The given system is:
[tex]\begin{gathered} 2x+y-3z=1\ldots(i) \\ 3x-y-4z=7\ldots(ii) \\ 5x+2y-6z=5\ldots(iii) \end{gathered}[/tex]Add (i) and (ii) to get:
[tex]\begin{gathered} 2x+y-3z=1 \\ + \\ 3x-y-4z=7 \\ 5x-7z=8\ldots(iv) \end{gathered}[/tex]Multiply (ii) by 2 to get:
[tex]6x-2y-8z=14\ldots(v)[/tex]Add (iii) and (v) to get:
[tex]\begin{gathered} 6x-2y-8z=14 \\ + \\ 5x+2y-6z=5 \\ 11x-14z=19\ldots(vi) \end{gathered}[/tex]Multiply (iv) by 2 to get:
[tex]10x-14z=16\ldots(vii)[/tex]Subtract (vii) from (vi) to get:
[tex]\begin{gathered} 11x-14z=19 \\ - \\ 10x-14z=16 \\ x=3 \end{gathered}[/tex]Put x=3 in (iv) to get:
[tex]\begin{gathered} 5\times3-7z=8 \\ -7z=8-15 \\ -7z=-7 \\ z=1 \end{gathered}[/tex]Put x=3 and z=1 in (i) to get:
[tex]\begin{gathered} 2(3)+y-3(1)=1 \\ 6+y-3=1 \\ y+3=1 \\ y=-2 \end{gathered}[/tex]So the values are x=3,y=-2 and z=1.
Where are all the tutors at??? Like it won’t even let me ask a tutor
The scatter plot is given and objective is to find the best line of fit for given scatter plot.
Let's take the few points of scatter plot,
(0,8) ,( -1,8) , (-4,10) ,( -8,12),(-10,14) (-12,14)
Take the line and check which graph contains most of the points of scatter plot.
[tex]1)\text{ f(x)=}\frac{-1}{2}x+8[/tex]The graph is ,
now take ,
[tex]2)\text{ f(x)=x+8}[/tex]The graph is,
This graph contains only one point of scatter plot.
Take,
[tex]3)\text{ f(x)= 10}[/tex]Now the take the last equation,
[tex]4)\text{ f(x)=-2x+14}[/tex]this graph contains no point of the scatter plot.
From all the four graph of the lines it is observed that option 1) is the best line of fit for given scatter plot. because it contains 3 points of scatter plotes . which is more than the other graph of line.
Answer: Option 1)
Which of the following steps were applied to ABC obtain A’BC’?
Given,
The diagram of the triangle ABC and A'B'C' is shown in the question.
Required:
The translation of triangle from ABC to A'B'C'.
Here,
The coordinates of the point A is (2,5).
The coordinates of the point A' is (5,7)
The translation of the triangle is,
[tex](x,y)\rightarrow(x+3,y+2)[/tex]Hence, shifted 3 units right and 2 units up.
please help me and answer quick because my brainly keeps crashing before i can see the answer
The surface area of a sphere is given by the formula
[tex]SA=4*pi*r^2[/tex]we have
r=24/2=12 ft ----> the radius is half the diameter
substitute
[tex]\begin{gathered} SA=4*pi*12^2 \\ SA=576pi\text{ ft}^2 \end{gathered}[/tex]Your parents will retire in 25 years. They currently have $230,000 saved, and they think they will need $1,850,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds? Round your answer to two decimal places.
6.62% is annual interest rate must they earn to reach their goal.
What exactly does "interest rate" mean?
An interest rate informs you of how much borrowing will cost you and how much saving will pay off. Therefore, the interest rate is the amount you pay for borrowing money and is expressed as a percentage of the entire loan amount if you are a borrower.N = 25
PV = - $230,000
FV = $1,850,000
PMT = 0
CPT Rate
Applying excel formula:
=RATE(25,0,-230,000,1,850,000)
= 6.62%
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A recent survey asked respondents how many hours they spent per week on the internet. Of the 15 respondents making$2,000,000 or more annually, the responses were: 0,0,0,0,0, 2, 3, 3, 4, 5, 6, 7, 10, 40 and 70. Find a point estimate of thepopulation mean number of hours spent on the internet for those making $2,000,000 or more.
Given
The total frequency is 15 respondents
The responses were: 0,0,0,0,0, 2, 3, 3, 4, 5, 6, 7, 10, 40 and 70
Solution
The population mean is the sum of all the values divided by the total frequency .
[tex]undefined[/tex]What is an equation of a parabola with the given vertex and focus? vertex: (-2, 5)focus: (-2, 6)show each step
Explanation
the equation of a parabola in vertex form is give by:
[tex]\begin{gathered} y=a(x-h)^2+k \\ \text{where} \\ (h,k)\text{ is the vertex} \\ and\text{ the focus is( h,k}+\frac{1}{4a}) \end{gathered}[/tex]Step 1
so
let
a) vertex
[tex]\begin{gathered} vertex\colon(h.k)\text{ }\rightarrow(-2,5) \\ h=-2 \\ k=5 \end{gathered}[/tex]and
b) focus
[tex]\begin{gathered} \text{( h,k}+\frac{1}{4a})\rightarrow(-2,6) \\ so \\ h=-2 \\ \text{k}+\frac{1}{4a}=6 \\ \end{gathered}[/tex]replace the k value and solve for a,
[tex]\begin{gathered} \text{k}+\frac{1}{4a}=6 \\ 5+\frac{1}{4a}=6 \\ \text{subtract 5 in both sides} \\ 5+\frac{1}{4a}-5=6-5 \\ \frac{1}{4a}=1 \\ \text{cross multiply } \\ 1=1\cdot4a \\ 1=4a \\ \text{divide both sides by }4 \\ \frac{1}{4}=\frac{4a}{4}=a \\ a=\text{ }\frac{1}{4} \end{gathered}[/tex]Step 2
finally, replace in the formula
[tex]\begin{gathered} y=a(x-h)^2+k \\ y=\frac{1}{4}(x-(-2))^2+5 \\ y=\frac{1}{4}(x+2)^2+5 \\ \end{gathered}[/tex]therefore, the answer is
[tex]y=\frac{1}{4}(x+2)^2+5[/tex]I hope this helps you
Find the surface area and the volume of the figure below round your answer to the nearest whole number
The shape in the questionis a sphere having
Radius = 10ft
Finding the Surface area
The surface area of a square is given as
[tex]\text{Surface Area of sphere = 4}\pi r^2[/tex]putting the value for radius
[tex]\begin{gathered} \text{Surface Area of sphere = 4 }\times\frac{22}{7}\times\text{ 10}\times10 \\ \text{Surface Area of sphere = }\frac{4\text{ }\times22\times10ft\times10ft}{7} \\ \text{Surface Area of sphere = }\frac{8800ft^2}{7} \\ \text{Surface Area of sphere = 1257.14ft}^2 \\ \text{Surface Area of sphere }\cong1257ft^2\text{ ( to the nearest whole number)} \end{gathered}[/tex]The surface area of the sphere = 1257 square feet
Finding the volume
The volume of a sphere is given as
[tex]\text{volume of sphere = }\frac{4}{3}\pi r^3[/tex]putting the value of radius
[tex]\begin{gathered} \text{Volume of sphere = }\frac{4}{3}\times\frac{22}{7}\text{ }\times10ft\text{ }\times10ft\text{ }\times10ft \\ \text{Volume of sphere = }\frac{88000ft^3}{21} \\ \text{Volume of sphere = 4190.47ft}^3 \\ \text{Volume of sphere}\cong4190ft^3\text{ (to the nearest whole number)} \end{gathered}[/tex]Therefore, the volume of the sphere = 4190 cubic feet
Challenge A family wants to rent a car to go on vacation. Company A charges $75.50 and14¢ per mile. Company B charges $30.50 and 9¢ per mile. How much more does Company Acharge for x miles than Company B?For x miles, Company A charges dollars more than Company B.(Simplify your answer. Use integers or decimals for any numbers in the expression.)
Company A charges $75.50 and 14¢ per mile, then for x miles, Company A charges 75.5 + 0.14x dollars
Company B charges $30.50 and 9¢ per mile, then for x miles, Company B charges 30.5 + 0.09x dollars
Subtracting the second equation to the first one,
75.5 + 0.14x
-
30.5 + 0.09x
----------------------
45 + 0.05x
For x miles, Company A charges 45 + 0.05x dollars more than Company B.
Find the axis of symmetry, vertex and which direction the graph opens, and the y-int for each quadratic function
Solution
Part a
The axis of symmetry
Part b
The vertex
Vertex (2,3)
Part c
The graph opens downward
Part D
The y-intercept is the point where a graph crosses the y-axis. In other words, it is the value of y when x=0.
The y-intercept
[tex](0,-5)[/tex]Another
The y-intercept is the point where a graph crosses the y-axis. In other words, it is the value of y when x=0.
[tex]\begin{gathered} y=-2x^2+8x-5 \\ y=-2(0)+8(0)-5 \\ y=0+0-5 \\ y=-5 \end{gathered}[/tex]x=0 y=-5
[tex](0,-5)[/tex]For a period of d days an account balance can be modeled by f(d) = d^ 3 -2d^2 -8d +3 when was the balance $38
Given a modelled account balance for the period of d days as shown below:
[tex]\begin{gathered} f(d)=d^3-2d^2-8d+3 \\ \text{where,} \\ f(d)\text{ is the account balance} \\ d\text{ is the number of days} \end{gathered}[/tex]Given that the account balance is $38, we would calculate the number of days by substituting for f(d) = 38 in the modelled equation as shown below:
[tex]\begin{gathered} 38=d^3-2d^2-8d+3 \\ d^3-2d^2-8d+3-38=0 \\ d^3-2d^2-8d-35=0 \end{gathered}[/tex]Since all coefficients of the variable d from degree 3 to 1 are integers, we would apply apply the Rational Zeros Theorem.
The trailing coefficient (coefficient of the constant term) is −35.
Find its factors (with plus and minus): ±1,±5,±7,±35. These are the possible values for dthat would give the zeros of the equation
Lets input x= 5
[tex]\begin{gathered} 5^3-2(5)^2-8(5)-35=0 \\ 125-2(25)-40-35=0 \\ 125-50-75=0 \\ 125-125=0 \\ 0=0 \end{gathered}[/tex]Since, x= 5 is a zero, then x-5 is a factor.
[tex]\begin{gathered} d^3-2d^2-8d-35=(d-5)(d^2+3d+7)=0 \\ (d-5)(d^2+3d+7)=0 \\ d-5=0,d^2+3d+7=0 \\ d=0, \end{gathered}[/tex][tex]\begin{gathered} \text{simplifying } \\ d^2+3d+7\text{ would give} \\ d=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ a=1,b=3,c=7 \end{gathered}[/tex][tex]\begin{gathered} d=\frac{-3\pm\sqrt[]{3^2-4\times1\times7}}{2\times1} \\ d=\frac{-3\pm\sqrt[]{9-28}}{2} \\ d=\frac{-3\pm\sqrt[]{-17}}{2} \end{gathered}[/tex]It can be observed that the roots of the equation would give one real root and two complex roots
Therefore,
[tex]d=5,d=\frac{-3\pm\sqrt[]{-17}}{2}[/tex]Since number of days cannot a complex number, hence, the number of days that would give a balance of $38 is 5 days
There is a bag filled with 5 blue and 4 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting at least 1 blue?
The probability of getting exactly 1 blue marble from a bag which is filled with 5 blue and 4 red marbles is 40/81.
What is probability?Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
A bag is filled with 5 blue and 4 red marbles.
The total number of marble in the bag are,
5+4=9
One marble is taken at random from the bag, the color is noted and then it is replaced. The probability of getting blue marble is,
P(B)=5/9
probability of getting red marble is,
P(R)=4/9
The Probability of getting red marble in first pick and probability of getting blue marble in second pick
P1=5/9×4/9=20/81
The Probability of getting blue marble in first pick and probability of getting red marble in second pick is,
p2=4/9×5/9=20/81
The exactly 1 blue is taken out, when first marble is red and second is blue or the first one is blue and second one is red. Thus, the probability of getting exactly 1 blue is,
P=p1+p2
=20/81+20/81
40/81
Hence the probability of getting exactly 1 blue marble from a bag which is filled with 5 blue and 4 red marbles is 40/81.
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Referring to the figure, the polygons shown are similar. Findthe ratio (large to small) of their perimeters and areas.
SOLUTION
Consider the image below
The ratio of the side is given by
[tex]\begin{gathered} \text{large to small} \\ \frac{\text{large}}{small}=\frac{length\text{ of the side of the large triangle}}{Length\text{ of the side of small triangle }}=\frac{10}{5}=\frac{2}{1} \\ \\ \end{gathered}[/tex]Since the ratio of the side is the scale factor
[tex]\text{the scale factor =}\frac{2}{1}[/tex]hence The raio of the perimeters is the scale factor
Therefore
The ratio of their parimeter is 2 : 1
The ratio of the Areas is square of the scale factor
[tex]\text{Ratio of Area =(scale factor )}^2[/tex]
Hence
[tex]\begin{gathered} \text{ Since scale factor=}\frac{2}{1} \\ \text{Ratio of Area=}(\frac{2}{1})^2=\frac{2^2}{1^2}=\frac{4}{1} \\ \text{Hence} \\ \text{Ratio of their areas is 4 : 1} \end{gathered}[/tex]Therefore
The ratio of their Areas is 4 :1
The elimination method is used in place over substitution when one equation is not easily solved for ______________ variable.A) a standardB) a dependentC) an independentD) a single
Given:
There are given the statement about the elimination method and substitution method.
Explanation:
According to the concept:
One equation cannot be easily solved for a single variable.
Final answer:
Hence, the correct option is D.
In the given figure ABC is a triangle inscribed in a circle with center O. E is the midpoint of arc BC . The diameter ED is drawn . Prove that
Answer:
we can use two ways to write 180° along with the inscribed angle theorem to obtain the desired relation
Step-by-step explanation:
Given ∆ABC inscribed in a circle O where E is the midpoint of arc BC and ED is a diameter, you want to prove ∠DEA = 1/2(∠B -∠C).
SetupWe can add add arcs to make 180° in two different ways, then equate the sums.
arc EB +arc BA +arc AD = 180°
arc EC +arc CA -arc AD = 180°
Equating these expressions for 180°, we have ...
arc EB +arc BA +arc AD = arc EC +arc CA -arc AD
SolutionRecognizing that arc EB = arc EC, we can subtract (arc EB +arc BA -arc AD) from both sides to get ...
2·arc AD = arc CA -arc BA
The inscribed angle theorem tells us ...
arc AD = 2∠DEAarc CA = 2∠Barc BA = 2∠CMaking these substitutions into the above equation, we have ...
4∠DEA = 2∠B -2∠C
Dividing by 4 gives the relation we're trying to prove:
∠DEA = 1/2(∠B -∠C)
identify the amplitude and period of the function then graph the function and describe the graph of G as a transformation of the graph of its parent function
Given the function:
[tex]g(x)=cos4x[/tex]Let's find the amplitude and period of the function.
Apply the general cosine function:
[tex]f(x)=Acos(bx+c)+d[/tex]Where A is the amplitude.
Comparing both functions, we have:
A = 1
b = 4
Hence, we have:
Amplitude, A = 1
To find the period, we have:
[tex]\frac{2\pi}{b}=\frac{2\pi}{4}=\frac{\pi}{2}[/tex]Therefore, the period is = π/2
The graph of the function is shown below:
The parent function of the given function is:
[tex]f(x)=cosx[/tex]Let's describe the transformation..
Apply the transformation rules for function.
We have:
The transformation that occured from f(x) = cosx to g(x) = cos4x using the rules of transformation can be said to be a horizontal compression.
ANSWER:
Amplitude = 1
Period = π/2
Transformation = horizontal compression.
Find seco, coso, and coto, where is the angle shown in the figure.Give exact values, not decimal approximations.
step 1
Find out the value of cosθ
cosθ=8/17 ------> by CAH
step 2
Find out the value of secθ
secθ=1/cosθ
secθ=17/8
step 3
Find out the length of the vertical leg in the given right triangle
Applying the Pythagorean Theorem
17^2=8^2+y^2
y^2=17^2-8^2
y^2=225
y=15
step 4
Find out the value f cotθ
cotθ=8/15 -----> adjacent side divided by the opposite side
therefore
secθ=17/8cosθ=8/17cotθ=8/15I need help with homework . BC=5, angle A=25 degree.
AC = 2.332
AB = 5.517
Explanation:
Given:
BC = 5.
Angle B = 25 degree.
Angle C = 90 degree.
The objective is to find AC and AB.
By the trigonometric functions, Consider AB as hypotenuse, AC as opposite and BC as adjacent.
Then, the relationship between opposite (AC) and adjacent (BC) cnbe calculated by trigonometric ratio of tan theta.
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \tan 25^0=\frac{AC}{5} \\ AC=\tan 25^0\cdot5 \\ AC=2.332 \end{gathered}[/tex]Now, the length AB can be calculated by Pythagorean theorem,
[tex]\begin{gathered} AB^2=AC^2+BC^2 \\ AB^2=2.332^2+5^2 \\ AB^2=5.436+25 \\ AB^2=30.436 \\ AB=\sqrt[]{30.436} \\ AB=5.517 \end{gathered}[/tex]Let's check the value using trigonometric ratios.
For the relationship of opposite and hypotenuse use sin theta.
[tex]\begin{gathered} \sin \theta=\frac{opposite}{hypotenuse} \\ \sin 25^0=\frac{2.332}{y} \\ y=\frac{2.332}{\sin 25^0} \\ y=5.517 \end{gathered}[/tex]Thus both the answers are matched.
Hence, the length of the side AC = 2.332 and the length of the side AB = 5.517.
find the value of x so that the function has the given value
j(x) = -4/3x + 7; j (x) = -5
Answer:
x = 13 [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
j(x) = [tex]\frac{-4}{3}[/tex] x + 7 Substitute -5 for x
j(-5) = [tex]\frac{-4}{3 }[/tex] ( -5) + 7
or
j(-5) =[tex](\frac{-4}{3})[/tex] [tex](\frac{-5}{1})[/tex] + 7 A negative times a negative is a positive
j(-5) = [tex]\frac{20}{3}[/tex] + 7
j(-5) = [tex]\frac{20}{3}[/tex] + [tex]\frac{21}{3}[/tex] [tex]\frac{21}{3}[/tex] means the same thing as 7
j(-5) = [tex]\frac{41}{3}[/tex] = 13 [tex]\frac{2}{3}[/tex]
Which of the following ordered pairs is a solution to the graph of the system of inequalities? Select all that apply(5.2)(-3,-4)(0.-3)(0.1)(-4,1)
For this type of question, we should draw a graph and find the area of the common solutions
[tex]\begin{gathered} \because-2x-3\leq y \\ \therefore y\ge-2x-3 \end{gathered}[/tex][tex]\begin{gathered} \because y-1<\frac{1}{2}x \\ \therefore y-1+1<\frac{1}{2}x+1 \\ \therefore y<\frac{1}{2}x+1 \end{gathered}[/tex]Now we can draw the graphs of them
The red line represents the first inequality
The blue line represents the second inequality
The area of the two colors represents the area of the solutions,
Let us check the given points which one lies in this area
Point (5, -2) lies on the area of the solutions
∴ (5, -2) is a solution
Point (-3, -4) lies in the blue area only
∴ (-3, -4) not a solution
Point (0, -3) lies in the red line and the red line is solid, which means any point on it will be on the area of the solutions
∴ (0, -3) is a solution
Point (0, 1) lies in the blue line and the blue line is dashed, which means any point that lies on it not belong to the area of the solutions
∴ (0, 1) is not a solution
Point (-4, 1) lies on the area of the solutions
∴ (-4, 1) is a solution
The solutions are (5, -2), (0, -3), and (-4, 1)
Fill In the proportion No explanation just need answer got disconnected from last tutor
Explanation
Since the given shapes are similar, which implies that they are proportional,
Therefore; we will have
Answer:
[tex]\frac{AB}{EF}=\frac{BC}{FG}[/tex]The mean amount of time it takes a kidney stone to pass is 16 days and the standard deviation is 5 days. Suppose that one individual is randomly chosen. Let X = time to pass the kidney stone. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(16Correct,5Correct) b. Find the probability that a randomly selected person with a kidney stone will take longer than 17 days to pass it. 0.2Incorrectc. Find the minimum number for the upper quarter of the time to pass a kidney stone. 0.8Incorrect days.
Answer:
• (a)X ~ N(16, 5)
,• (b)0.4207
,• (c)19.37 days
Explanation:
(a)
• The mean amount of time = 16 days
,• The standard deviation = 5 days.
Therefore, the distribution of X is:
[tex]X\sim N(16,5)[/tex](b)P(X>17)
To find the required probabability, recall the z-score formula:
[tex]z=\frac{X-\mu}{\sigma}[/tex]When X=17
[tex]z=\frac{17-16}{5}=\frac{1}{5}=0.2[/tex]Next, find the probability, P(x>0.2) from the z-score table:
[tex]P(x>0.2)=0.4207[/tex]The probability that a randomly selected person with a kidney stone will take longer than 17 days to pass it is 0.4207.
(c)The upper quarter is the value under which 75% of data points are found.
The z-score associated with the 75th percentile = 0.674.
We want to find the value of X when z=0.674.
[tex]\begin{gathered} z=\frac{X-\mu}{\sigma} \\ 0.674=\frac{X-16}{5} \\ \text{ Cross multiply} \\ X-16=5\times0.674 \\ X=16+(5\times0.674) \\ X=19.37 \end{gathered}[/tex]The minimum number for the upper quarter of the time to pass a kidney stone is 19.37 days.
Use the given scale factor and the side lengths of the scale drawing to determine the side lengths of the real object. Scale factor. 4:1 10 in 10 in A C 12 in Scale drawing Object A. Side a is 6 inches long, side bis 6 inches long, and side cis 8 inches long. B. Side a is 14 inches long, side bis 14 inches long, and side cis 16 inches long. C. Side a is 40 inches long, side bis 40 inches long, and side c is 48 inches long D. Side a is 2.5 inches long, side bis 2.5 inches long, and side cis 3
As the scale factor is 4:1 it means that for each 4inches in scale drawing correspond to 1 inch in the object.
Then, to find the side lengths in the object you multiply the measure of each side in the scale drawing by 1/4:
[tex]\begin{gathered} 10in\cdot\frac{1}{4}=2.5in \\ \\ 10in\cdot\frac{1}{4}=2.5in \\ \\ 12in\cdot\frac{1}{4}=3in \end{gathered}[/tex]Then, side a is 2.5 inches, side b is 2.5in and side c is 3inchesPerform the indicated operation and write the answer in the form A+Bi
The Solution:
Given:
[tex](3+8i)(4-3i)[/tex]We are required to simplify the above expression in a+bi form.
Simplify by expanding:
[tex]\begin{gathered} (3+8i)(4-3i) \\ 3(4-3i)+8i(4-3i) \\ 12-9i+32i-24(-1) \end{gathered}[/tex]Collecting the like terms, we get:
[tex]\begin{gathered} 12-9i+32i+24 \\ 12+24-9i+32i \\ 36+23i \end{gathered}[/tex]Therefore, the correct answer is [option 3]
A bag of tokens contains 55 red, 44 green, and 55 blue tokens. What is the probability that a randomly selected token is not red? Enter your answer as a fraction.
Explanation
In the bag of tokens, we are told 55 red, 44 green, and 55 blue tokens. Therefore, the total number of tokens in the bag is
[tex]55+44+55=154[/tex]Hence to find the probability that a randomly selected token is not red becomes;
[tex]Pr(not\text{ red black})=\frac{n(green)+n(blue)}{n(tokens)}=\frac{44+55}{154}=\frac{99}{154}=\frac{9}{14}[/tex]Answer: 9/14
? Question
Rachel and Jeffery are both opening savings accounts. Rachel deposits $1,500 in a savings account that earns 1.5% interest,
compounded annually. Jeffery deposits $1,200 in a savings account that earns 1% interest per year, compounded
continuously.
If y represents the account balance after t years, which two equations form the system that best models this situation?
For the conditions stated, y=1500+2250t and y=1200+1200t, respectively, will be necessary equations because both Rachel and Jeffery are opening savings accounts. Rachel places $1,500 in a savings account that accrues annual compound interest of 1.5%. Jeffery places $1,200 in a savings account that accrues continuously compounded interest of 1% per year.
What is equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Here,
according to given condition,
y=1500+1500*1.5t
y=1500+2250t
y=1200+1200*1t
y=1200+1200t
So the required equation will be y=1500+2250t and y=1200+1200t for the conditions given as Rachel and Jeffery are both opening savings accounts. Rachel deposits $1,500 in a savings account that earns 1.5% interest, compounded annually. Jeffery deposits $1,200 in a savings account that earns 1% interest per year, compounded continuously.
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PLEASE READ BEFORE ANSWERING: ITS ALL ONE QUESTION HENCE "QUESTION 6" THEY ARE NOT INDIVIDUALLY DIFFERENT QUESTIONS.
First, lets note that the given functions are polynomials of degree 2. Since the domain of a polynomial is the entire set of real numbers, the domain for all cases is:
[tex](-\infty,\infty)[/tex]Now, lets find the range for all cases. In this regard, we will use the first derivative criteria in order to obtain the minimum (or maximim) point.
case 1)
In the first case, we have
[tex]\begin{gathered} 1)\text{ }\frac{d}{dx}f(x)=6x+6=0 \\ which\text{ gives} \\ x=-1 \end{gathered}[/tex]which corresponds to the point (-1,-8). Then the minimum y-value is -8 because the leading coefficient is positive, which means that the curve opens upwards. So the range is
[tex]\lbrack-8,\infty)[/tex]On the other hand, the horizontal intercept (or x-intercept) is the value of the variable x when the function value is zero, that is,
[tex]3x^2+6x-5=0[/tex]which gives
[tex]\begin{gathered} x_1=-1+\frac{2\sqrt{6}}{3} \\ and \\ x_2=-1-\frac{2\sqrt{6}}{3} \end{gathered}[/tex]Case 2)
In this case, the first derivative criteria give us
[tex]\begin{gathered} \frac{d}{dx}g(x)=2x+2=0 \\ then \\ x=-1 \end{gathered}[/tex]Since the leading coefficient is positive, the curve opens upwards so the point (-1,5) is the minimum values. Then, the range is
[tex]\lbrack5,\infty)[/tex][tex]\lbrack5,\infty)[/tex]and the horizontal intercepts do not exists.
Case 3)
In this case, the first derivative criteris gives
[tex]\begin{gathered} \frac{d}{dx}f(x)=-2x=0 \\ then \\ x=0 \end{gathered}[/tex]Since the leading coeffcient is negative the curve opens downwards and the maximum point is (0,9). So the range is
[tex](-\infty,9\rbrack[/tex]and the horizontal intercepts occur at
[tex]\begin{gathered} -x^2+9=0 \\ then \\ x=\pm3 \end{gathered}[/tex]Case 4)
In this case, the first derivative yields
[tex]\begin{gathered} \frac{d}{dx}p(t)=6t-12=0 \\ so \\ t=2 \end{gathered}[/tex]since the leading coefficient is postive the curve opens upwards and the point (2,-12) is the minimum point. Then the range is
[tex]\lbrack-12,\infty)[/tex]and the horizontal intercetps ocurr when
[tex]\begin{gathered} 3x^2-12x=0 \\ which\text{ gives} \\ x=4 \\ and \\ x=0 \end{gathered}[/tex]Case 5)
In this case, the leading coefficient is positive so the curve opens upwards and the minimum point ocurrs at x=0. Therefore, the range is
[tex]\lbrack0,\infty)[/tex]and thehorizontal intercept is ('0,0).
In summary, by rounding to the nearest tenth, the answers are:
Use mental math to find all of the quotients equal to 50. Drag the correct division problems into the box.
4
,
500
÷
900
450
÷
90
45
,
000
÷
900
4
,
500
÷
90
450
÷
9
Quotients equal to 50
Answer: 45,000 ÷ 900=50
Step-by-step explanation:
7. The cylinder shown has a radius of 3inches. The height is three times the radiusFind the volume of the cylinder. Round yoursolution to the nearest tenth.
Answer:
250 cubic inches
Explanation:
Given that:
Radius of the cylinder, = 3 in.
Height of the cylinder = 3r
= 3(3)
=9 in.
The formula to find the volume of a cylinder is
[tex]V=\pi r^2h[/tex]Plug the given values into the formula.
[tex]\begin{gathered} V=\pi3^29 \\ =81\pi \\ =254.469 \end{gathered}[/tex]Rounding to nearest tenth gives 250 cubic inches, which is the required volume of the cylinder.
How many ways can Rudy choose 4 pizza toppings from a menu of 16 toppings if each can only be chosen once
ANSWER:
1820 different ways
STEP-BY-STEP EXPLANATION:
We can use here combination rule for selection:
[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex]In this case n is equal to 16 and r is equal to 4, therefore, replacing and calculating the number in different ways, there:
[tex]\begin{gathered} _{16}C_4=\frac{16!}{4!(16-4)!}=\frac{16!}{4!\cdot12!} \\ \\ _{16}C_4=1820 \end{gathered}[/tex]So in total there are 1820 different ways Rudy can choose 4 pizza toppings.
sum 0f 5 times a and 6
Answer:
30a
Step-by-step explanation: