If the coordinates of (-6,4) satisfies the equations of the two lines, (-6,4) is the solution to the system of equations.
This means that if the two lines intersect at (-6,4), then (-6,4) is the solution to the system of equations.
This means that if you substitute -6 for x and 4 for y, both equations will be equal at (-6,4).
How to obtain the graphic solution for a system of equations?The graphic solution for a system of equations is obtained by the intersection point of all the lines that compose the system of linear equations, meaning that the ordered pair (x,y) of the intersection point will satisfy all the equations in the system.
Missing Information
This problem is incomplete, hence the answer was given in general terms.
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Noah went into a movie theater and bought 9 drinks and 4 candies, costing a total of $60. Nachelle went into the same movie theater and bought 10 drinks and 2 candies, costing a total of $57.50. Determine the price of each drink and the price of each candy.
Answer:
Drink: $5
Candy : $3.75
Step-by-step explanation:
Let d = the cost of a drink
Let c = the cost of a candy
9d + 4c = 60
10d + 2c = 57.50 ⇒ Mult. by -2 ⇒ -20d -4c = -115 Add this to the first equation
-20d - 4c = -115
9d + 4c = 60
-11d = -55 Divide both sides by -11
d = 5
A drink costs $5.00.
Plug in 5 for d in either of the two equations to solve for c
9d + 4c = 60
9(5) + 4x = 60
45 + 4c = 60 Subtract 45 from both sides
4c = 15 Divide both sides by 4
x = 3.75
A candy costs $3.75
A line passes through the point (9, 1) and has a slope of -4/3
Write an equation in slope-intercept form for this line.
Answer:
Step-by-step explanation:
the answer is y= -4x/3 + 13
a bullet of mass m and speed v passes completely through a pendulum bob of mass M. The bullet emerges with a speed v/2. Thependulum bob is suspended by a stiff rod of length and negligible mass. What is the minimum value of v such that the pendulum bob will barely swing through a complete vertical circle?
Sell Order 5: Price: $20, Quantity: 400
Since this order has the same price as Sell Order 2, it will be executed fifth.
1: Sell Order 3: Price: $30, Quantity: 300
2: Sell Order 1: Price: $25, Quantity: 500
3: Sell Order 4: Price: $25, Quantity: 100
4: Sell Order 2: Price: $20, Quantity: 200
5: Sell Order 5: Price: $20, Quantity: 400
1: Sell Order 3: Price: $30, Quantity: 300
Since this order has the highest price, it will be executed first.
2: Sell Order 1: Price: $25, Quantity: 500
Since this order has the second highest price, it will be executed second.
3: Sell Order 4: Price: $25, Quantity: 100
Since this order has the same price as Sell Order 1, it will be executed third.
4: Sell Order 2: Price: $20, Quantity: 200
Since this order has the third highest price, it will be executed fourth.
5: Sell Order 5: Price: $20, Quantity: 400
Since this order has the same price as Sell Order 2, it will be executed fifth.
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Question 27 of 40
The vertex of the parabola below is at the point (1,-5). Which of the following
could be this parabola's equation?
-10
-20-
20
(1.-5)
10
A. y= (x + 1)² +5
B. y= 2x² +5
O
OC. y=x5
OD. y=(x-1)2-5
The possible equation of the parabola is f(x) = (x - 1)² - 5
How to determine the possible equation of the parabolaFrom the question, we have the following parameters that can be used in our computation:
Vertex = (1, -5)
Rewrite the vertex as follows
So, we have the following representation
(h, k) = (1, -5)
A quadratic function can be represented as
f(x) = a(x - h)² + k
Where
Vertex = (h, k)
Substitute the known values in the above equation, so, we have the following representation
f(x) = a(x - 1)² - 5
Set a = 1
f(x) = (x - 1)² - 5
Hence, the function is (d) f(x) = (x - 1)² - 5
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What values of u and v make ΔHIJ ≅ ΔCDE?
u= ?
v= ?
Answer:
u = 8 ; v = 7
Step-by-step explanation:
5u = u + 32
5u - u = 32
4u = 32
4/4 u = 32/4
u = 8
v + 7 = 2v
2v - v = 7
v = 7
c. in cell d63, use the count function in the in-cell dropdown to calculate the number of members using the values in the animal field.
the number of members using the values in the animal field. then the value is 63
1. Application layer: this is the interface that connects a user to a network, the files or data are generated and seek from this layer. Protocols in this layer are FTP, TFTP, DNS, SMTP, SNMP etc.
2. Presentation layer: it is the sixth layer in the OSI model. It is used to present data in a well organized syntax and format to and application and also for document format encryption. Protocols in this layer are XDR, TLS, SSL and MIME.
3. Session layer: this layer is used to create and terminate sessions between the destination and source node, in a network. Protocols in this layer are PPTP, SAP, L2TP and NETBIOS.
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when approximating the area below a curve, using midpoint rectangles always produces the best approximation.
The statement given is true. When approximating the area below a curve, using midpoint rectangles always produces the best approximation.
A good way to estimate areas with rectangles is to make each rectangle cross the curve at the midpoint of that rectangle's top side. Midpoints always the best approximate for the area under the curve using a finite number of rectangles.
What to use the midpoint rule?The midpoint rule, also known as the rectangle method or mid-ordinate rule, is used to estimate the area under a simple curve. There are other methods to estimate the area, such as the left rectangle or right rectangle sum, but the midpoint rule gives the better approximate compared to the two methods.
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Cliff (W-2 wages: $16,228) and Deb (W-2 wages: $2,600) send their daughter Julia (born 10-1-2010) to daycare while they both worked. They paid $250 per month for daycare. They are filing MFJ. They can claim the credit for child and dependent care expenses. What is their eligible amount of work-related daycare expenses?
The eligible amount of work-related daycare expenses will be $2600
What is MFJ?Married filing jointly is a filing status for married couples, allowing them to file joint tax returns. When filing taxes under married filing jointly status, a married couple can record their respective incomes, deductions, credits, and exemptions on the same tax return.
Given here wages of the cliff are $16,228 and if the deb is $2,600
now the mfj is 35% hence cliffs credit is 35% × $16,228 = $5679.8
and daycare yearly expenses are = $250×12
= $3000
but deb's income is $2600 and thus credit cannot exceed deb's wages therefore the revised credit would be $2600
Hence, the eligible amount of work-related daycare expenses will be $2600
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In this exercise we want to identify primitive elements (generators) of a multiplicative group since they play a big role in the DHKE and many other public-key schemes based on the DL problem. You are given a prime p = 4969 and the corresponding multiplicative group Z*_969. Determine how many generators exist in Z*_969. What is the probability of a randomly chosen element a Z*_969 being a generator? Determine the smallest generator a Z*_969 with a > 1000. What measures can be taken in order to simplify the search for generators for arbitrary groups Z*_p?
1. Number of generators of Z*4969 = 1584
2. Probability of a randomly chosen element a Z*_969 being a generator = [tex]\frac{1584}{4968}[/tex]
3. 1001 is the smallest generator
4. Number of generators
∅(n) = n [tex](1 - \frac{1}{p_{1} } )(1 - \frac{1}{p_{2} } ).........(1 - \frac{1}{p_{n} } )[/tex]
1. Every relative prime of 4968 offers a generation if a is the generation of Z.
4968 = 4 × 1242
= 4 × 3 × 414
= 4 × 3 × 2 ×207
= 4 × 3 × 2× 3× 69
= 4 × 3 × 2 × 3 × 3 ×23
[tex]= 2^{3} * 3^{3} * 23[/tex]
Number of generators ∅ (4968) = 4968[tex](1 - \frac{1}{2} )(1 - \frac{1}{3} )(1 - \frac{1}{23} )[/tex]
Number of generators of Z*4969 = 1584
2. When a Z*4969 value is set, it becomes a generation and belongs to one of the 1584 elements.
The probability that a element is selected from Z*4968 becomes a generation is
= favorable elememt / total element
= [tex]\frac{1584}{4968}[/tex]
= 0.3188
3. To find the smallest generator a Z*_969 with a > 1000.
a > 1000
Every relative prime of 4968 gives a generation of Z*4969
G C D (1001 4968) = 1
Hence, 1001 is the smallest generator
4. Number of generators
∅(n) = n [tex](1 - \frac{1}{p_{1} } )(1 - \frac{1}{p_{2} } ).........(1 - \frac{1}{p_{n} } )[/tex]
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A piggy bank contains 350 pennies
and nickels worth $11.90. How many
pennies are in the piggy bank?
Answer:
140 pennies
Step-by-step explanation:
Information:
1 penny (cent) = $0.011 nickel = $0.05Define the variables:
Let x be the number of pennies.Let y be the number of nickels.If the piggy bank contains 350 pennies and nickels:
[tex]\implies x+y=350[/tex]
If the piggy bank contains pennies and nickels worth $11.90:
[tex]\implies 0.01x+0.05y=11.90[/tex]
Rearrange the first equation to make y the subject:
[tex]\implies y=350-x[/tex]
Substitute the expression for y into the second equation and solve for x:
[tex]\implies 0.01x+0.05(350-x)=11.90[/tex]
[tex]\implies 0.01x+17.5-0.05x=11.90[/tex]
[tex]\implies -0.04x=-5.6[/tex]
[tex]\implies x=140[/tex]
Therefore, there are 140 pennies in the piggy bank.
A husband and wife plan to save money for their daughter's college education in 5 years. They decide to purchase an annuity with a semiannual payment earning 10.5% compounded semiannually. Find the future value of the annuity in 5years if the semiannual payment is $3150. Round your answer to the nearest cent.
The future value of the annuity is ?
Answer:
$40,601.92
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 1.5/100
r = 0.015 per year,
Then, solve the equation for P
P = I / ((1 + r/n)nt - 1)
P = 3150 / ((1 + 0.015/2)(2)(5) - 1)
P = 3150 / ((1 + 0.0075)(10) - 1)
P = $40,601.92
Summary:
The principal investment required to get a total interest of $3150 from compound interest at a rate of 1.5% per year compounded 2 times per year over 5 years is $40,601.92.
A figure dilated by a factor of 6. By what factor will the perimeter of the figure change.
6. If A and B are supplementary angles
and mA = 8m ZB, find m2 A and m2 B.
[A] 78.75, 11.25
[C] 160, 20
[B] 80, 10
(D) 157.5, 22.5
Answer:
C) 160, 20-----------------------
Given:Angles A and B are supplementary,Angle A is 8 times the angle B.Find the angle measures:We know supplementary angles sum to 180 deg:
m∠A + m∠B = 180,And we are given:
m∠A = 8 m∠BSubstitute the second equation into the first one and solve for m∠B:
8m∠B + m∠B = 1809m∠B = 180m∠B = 180/9m∠B = 20Find m∠A:
m∠A = 8*20m∠A = 160Correct choice is C.
State the domain and range of the following relation: {(2,4), (-1,8), (4,-2), (5,6), (2,-2)}. State whether the relation is a function.
The domain is {2, -1, 4, 5} and the relation is not a function
How to determine the domain?From the question, we have the following parameters that can be used in our computation:
{(2,4), (-1,8), (4,-2), (5,6), (2,-2)}
The domain is the set of the x values
So, we have the following representation
x = {2, -1, 4, 5, 2}
Remove repeated entries
x = {2, -1, 4, 5}
So, the domain is {2, -1, 4, 5}
Also, the relation is not a function
This is because the x value 2 has several y values
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Using the MGFs that you have derived in problem 1 above (and/or in lecture notes), identify the distributions of the random variables with the following moment-generating functions.
a) M(t)=(1−4t)^2 b) M(t)= 1/(1−3.2t)
c) M(t)= e^(−5t∣6t^2)
MGFs means moment generating function. Every distribution function has a unique mgf
Make X a random number. We say that X has a moment generating function, and the function
Mₓ(t) = E(e^tx) is referred to as the moment generating function of X
However, not all random variables have a moment generating function. However, every random variable has a unique function—an additional transform with properties comparable to those of the mgf.
The second creating capability (mgf) is a capability frequently used to describe the circulation of an irregular variable.
The moment-generating function is extremely useful for the following reasons:
1. Moments can be easily calculated with it; At zero, its derivatives are equivalent to the random variable's moments;
2. The mgf of a probability distribution is what makes it unique.
The question is incomplete so, I've answered in general
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how would you explain finding the slope to classmate
Answer/Step-by-step explanation:
Since the axes are labelled and there are nice points marked on the line, you can practically SEE the slope here without any calculating, just by counting. Start with a point and find the directions to the next point. To get from one point to the next, go UP2 and OVER3.
"UP2 and OVER3" is the slope 2/3. Double check that you get a slope that is positive because the line is going up to the right, it should have positive slope.
If the teacher is insisting that you use the slope formula, then name two of the points, such as (0, 4) and (3, 6). First subtract the y's, 6 - 4 is 2, put that on top of a fraction. Then subtract the x's, 3 - 0 is 3, put that on the bottom of a fraction. You get 2/3 again. Doesn't matter what points you use, since they are all on the same line it will come out the same.
592 × 43 in standard algorithm answer needs to be showed
Answer:
25456
Step-by-step explanation:
A tank is full of water. The tank is a right circular cylinder lying on its side (length is parallel to horizon), with radius 2 m, and length 5 m. Find the work required to pump the water out of a spout that rises 2 m above the tank. Set up the integral, but do NOT evaluate. The base of a solid is a circular disk with radius
W =∫ lower power (-r) to higher power (r + h) (h + r - x) 2pgl [tex]\sqrt{r^2+x^2}[/tex] dx is the integral for the effort needed to pump water out of a spout that is 2 m above the tank.
What is meant by Integral?Integral: In mathematics, an integral is either a number representing the region under a function's graph for a certain interval or a new function, the derivative of which is the original function (indefinite integral).
r = 2m
l= 5m
sinθ=x/r
[tex]dv=2l\sqrt{r^2+x^2} dx[/tex]
Let g be the acceleration brought on by gravity, and let p be the density of water.
dm = p dv
dw = dmg (h + r - x)
dw = pg (h + r - x) dx
dw = 2lpg (h + r - x) [tex]\sqrt{r^2+x^2}[/tex] dx
w = ∫dw
w = ∫ lower power (-r) to upper power (r + h) 2pgl (h + r - x) [tex]\sqrt{r^2+x^2}[/tex] dx
Therefore, the integral for the work required to pump the water out of a
spout that rises 2 m above the tank is
w = ∫ lower power (-r) to upper power (r + h) 2pgl (h + r - x) [tex]\sqrt{r^2+x^2}[/tex] dx
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An instructor has given a short quiz consisting of two parts. For a randomly selected student, let X = the number of points earned on the first part and Y = the number of points earned on the second part. The accompanying table shows the number of students who obtained the indicated points for X (rows) and Y (column). The class is composed of 100 students. Y 10 15 6 2 10 15 20 10 10 1 15 14 1 Compute the correlation between the scores of students from the two parts of the quiz.
E(max(X, Y )) = PxPy max(x, y)p(x, y)
= max(0, 0)p(0, 0)+max(0, 5)p(0, 5)+· · ·+max(10, 10)p(10, 10)+max(10, 15)p(10, 15)
= 0 ∗ 0.02 + 5 ∗ 0.06 + · · · + 10 ∗ 0.14 + 15 ∗ 0.01 = 9.6.
fX(x) = R 10(2x + y − 2xy)dy = x +12, 0 ≤ x ≤ 1.
fY (y) = R 10
(2x + y − 2xy)dx = 1, 0 ≤ y ≤ 1.
Since f(x, y) 6= fX(x)fY (y), X and Y are not independent.
Column=A column is a recurring piece or article in a newspaper, magazine or other publication, where a writer expresses their own opinion in few columns allotted to them by the newspaper organisation. Columns are written by columnists.
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figure below to answer the following question.
12.25 cm,
W 48°
T
13.5 cm
13.5 cm
to
55%
U
12.25 cm
The figure is not drawn to scale.
What is the value of x, in degrees?
The value of x, in degrees, is given as follows:
A. 48.
What are similar triangles?Similar triangles are triangles that share these two features given as follows:
Congruent angle measures.Proportional side lengths.The similar triangles in this problem are listed as follows:
WUV and WUT.
In triangle UWV, the length of the side adjacent to the angle of 48º has a length of 13.5 cm.
In triangle WUT, the length of the side adjacent to the angle of x has a length of 13.5 cm.
Reminding the two features of similar triangles, namely congruent angle measures and proportional side lengths, the measure of angle x is given as follows:
x = 48º.
(as the equivalent side length is the same, hence the angle measure is also the same).
This means that option A is correct.
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Simplify for all questions
The required simplified solution of the expression is given as,
1. -2√15 2.3c 4. -5
3. √6 5. 2a
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
1.
[tex]=\sqrt{(3 -\sqrt{15} )^2} - \sqrt{(3 +\sqrt{15} )^2} \\=3 -\sqrt{15} - (3 +\sqrt{15})\\=3 -\sqrt{15} -3 -\sqrt{15}\\= -2\sqrt{15}[/tex]
Similarly, the solution of the various expression can be determined.
2.3c
3. √6
4. -5
5. 2a
Thus, the solution of the expression are given above
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using traditional methods it takes 90 hours to receive an advanced driving license. a new training technique using computer aided instruction (cai) has been proposed. a researcher believes the new technique may lengthen training time and decides to perform a hypothesis test. after performing the test on 190 students, the researcher fails to reject the null hypothesis at a 0.02 level of significance.
The conclusion is that there is no sufficient evidence at the 0.02 level of significance that the new technique lengthens the training time.
Given,
The mean time taken to receive advanced driving license, through traditional methods [tex]\mu = 90[/tex] hours
The researcher believes the new technique may lengthen the training time
Researcher conducts hypothesis test of n = 190 students
The researcher fails to reject the null hypothesis at significance level, [tex]\alpha = 0.02[/tex]
Test hypothesis :-
[tex]H_0[/tex] :The mean time it takes for the new technique to receive an advanced driving license is 90 hours, i.e. [tex]\mu = 90[/tex].
[tex]H_a[/tex]: The mean time it takes for the new technique to receive an advanced driving license is greater than 90 hours, i.e. [tex]\mu > 90[/tex].
Failure to reject the null hypothesis means that our sample did not provide enough evidence to conclude that the effect exists. However, the lack of evidence does not prove that the effect does not exist.
As a result, the average time for the new technique to obtain an advanced driving licence is less than 90 hours.
Thus,, the researcher's belief that the new technique would lengthen training time was incorrect.
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solving systems using substitution 4y=x ; 3x-y=70
Answer:
x= 56/3
y= 14/3
Step-by-step explanation:
for process look at provided image
MODELING REAL LIFE There are a total of 64 students in a filmmaking club and a yearbook club. The filmmaking club has 14 more students than the yearbook club.
a. Write a system of linear equations that represents this situation. Let x represent the number of students in the filmmaking club and y represent the number of students in the yearbook club.
System of equations: x=?
?x+?y=64
b. How many students are in the filmmaking club? the yearbook club?
There are . students in the filmmaking club and students in the yearbook club.
(a) The System of equations that representing this situation is
x= y+14; x+y = 64
(b) There are 39 students in the film-making club and 25 students in the yearbook club.
In the given question, there are a total of 64 students in a film-making club and a yearbook club.
The film-making club has 14 more students than the yearbook club.
a. We have to write a system of linear equations that represents this situation.
Let x represent the number of students in the film-making club
Let y represent the number of students in the yearbook club.
As given that the film-making club has 14 more students than the yearbook club.
So x = y+14
Total students are 64.
So x+y = 64
System of equations:
x= y+14
x+y = 64
b. Now we have to find how many students are in the film-making club and the yearbook club.
The system of equations are;
x= y+14...................(1)
x+y = 64...................(2)
Now putting the value of x in equation 2.
y+14+y = 64
2y+14 = 64
Subtract 14 on both side, we get;
2y = 50
Divide by 2 on both side, we get;
y = 25
Now putting the value of y in equation 1.
x = 25+14
x = 39
There are 39 students in the film-making club and 25 students in the yearbook club.
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The heights of two different children were recorded in the chart.
a cart of two children's heights from age 0 months to 60 months
Draw a conclusion based on the data provided.
Answer:
based on the data i can draw a conclusion that child two and child one both grow taller as their time (months) increases. child 2 grows at a faster rate than child 1.
Step-by-step explanation:
Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.The owner of a football team claims that the average attendance at games is over 523 , and he is therefore justified in moving the team to a city with a larger stadium. Assuming that a hypothesis test to support this claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.
Answer:
The statement that the mean attendance is higher than 523 does not have enough facts to stand up.
What is null hypothesis?
A null hypothesis is an educated guess or a prediction of the expected outcome of a particular experiment. It is a statement that assumes there is no difference between two groups or no association between two variables. The null hypothesis is often the opposite of the alternative hypothesis, which is the prediction that the researcher is hoping to prove.
Example 1: In a study of the effectiveness of a new drug for treating depression, the null hypothesis would be that the drug has no effect on depression levels.
Example 2: In a study of the association between smoking and lung cancer, the null hypothesis would be that there is no association between the two variables.
Example 3: In a study of the effect of a new educational program on student performance, the null hypothesis would be that the program has no effect on student performance.
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group consisting of anne, bert, carl, and diana is about to select one out of five possible alternatives, a, b, c, d, e. the true utilities of the four individuals for the five alternatives are as follows:
a) U(6) UC) Ud) U(e) Anne 0.9 0.8 0.6 0.5 0.4 Bert 0.6 1.0 0.5 0.3 0.4 Carl 0.4 0.3 0.7 0.9 0.2 Diana 0.7 0.6 0.5 0.2 0.1 Which alternative will be selected if the following decision making methods are used: (i) the decision is based on the traditional voting procedure (each voter gets one vote). (ii) each person is asked for their top two choices, and the alternative that is chosen by the maximum number of people is selected. (iii) the group uses the Borda count with 5 points for the most preferred alternative, and 1 point for the least preferred alternative. (iv) the group follows a dot-voting scheme, where each person gets 10 "dots", and they assign the number of dots to each alternative that are roughly proportional to their Utility. (v) the group uses the "maximin rule" which prescribes that the group should prefer the alternative in which the worse-off person is as well-off as possible.
(vi) the sum of individual utilities is maximized for the group. Discuss the pros and cons of the group decision making methods listed above.
(ii) each person is asked for their top two choices, and the alternative that is chosen by the maximum number of people is selected
the best is always to look for points on the line that are exactly corner points of grid squares.
the true utilities of the four individuals for the five alternatives
(0.3, 0.4) and (0.6, 0.8)
so, the linear equation is
y = ax + b
0.4 = a×0.3 + b
0.8 = a×0.6 + b
let's subtract the second from the first equation :
-0.4 = a×-0.3 + 0
a = -0.4/-0.3 = 0.4/0.3 = 4/3
so, the equation is
y = (4/3)x
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Which statement is true about the functions f(x)=-15x^2+32 and g(x)=-17x^2+5x+32? a. f(x) and g(x) have the same zeros. b. f(x) has a higher maximum than g(x). c. f(x) and g(x) have the same y intercept. d. f(x) and g(x) are odd functions.
None of the options are valid because the specified functions are both parabolic.
Explain about the Functions?Functions represent the connection between two groups of values. For instance, if y=f(x), each value of x has a corresponding value in the set of y. The dependent variable is Y, and the independent variable is x.
An example of a rule is a function, which produces one output for a single input. Alex Federspiel is the picture's author. Y=X2 is an illustration of this. You only get one output for y if you enter anything for x. The fact that x is the input value leads us to say that y is a function of x. In mathematics and the sciences, functions are fundamental for constructing physical relationships.
Given functions in this case are
f(x)=-15x2+32
g(x)=-17x2+5x+32.
The functions' zeros are
x = 1.461, -1.233, and 1.527.
When g(x) has a higher maximum than f(x), f(x)intercept exceeds g. (x).
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Joan
made 3 quarts of soup. She
ate 1/7 of the soup each day for
a week. How much soup did she
eat each day?
Answer:
21 quarts of soup
Step-by-step explanation: I take . as a mutiply
This is easy you just need to take [tex]3 : \frac{1}{7} = \frac{3}{1} : \frac{1}{7} = \frac{3}{1} . \frac{7}{1} = \frac{3 . 7 }{1 . 1} = \frac{21}{1} = 21[/tex] quarts of soup
Write the equation of each line in slope-intercept form.
Answer:
24. y= -1/3x+1
25. y= -2/-1x+3