5x-2
Answers
The output values of f(-3), f(0) and f(2) of the function f( x ) = 5x - 2 are -17, -2 and 8 respectively.
What are the output values of f(-3), f(0) and f(2) in the given function?A function is simply a relationship that maps one input to one output.
Given the data in the question;
f( x ) = 5x - 2f( -3 ) = ?f( 0 ) = ?f( 2 ) = ?For f( - 3 );
To find the output value of f( -3 ), replace all the occurrence of x with -3 in the function and simplify.
f( x ) = 5x - 2
f( -3 ) = 5(-3) - 2
f( -3 ) = -15 - 2
f( -3 ) = -17
For f( 0 );
To find the output value of f( 0 ), replace all the occurrence of x with 0 in the function and simplify.
f( x ) = 5x - 2
f( 0 ) = 5(0) - 2
f( 0 ) = 0 - 2
f( 0 ) = -2
For f( 2 );
To find the output value of f( 2 ), replace all the occurrence of x with 2 in the function and simplify.
f( x ) = 5x - 2
f( 2 ) = 5(2) - 2
f( 2 ) = 10 - 2
f( 2 ) = 8
Therefore, the output value of f( 2 ) is 8, this forms an ordered pair of ( 2, 8 ).
Learn more about functions here: brainly.com/question/2541698
#SPJ1
Lulu the Lucky puts chests of gems into her treasure vault.
Each chest holds the same number of gems. The table
below shows the number of gems Lulu received from
three different adventures and the number of chests she
needed to hold the gems.
Number of gems
Number of chests
Adventure A
600
2
Adventure B
1500
5
Adventure C
4800
16
Write an equation to describe the relationship between
g, the number of gems, and c, the number of chests.
Answers
The equation that represents the relationship of gems 'g' and chest 'c' is 300c = g.
What are equations?A mathematical statement that uses the word "equal to" between two expressions with the same value is called an equation. Like 3x + 5 = 15, for instance. Equations come in a wide variety of forms, including linear, quadratic, cubic, and others. Point-slope, standard, and slope-intercept equations are the three main types of linear equations.So, the equation representing the relation of 'g' and 'c':
We can observe that:
600/2 = 3001500/5 = 3004800/16 = 300So, we can conclude that:
g/c = 300300c = gTherefore, the equation that represents the relationship of gems 'g' and chest 'c' is 300c = g.
Know more about equations here:
https://brainly.com/question/28937794
#SPJ13
is 6x0=O and example of distributive property?
Answers
we have that
Distributive property is the product of a factor and a sum (or difference) equals the sum (or difference) of the product
In this exanple
6x*0=0
Is not the product of a factor and a sum or difference
Which of these could be the dimensions of a unit cube? Select all that apply. 1 ft. by 1 ft. by 1 ft. 1 in. by 2 in. by 1 in. 1 ft. by 1 in. by 1 cm El mm by mi byl mm 1 m by 1 m by 2 m
Answers
Since it is a cube, all its three dimensions must be equal.
Also the term 'unit cube' is used which suggests that the volume of the cube should be 1 units.
Consider that the 2nd and 5th options are incorrect as the dimensions are note equal.
Consider the third dimension, note that before analyzing the numeric part we should make sure that the units are same for all three dimensions.
Here, the units are different, and we know that,
[tex]1\text{ ft }\ne1\text{ in }\ne1\text{ cm}[/tex]So the third option is also incorrect.
Consider that the options 1st and 4th consist all three dimensions same. Also their product yields 1 in the same cubic units.
So they both represent a unit cube.
Therefore, options 1st and 4th are the correct choices.
Blossom's Computer Repair Shop started the year with total assets of $318000 and total liabilities of $211000. During the year, the
business recorded $505000 in computer repair revenues, $311000 in expenses, and Blossom paid dividends of $50200. Stockholders'
equity at the end of the year was
Answers
Ur welcome
Find the areas of the figures for parts (a) and (b) below.
Answers
SOLUTION:
Case: Area of plane shapes
Method:
a) Parallelogram
To find the area we need to find the perpendicular height (using Pythagoras theorem)
[tex]\begin{gathered} h^2+7^2=25^2 \\ h^2+49=625 \\ h^2=625-49 \\ h^2=576 \\ h=\sqrt{576} \\ h=24 \end{gathered}[/tex]The Area of a parallelogram is given as:
[tex]\begin{gathered} A=bh \\ A=23\times24 \\ A=552\text{ }ft^2 \end{gathered}[/tex]b) Triangle
To find the area of the triangle, we need to find the base first
First, lets find 'a'
[tex]\begin{gathered} a^2+60^2=70^2 \\ a^2+3600=4900 \\ a^2=4900-3600 \\ a^=\sqrt{1300} \\ a=36.06 \end{gathered}[/tex]The base, b
b= 2(a)
b= 2 (36.06)
b= 72.12
The area of the triangle is:
[tex]\begin{gathered} A=\frac{1}{2}bh \\ A=\frac{1}{2}\times72.12\times60 \\ A=2163.6 \end{gathered}[/tex]Final answer:
a) Parallelogram,
A= 552 square feet
b) Triangle
A= 2163.6 square feet
Two lines intersect in the diagram shown below. 127° to What is the value of x? Hide All 37 53 127 D 217 O
Answers
x=127º
1) Since those angles x, and 127º share a common vertex we can state that these are Vertical Angles
2) Therefore they are congruent to each other. And we can state:
x = 127º as well.
Line segment MN is the image of CD after a dilation by a factor k with a center at point A. Using your ruler, determine the value of k to the nearest hundredth. Show the work that leads to your answer.
Answers
Methjod th find the asnswer to thsi question.
First of mark a point on the line segment CD. Then, draw a perpendicular from that point to the a point to the line segment MN.
Then, mesure the length of the line segment.
Thus, the value of k is obtained.
why does a cubic graph have both an x intercept and a y intercept
Answers
Answer:
All cubic function has domain (-∞,∞) and range (-∞,∞)
Step-by-step explanation:
since birth hakem has had a savings account that started at $3,000 and had been growing at a rate of 13% per year the amount of money in the account can be modeled by the equation y equals P =(1.13)^ Z where why is the value of the count is the number of years and pee was original deposit amount is it possible for hakem account to grow to $31812 11.42 in hakem lifetime?( try to figure out the bounds of the perameter)
Answers
Solution
For this case we have the following formula:
[tex]y=3000(1.13)^x^{}[/tex]And we want to find the value for t in order to have y = 3181211.42 , solving for y we got:
[tex]3181211.42=3000(1.13)^x[/tex]and solving for x we got:
[tex]\ln (\frac{3181211.42}{3000})=x\cdot\ln (1.13)[/tex][tex]x=56.99\approx57[/tex]for this case we need 57 years to reach the amount so then assuming that a person lives about 80 years , then is possible
yes
use prowers and multiplication to write the equation whose value is 10 to the 11th power
Answers
if we have
(10^9)(10^2)
adds the exponents
10^(9+2)
10^11
If you have
10^18/ 10^7
subtract the exponents
10^(18-7)
10^11
If you have
(10^6)^2/10
First multiply the exponents
10^(6*2)/10
10^12/10
subtract exponents
10^(12-1)
10^11
As a town gets smaller, the population of its high school decreases 6% each year. The senior class has 320 students now. In how many years will the high school have 100 students?
Answers
From the details provided, we know that the population of the town gets smaller, that is, a decline and not a growth. The annual rate of decline (or decay) is 6% (or 0.06). The formula for this is given as shown below;
[tex]y=a(1-r)^x_{}[/tex]The variables here are;
[tex]\begin{gathered} a=\text{initial value} \\ r=\text{rate of decline} \\ x=\text{period (in years)} \end{gathered}[/tex]The equation to represent the decline of this town's student population shall be;
[tex]\begin{gathered} y=320(1-0.06)^n \\ Simplified,\text{ we now have;} \\ y=320(0.94)^n \end{gathered}[/tex]When the population ofnthe town becomes 100, then we can replace variable y with 100. Since the formula is used to find the current population, and we have been given the population after a certain number of years, then our y is now 100.
We can now determine the number of years (variable n) that it takes before the population declines to 100 as shown below;
then our y is now 100.
We can now
Given:• UZ | VW• UV ZUZ306Nw4511Which is closest to mZW?26.630°60°63.49
Answers
From the image, given that UZ is parallel to VW, UV is congruent to UZ. We can redraw the image to include some extra details.
The image is below;
With the image above, we can the find the angle W, using tangent function of trigonometry.
This is seen below;
[tex]\begin{gathered} \tan w=\frac{opposite}{\text{Adjacent}} \\ \text{opposite =30ft} \\ \text{Adjacent}=15ft \\ \therefore\tan w=\frac{30}{15} \\ \tan w=2 \\ w=\tan ^{-1}2 \\ w=63.4^0 \end{gathered}[/tex]The angle closest to m
Answer: 63.4
A study found that 36% of the assisted reproductive technology (ART) cycles resulted in pregnancies. Twenty-six percent of the ART pregnancies resulted in multiple births. (a) Find the probability that a random selected ART cycle resulted in a pregnancy and produced a multiple birth. (b) Find the probability that a randomly selected ART cycle that resulted in a pregnancy did not produce a multiple birth.(c) Would it be unusual for a randomly selected ART cycle to result in a pregnancy and produce a multiple birth?
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
assisted reproductive technology (ART) cycles:
pregnancies = 36%
pregnancies resulted in multiple births = 26%
Step 02:
a.
p (pregnancies) = 36% = 36/100 = 0.36
pregnancies resulted in multiple births = 26% = 26/100 = 0.26
p(pregnancies resulted in multiple births) = 0.36*0.26 = 0.0936
b.
p (pregnancy did not produce a multiple birth) = 1 - 0.0936 = 0.9064
c.
Indeed, the probability of multiple pregnancies is low 9.36%.
That is the full solution.
Help me pleaseeee quicklyyyyy
Answers
∠6 and ∠5 are alternative interior angle thus the measure of angles ∠5 = 45° , ∠6 = 45° ,∠7 = 45° and ∠8 = 135°.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
Angles 1,2,7 are the interior angles of a triangle and we know that the sum of all interior angles inside a triangle is 180°.
Therefore, ∠1 + ∠2 + ∠7 = 180°
Given, ∠1 = 70° and ∠2 = 65°
∠7 = 180° - (70 + 65) = 45°
Now, ∠8 = 180 - ∠7 ⇒ ∠8 = 135°
Now, ∠7 = ∠6 (vertical opposite angle) so ∠6 = 45°
∠6 = ∠5 (alternative interior angle) so ∠5 = 45°
Hence "∠6 and ∠5 are alternative interior angle thus the measure of angles ∠5 = 45° , ∠6 = 45° ,∠7 = 45° and ∠8 = 135°".
For more about the angle,
brainly.com/question/13954458
#SPJ1
A rectangular pool is 7 meters wide and 12 meters long. If you swim diagonally from one corner to the other, how many meters will you swim? Approximate the answer to the nearest tenth.
Answers
Answer: 15cm
Step-by-step explanation:
Your welcome
Question
Find the values for x and y .
Answers
Step-by-step explanation:
6x+3=75° ( being alternate angle )
6x = 72°
x=12
75+45+y= 180
y= 60°
The function g is defined as follows for the domain given g(x) = 3x - 2 , omain = \{- 2, - 1, 0, 1\} Write the range of g using set notation. Then graph g
Answers
Given: The function below
[tex]\begin{gathered} g(x)=3x-2 \\ Domain:\lbrace-2,-1,-0,1\rbrace \end{gathered}[/tex]To Determine: The range and the graph of g
Solution
The range is as given below
[tex]\begin{gathered} x=-2 \\ g(-2)=3(-2)-2=-6-2=-8 \\ x=-1 \\ g(-1)=3(-1)-2=-3-2=-5 \end{gathered}[/tex][tex]\begin{gathered} x=0 \\ g(0)=3(0)-2=0-2=-2 \\ x=1 \\ g(1)=3(1)-2=3-2=1 \end{gathered}[/tex]Hence, the range is
{-8, -5, -2, 1}
Let us form a table showing the domain(x) and the range (g(x))
Let us use the table to plot graph of the domain(x) against the range(g(x)) as below
Use the distance formula to find the distance between the points given.(-9,3), (7, -6)
Answers
Given the points:
[tex](-9,3),(7,-6)[/tex]You need to use the formula for calculating the distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1^})^2[/tex]Where the points are:
[tex]\begin{gathered} (x_1,y_1) \\ (x_2,y_2) \end{gathered}[/tex]In this case, you can set up that:
[tex]\begin{gathered} x_2=7 \\ x_1=-9 \\ y_2=-6 \\ y_1=3 \end{gathered}[/tex]Then, you can substitute values into the formula and evaluate:
[tex]d=\sqrt{(7-(-9))^2+(-6-3)^2}[/tex][tex]d=\sqrt{(7+9)^2+(-9)^2}[/tex][tex]d=\sqrt{(16)^2+(-9)^2}[/tex][tex]d=\sqrt{256+81}[/tex][tex]d=\sqrt{337}[/tex][tex]d\approx18.36[/tex]Hence, the answer is:
[tex]d\approx18.36[/tex]