Answers
Answer:
Option is the the. correct answer A
Related Questions
Find the 1st term, last term and the sum for the finite arithmetic series.
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Answer:
Given that,
[tex]\sum ^{30}_{n\mathop=2}(3n-1)[/tex]Simplifying we get,
[tex]\sum ^{30}_{n\mathop{=}2}(3n-1)=\sum ^{30}_{n\mathop{=}2}3n+\sum ^{30}_{n\mathop{=}2}1[/tex][tex]=3\sum ^{30}_{n\mathop{=}2}n+\sum ^{30}_{n\mathop{=}2}1[/tex]we have that,
[tex]\sum ^n_{n\mathop=1}1=n[/tex]If n is from 2 to n we get,
[tex]\sum ^n_{n\mathop{=}2}1=n-1[/tex]Also,
[tex]\sum ^k_{n\mathop=1}n=\frac{k(k+1)}{2}[/tex]If n is from 2 to n we get,
[tex]\sum ^k_{n\mathop=2}n=\frac{k(k+1)}{2}-1[/tex]Using this and substituting in the required expression we get,
[tex]=3\lbrack\frac{30\times31}{2}-1\rbrack+30-1[/tex][tex]=3(464)+29[/tex][tex]=1421[/tex]Answer is: 1421
The volume, V, of a cube with edge length s cm is given by the equation V=s3.Is the volume of a cube with edge length s=3 greater or less than the volume of a sphere with radius 3?If a sphere has the same volume as a cube with edge length 5, estimate the radius of the sphere?Compare the outputs of the two volume functions when the inputs are 2?
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We have that the volume of sphere is
[tex]\begin{gathered} V_s=\frac{4}{3}\pi\cdot r^3 \\ \end{gathered}[/tex]and the volume of a cube is
[tex]V_c=s^3[/tex]so if s=r=3. The volume of the sphere is greater.
If they have the same volume, we get that
[tex]\begin{gathered} \frac{4}{3}\pi\cdot r^3=125\rightarrow \\ r^3=\frac{3}{4\cdot\pi}\cdot125\approx29.84\approx30 \\ r=\sqrt[3]{30}\approx3.10 \end{gathered}[/tex]when s=r=2 we have that
[tex]\begin{gathered} V_s=\frac{4}{3}\pi\cdot8=\frac{32}{3}\pi \\ V_c=8 \end{gathered}[/tex]so the volume of the sphere is greater
I need to help finding the length of the arc shown in red..
Answers
We have the next formula to find the length is
[tex]\text{arc length }=\text{ 2}\pi r(\frac{\theta}{360})[/tex]where
r=10
theta=45°
[tex]\begin{gathered} \text{arc length=}2\pi(10)\frac{45}{360}=\frac{5}{2}\pi \\ \end{gathered}[/tex]the arc length is 5/2 pi cm
Evaluate the expression when m=9 and n=7.
5m +n
Correction: m = 7 and n = 9
Answers
We have the expression:
[tex]5m+n\text{.}[/tex]We must evaluate the expression for:
• m = 7,
,• n = 9.
Replacing the values of m and n in the expression above, we get:
[tex]5\cdot7+9=35+9=44.[/tex]Answer
44
Lesson 6.07: In a random sample of 74 homeowners in a city, 22 homeowners said they wouldsupport a ban on nonnatural lawn fertilizers to protect fish in the local waterways. The samplingmethod had a margin of error of +3.1%. SHOW ALL WORK!A) Find the point estimate.B) Find the lower and upper limits and state the interval.
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Confidence interval is written in the form,
(point estimate +/- margin of error)
The given scenario involves population proportion
The formula for the point estimate is
p' = x/n
where
p' = estimated proportion of success. p' is a point estimate for p which is the true proportion
x represents the number of success
n represents the number of samples
From the information given,
n = 74
x = 22
p' = 22/74 = 0.297
The formula for finding margin of error is expressed as
[tex]\begin{gathered} \text{margin of error = z}_{\frac{\alpha}{2}}(\sqrt[]{\frac{p^{\prime}q^{\prime}}{n}} \\ q^{\prime}\text{ = 1 - p'} \\ q^{\prime}\text{ = 1 - 0.297 = 0.703} \end{gathered}[/tex]A) The point estimate is 0.297
B) margin of error = +/-3.1% = 3.1/100 = +/- 0.031
Thus,
the lower limit would be 0.297 - 0.031 = 0.266
Expressing in percentage, it is 0.266 x 100 = 26.6%
the upper limit would be 0.297 + 0.031 = 0.328
Expressing in percentage, it is 0.328 x 100 = 32.8%
Thus, the confidence interval is between 26.6% and 32.8%
how do you work the problem 3k+16=5k?
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We have the following:
[tex]3k+16=5k[/tex]solving for k
[tex]\begin{gathered} 5k-3k=16 \\ k=\frac{16}{2} \\ k=8 \end{gathered}[/tex]The value of k is 8
Section 11 - Topic 5Probability and Independence• In your own words, describe what the word independeyou.Now describe dependent..
Answers
In probability , there are two events independent events and dependent events.
Independent Events :
Two events A and B are said to be independent if the fact that one event has occurred does not affect the probability that the other event will occur.
Example
. Choosing a marble from a jar AND landing on heads after tossing a coin.
Dependent Events :
If whether or not one event occurs does affect the probability that the other event will occur, then the two events are said to be dependent.
Example
Buying ten lottery tickets and winning the lottery.
Solve the equation for solutions in the interval [0°, 360°). Round to the nearest degree.
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We will have the following:
[tex]\sin (2\theta)=-\frac{1}{2}\Rightarrow2\theta=2\pi n_1+\frac{7\pi}{6}[/tex][tex]\Rightarrow\theta=\pi n_1+\frac{7\pi}{12}[/tex]Now, we will solve for the following:
[tex]\Rightarrow\pi n_1+\frac{7\pi}{12}\le2\pi\Rightarrow\pi n_1\le\frac{17\pi}{12}[/tex][tex]\Rightarrow n_1\le\frac{17}{12}[/tex]This value in degrees is:
[tex]\frac{17}{12}\text{radians}=81.169\text{degrees}[/tex]So, the solution is located in the interval:
[tex]\lbrack0,81\rbrack[/tex]John starting playing video games as soon as he got home from school. He played videogames for 45 minutes. Then, it took John 30 minutes to finish his homework. When Johnfinished his homework, it was 4:25 P.M. What time did John get home from school?
Answers
Given:
After coming from school to home,
He played video games for 45 minutes.
Then he took 30 minutes to finish his homework.
When John finished his homework, it was 4:25 PM.
To find:
The time at which John got home from school
Explanation:
According to the problem,
Total time to play video games and do homework is,
[tex]\begin{gathered} 45mins+30mins=75mins \\ =1hr15mins \end{gathered}[/tex]So, the time he got home from school will be,
[tex]4:25P.M.-1hr15mins=3:10P.M.[/tex]Final answer:
The time he got home from school is 3:10 P.M.
If sin A = 3/5 and cos B = 20/29 and angles A and B are in Quadrant 1, find the valueof tan(A + B).
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Our approach is to use SOHCAHTOA to derive values for sine and cosines of both A and B.
[tex]\begin{gathered} \sin A=\frac{3}{5},\text{ cosA=}\frac{\sqrt[]{5^2-3^2}}{5}=\frac{4}{5} \\ \cos B=\frac{20}{29},\text{ sinB=}\frac{\sqrt[]{29^2-20^2}}{29}=\frac{21}{29} \end{gathered}[/tex][tex]\begin{gathered} \tan (A+B)=\frac{\tan A+\tan B}{1-\text{tanAtanB}}\text{ WHERE} \\ \tan A=\frac{\sin A}{\cos A},\tan B=\frac{\sin B}{\cos B} \end{gathered}[/tex][tex]\begin{gathered} \tan (A+B)=\frac{\frac{\frac{3}{5}}{\frac{4}{5}}+\frac{\frac{21}{29}}{\frac{20}{29}}}{1-\frac{\frac{3}{5}}{\frac{4}{5}}\times\frac{\frac{21}{29}}{\frac{20}{29}}}=\frac{\frac{3}{4}+\frac{21}{20}}{1-\frac{3}{4}\times\frac{21}{20}}=\frac{\frac{9}{5}}{1-\frac{63}{80}}=\frac{\frac{9}{5}}{\frac{17}{80}} \\ \tan (A+B)=8.47 \end{gathered}[/tex]tan (A+B) = 8.47
Find the equation of the tangent line to the curve y = x^3- 4x - 5 at the point (2, -5).Tangent Line Equation:
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Let's find the derivative of y:
[tex]\begin{gathered} y=x^3-4x-5 \\ \frac{dy}{dx}=3x^2-4 \end{gathered}[/tex]Evaluate the derivative for x = 2:
[tex]\frac{dy}{dx}\begin{cases} \\ x=2\end{cases}=3(2)^2-4=12-4=8[/tex]Now, we have the slope, let's use the point-slope formula to find the equation:
[tex]\begin{gathered} y-y1=m(x-x1) \\ _{\text{ }}where\colon \\ (x1,y1)=(2,-5) \\ m=8 \\ y+5=8(x-2) \\ y+5=8x-16 \\ y=8x-21 \end{gathered}[/tex]Answer:
y = 8x - 21
11 gallons Blue Car 2 of gas 35.4 miles A gallons 27 miles Silver Car 5 14. You are running a fuel economy study. You want to find out which car can travel a greater distance on 1'gallon of gas. a. What is the gas mileage, in miles per gallon, for the blue car? b. What is the gas mileage, in miles per gallon, for the silver car? c. Which car could travel the greater distance on 1 gallon of gas?
Answers
Answer:
a) 23.67 miles per gallon
b) 34 miles per gallon
c) The silver car could travel a greater distance.
Step-by-step explanation:
a)
Conversion of the mixed numbers to fractions:
[tex]1\frac{1}{2}=\frac{1\ast2+1}{2}=\frac{2+1}{2}=\frac{3}{2}[/tex][tex]35\frac{1}{2}=\frac{35\ast2+1}{2}=\frac{70+1}{2}=\frac{71}{2}[/tex]Gas mileage:
3/2 gallons - 71/2 miles
1 gallons - x miles
Simplifying the top line by 2.
3 gallons - 71 miles
1 gallon - x miles
3x = 71
x = 71/3
x = 23.67 miles per gallon
b)
Conversion of the mixed number to fraction:
[tex]27\frac{1}{5}=\frac{27\ast5+1}{5}=\frac{135+1}{5}=\frac{136}{5}[/tex]Mileage:
4/5 gallons - 136/5 miles
1 gallon - x miles
Simplifying the top line by 5
4 gallons - 136 miles
1 gallon - x miles
4x = 136
x = 136/4
x = 34 miles per gallon
c)
Blue car: 23.67 miles per gallon
Silver car: 34 miles per gallon
Silver car could travel a greater distance.
Through (1,-2) parallel to y=-2x+5
Answers
Answer:
Step-by-step explanation:The line parallel to y = -2x + 5 that passes through the point(1,1)
Has the same slope, m but a different y intercept (0,b)
So lets start by using the given point (1, 1) and the slope intercept form of the line to calculate b
y = mx + b
m = -2
1 = -2(1) + b
1 = -2 + b
Add 2 to both sides of the equation to solve for b
1 + 2 = b
3 = b
The line is
y = -2x + 3
What is the length of the arc ? ( Precalc )
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We're going to use the following formula:
[tex]L=2\cdot\pi\cdot r\cdot\frac{\theta}{360}[/tex]If we replace our values:
[tex]L=2\cdot\pi\cdot3\cdot\frac{60}{360}=\pi[/tex]Therefore, the length is pi.
Identify the range of the function shown in the graph. 10 8 4 -10-8-4-2 8 10 O A. -2< y < 2 O B. {-2, 2) O C. y is all real numbers OD. Y > 0
Answers
Answer
Option B is correct.
Range: y is all real numbers.
Explanation
The range of a function refers to the region of values where the function can exist. It refers to the values that the dependent variable [y or f(x)] can take on. It is the region around the y-axis that the graph of the function spans.
For this question, we can see that the graph spans over the entire y-axis.
Hence, the range of this function shown in the graph is all real number.
Hope this Helps!!!
The area of an equilateral triangle is decreasing at a rate of 3 cm2/min. Find the rate (in centimeters per minute) at which the length of a side is decreasing when the area of the triangle is 100 cm2.
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The rate at which the length of a side is decreasing when the area of the triangle is 100 cm² is equal to -0.227 centimeters per minute.
What is rate of change?Rate of change is a type of function that describes the average rate at which a quantity either decreases or increases with respect to another quantity.
How to calculate the area of an equilateral triangle?Mathematically, the area of an equilateral triangle can be calculated by using this formula;
A = (√3/4)s²
Where:
A represents the area of an equilateral triangle.s represents the side length of an equilateral triangle.Next, we would determine the side length of a square by making s the subject of formula as follows:
s = (√4A)/√3
s = (√4 × 100)/√3
Side length, s = 15.20
Note: The rate of change (dA/dt) is negative because it is decreasing.
By applying chain rule of differentiation, the rate of change (dA/dt) in area of this equilateral triangle with respect to time is given by:
dA/dt = (√3/4)(2s)ds/dt
dA/dt = (√3/4) × (2 × 15.20) × -3
dA/dt = -0.227 centimeters per minute.
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The table gives a set of outcomes and their probabilities. Let A be the event the outcome is divisible by 3". Find P(A). 12 Outcome Probability Tim elaps 1 0.14 PAUS 2 0.02 3 0.19 Smart out of 4 0.01 5 0.04 7 6 0.17 7 0.15 8 0.28
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Here, we want to get the probability that a selected outcome is divisible by 3
What we have to do here is ti select numbers that are multiples of 3 and add their probabilities
From the given table, the outcomes that are multiples of 3 are;
3 and 6 only
So, we proceed to add the probabilities of these outcomes
Mathematically, we have this as;
[tex]P(A)\text{ = 0.19 + 0.17 = 0.36}[/tex]How many different lineups can Coach Lay create using 10 girls to fill 5 spots on the basketball court. Positions do not matter.
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This is the formula for combinations
In this case, n = 10 and k = 5
C = 10!/(10-5)!(5)! = 3628800/(120)(120) = 3628800/14400 = 252
Answer:
252 different line u
All changes saved16. Suppose you invest $7500 at an annual Interest rate of 4.2% compounded continuously. How much will you have in the account after 2 years? Round the solution to the nearest dollar.$8158$17,372$17,373$8157
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We have to use the continuous compound interest formula
[tex]A=P\cdot e^{rt}[/tex]Where P = 7500, r = 0.042, t = 2. Let's replace and solve
[tex]\begin{gathered} A=7500\cdot e^{0.042\cdot2} \\ A\approx8,157 \end{gathered}[/tex]Hence, the answer is $8,157.The dog looked at the cat warily A with interestb viciously c hungrily d with caution
Answers
Answer
Option D is correct.
The dog looked at the cat with caution.
is the same as
The dog looked at the cat warily.
Explanation
The word warily means 'using caution' or 'cautiously'.
Hope this Helps!!!
At a point on the ground 35 ft from base of a tree, the distance to the top of the tree is 1 ft more than 3 times the height of the tree. Find the height of the tree. The height of the tree is ___. (ft^3, ft^2, or ft)(Simply your answer. Round to the nearest foot as needed)
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At a point on the ground 35 ft from the base of a tree, the distance to the top of the tree is 1 ft more than 3 times the height of the tree. Find the height of the tree
see the attached figure to better understand the problem
Applying the Pythagorean Theorem
(3h+1)^2=h^2+35^2
9h^2+6h+1=h^2+1,225
solve for h
9h^2-h^2+6h+1-1,225=0
8h^2+6h-1,224=0
Solve the quadratic equation
Using a graphing tool
the solution is
h=12 ftFind conditions on k that will make the matrix A invertible. To enter your answer, first select 'always', 'never', or whether k should be equal or not equal to specific values, then enter a value or a list of values separated by commas.
Answers
To be a matrix to be invertible the determinant of the matrix must be non zero thus for k ≠ 2 the matrix will be invertible.
What is a matrix?matrix, a collection of numbers lined up in rows and columns to produce a rectangular array.
In computer graphics, where they have been used to describe picture transformations and other alterations.
The elements of the matrix, also known as the entry, are the numerals.
A matrix will be invertible only and only if the determinant is non-zero.
Given the matrix A.
The determinant of A is that |A| will be,
|A| = -3(8 - 8) - 0(-k + 2) - 3(-4k + 8) ≠ 0
0 + 0 + -3(-4k + 8) |A| ≠ 0
-4k + 8 ≠ 0
-4k ≠ -8
k ≠ 2
Hence "To be a matrix to be invertible the determinant of the matrix must be non zero thus for k ≠ 2 the matrix will be invertible".
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50 Points
A rectangle has sides measuring (2x + 5) units and (3x + 7) units.
Part A: What is the expression that represents the area of the rectangle? Show your work.
Part B: What are the degree and classification of the expression obtained in Part A?
Part C: How does Part A demonstrate the closure property for the multiplication of polynomials?
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The expression that represents the area of the rectangle is 6x²+29x+35.
Given that, a rectangle has sides measuring (2x + 5) units and (3x + 7) units.
What is the area of a rectangle?The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.
Part A:
Now, area = (2x+5)(3x+7)
= 2x(3x+7)+5(3x+7)
= 6x²+14x+15x+35
= 6x²+29x+35
So, the area of a rectangle is 6x²+29x+35
Part B:
A polynomial's degree is the highest or the greatest power of a variable in a polynomial equation.
Here, the degree of the expression 6x²+29x+35 is 2.
Part C:
Closure property of multiplication states that if any two real numbers a and b are multiplied, the product will be a real number as well.
Here, we obtained product of two binomials is trinomial
Therefore, the expression that represents the area of the rectangle is 6x²+29x+35.
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Anna's room is a rectangle. Its length is 15 feet and its width is 4 yards. What is the perimeter of the room?
Answers
Answer:
38
Step-by-step explanation:
Perimeter is basically each side added together. 15 + 15 + 4 + 4 is 38. Therefore, it's 38.
9. A researcher gathered data on hours of video games played by school-aged children and young adults. She collected the following data:601241215171711409914110131015163915121698131016651717129(a) Complete the frequency distribution for the data.HoursFrequencyRelative Frequency0-23-56-89-1112-1415-17(b) Which of the following is the correct histogram for this data?246810Hours0369121518Frequency[Graphs generated by this script: setBorder(54,40,20,15); initPicture(0,18,0,10);axes(34,2,1,null,2); fill="blue"; textabs([165,0],"Hours","above");line([0,-0.2],[0,0.2]); text([0,0],"0","below");line([3,-0.2],[3,0.2]); text([3,0],"3","below");line([6,-0.2],[6,0.2]); text([6,0],"6","below");line([9,-0.2],[9,0.2]); text([9,0],"9","below");line([12,-0.2],[12,0.2]); text([12,0],"12","below");line([15,-0.2],[15,0.2]); text([15,0],"15","below");line([18,-0.2],[18,0.2]); text([18,0],"18","below");textabs([0,115],"Frequency","right",90);rect([0,0],[3,6]);rect([3,0],[6,4]);rect([6,0],[9,5]);rect([9,0],[12,7]);rect([12,0],[15,6]);rect([15,0],[18,10]);]246810121416Hours061218Frequency[Graphs generated by this script: setBorder(54,40,20,15); initPicture(0,18,0,16);axes(34,2,1,null,2); fill="blue"; textabs([165,0],"Hours","above");line([0,-0.32],[0,0.32]); text([0,0],"0","below");line([6,-0.32],[6,0.32]); text([6,0],"6","below");line([12,-0.32],[12,0.32]); text([12,0],"12","below");line([18,-0.32],[18,0.32]); text([18,0],"18","below");textabs([0,115],"Frequency","right",90);rect([0,0],[6,10]);rect([6,0],[12,12]);rect([12,0],[18,16]);]2468101214Hours061218Frequency[Graphs generated by this script: setBorder(54,40,20,15); initPicture(0,18,0,14);axes(34,2,1,null,2); fill="blue"; textabs([165,0],"Hours","above");line([0,-0.28],[0,0.28]); text([0,0],"0","below");line([6,-0.28],[6,0.28]); text([6,0],"6","below");line([12,-0.28],[12,0.28]); text([12,0],"12","below");line([18,-0.28],[18,0.28]); text([18,0],"18","below");textabs([0,115],"Frequency","right",90);rect([0,0],[6,12]);rect([6,0],[12,14]);rect([12,0],[18,12]);]2468Hours0369121518
Answers
Remember that the frequency refers to the number of times a data shows up. In this case, the frequency is the number of data that falls into each interval.la
To find the relative frequency is calculated by dividing each frequency by 38 (the total number of data).
[tex]\begin{gathered} \frac{6}{38}=0.1579 \\ \frac{4}{38}=0.1053 \\ \frac{4}{38}=0.1053 \\ \frac{8}{38}=0.2105 \\ \frac{7}{38}=0.1842 \\ \frac{9}{38}=0.2368 \end{gathered}[/tex]Let's include the relative frequencies in the table.
On the other hand, the correct histogram has to show the frequencies in the same order. The following histogram shows the correct frequency distribution.
You start at (9,2). you move left 9 units. where do you end
Answers
If you start at (9,2) and then move left 9 units, you'll end up at (0, 2)
Ali borrowed Php22,000 for 3months at the discount rate of 5 ¼ % from a bank. Find the (a) bank’s discount and (b) proceeds.
Answers
If an M amount is borrowed for a time t at a discount rate of r per year, then the discount D is calculated as
[tex]\begin{gathered} D=M\cdot r\cdot t \\ \\ \text{where} \\ r\text{ is expressed in decimals} \end{gathered}[/tex][tex]\begin{gathered} \text{Given} \\ M=22000 \\ r=5\frac{1}{4}\%\rightarrow5.25\%\rightarrow0.0525 \\ t=\mleft(\frac{3}{12}\mright)\text{or }0.25\text{ (3 months out of 1 year or 12 months} \end{gathered}[/tex]Substitute the following values to get the bank's discount.
[tex]\begin{gathered} D=Mrt \\ D=(22000)(0.0525)(\frac{3}{12}) \\ D=288.75 \end{gathered}[/tex]Therefore, the bank's discount is Php 288.75.
To calculate for proceeds, subtract the amount borrowed by the bank's discount.
[tex]\begin{gathered} P=M-D \\ P=22000-288.75 \\ P=21711.25 \end{gathered}[/tex]The proceeds given to Ali is Php 21,711.25.
l show how the distributive property can make the arithmetic simpler in the following problems5(108)
Answers
Firstly Example of Distributive property can be shown below.
GIiven: 6(9 - 4)
6 x 9 - 6 x 4
54 - 24 = 30
a) 3(50.15)
3(50 + 0.15)
3x50 + 3 x0.15
150 + 0.45 = 150.45
(b) 5(108)
5(100 + 8)
5x100 + 5x8
500 + 40 = 540
Please help me I need the answer asap.
Answers
Therefore the right answer is option D = 1. The values of the variables will be obtained when the system of linear equations is solved; this is referred to as the solution of a linear equation.
What are linear equations?An equation with the form Ax+By=C is referred to as a linear equation. It consists of two variables combined with a constant value that exists in each of them. The values of the variables will be obtained when the system of linear equations is solved; this is referred to as the solution of a linear equation. If an equation has the formula y=mx+b, with m representing the slope and b the y-intercept, it is said to be linear.A two-variable linear equation can be thought of as a linear relationship between x and y, or two variables whose values rely on each other (often y and x) (usually x).Hence,
The correct Option is D = 1
Given
[tex]x^2+x-1\\[/tex] = 0
[tex]\frac{1-x}{2x^2} +\frac{ x^2}{2x-2}[/tex] = ?
From [tex]x^2+x-1\\[/tex] = 0
[tex]x^2 = 1-x[/tex]
Therefore,
[tex]\frac{1-x}{2x^2} +\frac{ x^2}{2x-2}[/tex] = [tex]\frac{x^2}{2x^2} + \frac{x^2}{2(x-1)}[/tex]
[tex]\frac{1}{2} + \frac{x^2}{2(x-1)}[/tex]
[tex]\frac{1}{2} + \frac{1}{2}[/tex]
= 1
Therefore the right answer is option D = 1
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The graph of f(a) = > has been transformed to create the graph of g(s) =
Answers
EXPLANATION
The graph of the parent function: f(x) = 1/x has the following form:
Translating the function two units to the left, give us the Image function:
This function is obtained by adding two units to the denominator.
In conclusion, the solution is -2