Answer:
\(1)x = 8 \\ x + y + 2 = 8 + y + 2 = 10 + y \\ 2)x = 9 \\ x + y + 2 = 9 + y + 8 = 17 + y \\ 3)y = 3 \\ x + y + 2 = x + 3 + 2 = x + 5 \\ 4) y = 0 \\ x + y + 2 = x + 0 + 2 = x + 2 \\ 5)x = 6 \: y = 2 \\ x + y + 2 = 6 + 2 + 2 + = 10 \\ thank \: you\)
Which value, when placed in the box, would result in a system of equations with infinitely many solutions?
y = -2x + 4
6x + 3y =
a. -12
b. -4
c. 4
d. 12
Answer:
d. 12
Step-by-step explanation:
if you rewrite the first as 2x + y = 4 and then multiply it by 3, it is equal to the second equation if the right hand side is 12.
If a system of equations contains dependent equations (ie., equal give or take a scale factor), then there is not one single solution but many.
Answer: its d, 12
Step-by-step explanation:
On September 1, 2010, you decided to put $ 16000 in a money market fund. On March 1, 2015, you deposit another $ 13000 and on January 1, 2018, you added another $ 12000. This fund pays interest at the annual rate of 7.2%, compounded monthly. Find the future value of the fund on January 1, 2018, just after the third deposit.
a.5 41571.76
b$41856.39 $41203.09
c. $41660.91
d.$ 38213.59
The future value of the fund on January 1, 2018, just after the third deposit, is approximately $47,986.47.
To find the future value of the fund on January 1, 2018, just after the third deposit, we can use the compound interest formula:
\(FV = P(1 + r/n)^{nt}\)
Where:
FV = Future Value
P = Principal amount (initial investment)
r = Annual interest rate (expressed as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
Let's calculate the future value step by step:
First deposit:
P = $16000
r = 7.2% = 0.072 (as a decimal)
n = 12 (compounded monthly)
t = 4.333 years (from September 1, 2010, to March 1, 2015)
\(FV_1 = 16000(1 + 0.072/12)^{(12*4.333)}\\= 16000(1 + 0.006)^{52}\\= 16000(1.006)^{52}\\= 20,296.43\)
Second deposit:
P = $13000
r = 7.2% = 0.072 (as a decimal)
n = 12 (compounded monthly)
t = 2.917 years (from March 1, 2015, to January 1, 2018)
\(FV_2 = 13000(1 + 0.072/12)^{(12*2.917)}\\= 13000(1 + 0.006)^{35}\\= 15,618.04\)
Third deposit:
P = $12000
r = 7.2% = 0.072 (as a decimal)
n = 12 (compounded monthly)
t = 0.084 years (from January 1, 2018, to January 1, 2018)
\(FV3 = 12000(1 + 0.072/12)^{(12*0.084)}\\= 12000(1 + 0.006)\\= $12,072.00\\\)
Adding up the future values:
\(Total FV = FV_1 + FV_2 + FV_3\)
= $20,296.43 + $15,618.04 + $12,072.00
≈ $47,986.47
Therefore, the future value of the fund on January 1, 2018, just after the third deposit, is approximately $47,986.47.
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please help me answer the question in the photo
Step-by-step explanation:
please mark me as brainlest
ans
\( \frac{3x}{x + 4} \)
14. A regular octagon is pictured below. If the measure of one of its angles is (2x? - 40% - 15), find the value(s)
of x that will make it true.
All angles and sides are equal. I will give brainliest if you answer within 10 minutes
convert 62 1/4 into decimal form.
Answer:
62 1/4 = 62.25
Step-by-step explanation:
Turn the improper fraction into a mixed number then divide as an equation.
62 x 4 = 248
248 + 1 = 249.
Put the 249 over the 4 and divide.
249/4 = 249 ÷ 4 = 62.25
The given fraction in decimal form is 62.25.
What are decimal numbers?The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. The base-10 number system, arguably the most widely used number system, is referred to as decimal. The 10 single-digit digits of the decimal number system are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The number following nine is 10. 19 is followed by 20, and so on.So, 62¼:
Get it in decimals as follows:
62¼62(4) + 1/4248 + 1/4249/462.25Therefore, the given fraction in decimal form is 62.25.
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the table shows the number of 7th- and 8th-grade students who belong to an after-school club
Answer: whats the question though
Step-by-step explanation:
A constant net force on a railroad car produces constant:
a. velocity
b. acceleration
c. both of these
d. neither of these
Answer:
B. Acceleration
Step-by-step explanation:
For the sequence a_n=3/n+1Find 1st term:Find Second Term:Find third term:Find fourth term:find 100th term:
Given:
The sequence is
\(a_n=\frac{3}{n+1}\)Required:
Find the first term, the second term, the third term, the fourth term and the 100th term.
Explanation:
The given sequence is:
\(a_{n}=\frac{3}{n+1}\)Substitute n = 1
\(\begin{gathered} a_1=\frac{3}{1+1} \\ a_1=\frac{3}{2} \end{gathered}\)Substitute n = 2
\(\begin{gathered} a_2=\frac{3}{2+1} \\ a_2=\frac{3}{3} \\ a_2=1 \end{gathered}\)Substitute n = 3
\(\begin{gathered} a_3=\frac{3}{3+1} \\ a_3=\frac{3}{4} \end{gathered}\)Substitute n = 4
\(\begin{gathered} a_4=\frac{3}{4+1} \\ a_4=\frac{3}{5} \end{gathered}\)The term of the sequence are:
\(\frac{3}{2},1,\frac{3}{4},\frac{3}{5}\)The given series is in HP
We will write it in AP as:
\(\frac{2}{3},1,\frac{4}{3},\frac{5}{3}\)So the common difference of the given sequence is:
\(\begin{gathered} 1-\frac{2}{3}=\frac{1}{3} \\ \frac{4}{3}-1=\frac{1}{3} \\ \frac{5}{3}-\frac{4}{3}=\frac{1}{3} \end{gathered}\)The nth term of the AP series is given by the formula:
\(a_n=a+(n-1)d\)where a = first term
n = number of terms
d = common difference
\(\begin{gathered} a_{100}=\frac{2}{3}+(100-1)\times\frac{1}{3} \\ a_{100}=\frac{2}{3}+99\times\frac{1}{3} \\ a_{100}=\frac{2+99}{3} \\ a_{100}=\frac{101}{3} \end{gathered}\)This is the 100th term for the AP.
The 100th term of the given HP sequence is:
\(\frac{3}{101}\)Final Answer:
\(\begin{gathered} First\text{ term = }\frac{3}{2} \\ Second\text{ term = 1} \\ Third\text{ term = }\frac{3}{4} \\ Fourth\text{ term = }\frac{3}{5} \\ 100th\text{ term = }\frac{3}{101} \end{gathered}\)What is the value of b2 4ac for the following equation x2 5x 4 0 16 25 9 next question?
The value of b² - 4ac for the equation x² + 5x + 4 = 0 is 9.
What is the discriminant of a polynomial?
The discriminant of a polynomial is a function of its coefficients and is represented by the capital ‘D’ or Delta symbol (Δ). It shows the nature of the roots of any quadratic equations where a, b, and c are real numbers.
It is represented as ‘D’
D = b² - 4ac
Where,
a is the coefficient of x²
b is the coefficient of x
c is a constant term
x² + 5x + 4 = 0
We have given:
x² + 5x + 4 = 0
Comparing the equation with the standard form.
a = 1, b = 5 and c = 4
Substituting it in the formula
D = 5² - 4 × 1 + 4
By further calculation
D = 25 - 16
D = 9,
The quadratic roots are real and distinct
Therefore, the value of b² - 4ac is 9.
Hence, The value of b² - 4ac for the equation x² + 5x + 4 = 0 is 9.
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Andrew pays a monthly membership fee of $10 at his gym. Each time he uses the gym, he pays $5. Last month, Andrew spent a total of $65 for membership and gym use. If the equation 10 + 5 x = 65 models the situation, how many times did he use the gym last month?
11
12
13
15
Answer:
11
Step-by-step explanation:
If we input 11 into the equation, we get: 10 + 5(11) = 65.
5 x 11 = 55
55 + 10 = 65
Therefore x = 11
Answer:
11 or a
Step-by-step explanation:
calculate 6 P 6 note n p r equals n Over N - r
The value of 6P6 is 720
How to evaluate the expression?The expression is given as:
6P6
This is calculated using:
\(^nP_r = \frac{n!}{(n - r)!}\)
So, we have:
\(^6P_6 = \frac{6!}{(6 - 6)!}\)
Evaluate the difference
\(^6P_6 = \frac{6!}{0!}\)
As a general rule;
0! = 1
So, we have:
\(^6P_6 = 6!\\\)
Expand
\(^6P_6 = 6 * 5 * 4 * 3 * 2 * 1\)
Evaluate
\(^6P_6 = 720\)
Hence, the value of 6P6 is 720
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A square-based pyramid has a base side length of 10 feet and a height of 15 feet.
What is the volume of this pyramid?
Enter your answer in the box.
Answer: 500 ft^3
Step-by-step explanation: V=a2h
3=102·15
3=500
Sorry for the late response!! That's the correct answer I took the test. I hope this helped. <3
Please help me! I’ll mark you brainiest
Answer:
c
Step-by-step explanation:
It is given that the line AB is Perpendicular Bisector of IK. It means the line AB is perpendicular on IK and the point J divides the line IK in two equal parts.
If a line is bisector of another line, then the point of intersection divides the second line is two equal parts.
Therefore the distance between intersection point and the endpoints of the second line are the same.
The intersection point is J and the end points of IK are I and K. So, we can say that IJ = JK.
Formalize the following in terms of atomic propositions r, b, and w, first making clear how they correspond to the
English text. (a) Berries are ripe along the path, but rabbits have not been seen in the area.
(b) Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.
(c) If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.
(d) It is not safe to walk along the path, but rabbits have not been seen in the area and the berries along the path are ripe.
e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to
pave been seen in the area.
Walking is not safe on the path whenever rabbits have been seen in the area and berries are ripe along the path.
Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path. This is formalized by using the →(if-then) and ∧(logical and) operators.
Given information and corresponding atomic propositions:
We need to formalize the given statements in terms of atomic propositions r, b, and w, which are defined as follows:
r: Rabbits have been seen in the area.
b: Berries are ripe along the path.
w: Walking on the path is safe.
Now, let us formalize each of the given statements in terms of these atomic propositions:
a) Berries are ripe along the path, but rabbits have not been seen in the area.
b: Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.
c: If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.
d: It is not safe to walk along the path, but rabbits have not been seen in the area, and the berries along the path are ripe.
e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.
Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path.
The formalizations in terms of atomic propositions are:
a) b ∧ ¬r.b) ¬r ∧ w ∧
b.c) (b → w) ∧ (¬r → w).
d) ¬w ∧ ¬r ∧
b.e) (¬r ∧ ¬b) → w.b ∧
Berries are ripe along the path, but rabbits have not been seen in the area.
This is formalized by using the ∧(logical and) operator.
(¬r ∧ ¬b) → w: It means For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.
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Let X 1 ,X 2 ,…,Xn be iid Bern(p) random variables, so that Y=∑ i=1n X i is a Bin(n,p) random variable. (a) Show that Xˉ =Y/n is an unbiased estimator of p. (b) Show that Var( Xˉ )=p(1−p)/n. (c) Show that E{ Xˉ (1− Xˉ )}=(n−1)[p(1−p)/n]. (d) Find the value of c such that c Xˉ (1− Xˉ ) is an unbiased estimator of p(1−p)/n.
a) X is an unbiased estimator of p. b) The Var(X) is p(1-p)/n. c) The E[X(1-X)] is (n-1)[p(1-p)/n]. d) The value of c is c = 1/(n-1).
(a) To show that X = Y/n is an unbiased estimator of p, we need to show that E[X] = p.
Since Y is a sum of n iid Bern(p) random variables, we have E[Y] = np.
Now, let's find the expected value of X:
E[X] = E[Y/n] = E[Y]/n = np/n = p.
Therefore, X is an unbiased estimator of p.
(b) To find the variance of X, we'll use the fact that Var(aX) = a^2 * Var(X) for any constant a.
Var(X) = Var(Y/n) = Var(Y)/n² = np(1-p)/n² = p(1-p)/n.
(c) To show that E[X(1-X)] = (n-1)[p(1-p)/n], we expand the expression:
E[X(1-X)] = E[X - X²] = E[X] - E[X²].
We already know that E[X] = p from part (a).
Now, let's find E[X²]:
E[X²] = E[(Y/n)²] = E[(Y²)/n²] = Var(Y)/n² + (E[Y]/n)².
Using the formula for the variance of a binomial distribution, Var(Y) = np(1-p), we have:
E[X²] = np(1-p)/n² + (np/n)² = p(1-p)/n + p² = p(1-p)/n + p(1-p) = (1-p)(p + p(1-p))/n = (1-p)(p + p - p²)/n = (1-p)(2p - p²)/n = 2p(1-p)/n - p²(1-p)/n = 2p(1-p)/n - p(1-p)²/n = [2p(1-p) - p(1-p)²]/n = [p(1-p)(2 - (1-p))]/n = [p(1-p)(1+p)]/n = p(1-p)(1+p)/n = p(1-p)/n.
Therefore, E[X(1-X)] = E[X] - E[X²] = p - p(1-p)/n = (n-1)p(1-p)/n = (n-1)[p(1-p)/n].
(d) To find the value of c such that cX(1-X) is an unbiased estimator of p(1-p)/n, we need to have E[cX(1-X)] = p(1-p)/n.
E[cX(1-X)] = cE[X(1-X)] = c[(n-1)[p(1-p)/n]].
For unbiasedness, we want this to be equal to p(1-p)/n:
c[(n-1)[p(1-p)/n]] = p(1-p)/n.
Simplifying, we have:
c(n-1)p(1-p) = p(1-p).
Since this should hold for all values of p, (n-1)c = 1.
Therefore, the value of c is c = 1/(n-1).
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Henry rolls 2 number cubes numbered one through six while playing his favorite boardgame. He will get a second turn if he rolls a sum that is an even number less than 10. What are Henry’s chances of getting a second turn when he rolls a number cube?
Answer:
Henry's chances of getting a second turn when he rolls a number cube is 7/18
solve the following equations
63= 12x -21
Answer:
X=7
take the -21 to the other side of the equation, when you do this it goes from a negative to a positive so we now have 63+21=12x
if we add 63 and 12 we get 84 decide by 12 because we have 12x and we get 7
Ayuda ¿10 y 12 son divisibles por?
Answer:
2
Step-by-step explanation:
10/2=5
12/2=6
espero que esto ayude!
Answer:
Son divisibles por 1 y 2
Step-by-step explanation:
Two sample t tests are designed to learn if there is support for a relationship between variables when:
Two sample t-tests are designed to learn if there is support for a relationship between variables when there are two independent groups and we want to compare their means.
Specifically, the two sample t-test is used to determine whether the means of two groups are significantly different from each other. The test is based on the assumption that the populations from which the samples are drawn are normally distributed, and that the variances of the two populations are equal.
If these assumptions are met, we can use the two sample t-test to test the null hypothesis that the means of the two groups are equal. The test produces a t-statistic and a p-value, which can be used to determine whether the null hypothesis should be rejected or not.
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The U.S. Senate consists of 100 senators, with 2 from each of the 50 states. There are 50 Democrats in the Senate. A committee of size 10 is formed, by picking a random set of senators such that all sets of size 10 are equally likely. a) Find the expected number of Democrats on the committee. b) Find the expected number of states represented on the committee (by at least one senator) c) Find the expected number of states such that both of the state's senators are on the committee.
Note that based on probabilities,
The expected number of Democrats on the committee is 5.
The expected number of states represented on the committee is 26.
The expected number of states such that both of the state's senators are on the committee is 9.09.
How is this so ?a) The probability that a randomly chosen senator is a Democrat is 50/100 = 1/2.
So, the expected number of Democrats on a committee of size 10 is
1/2 * 10 = 5.
b) The minimum number of states that can be represented on a committee of size 10 is 2, and the maximum numberis 50.
The expected number of states representedon the committee is the average of these two values, which is (2 + 50)/ 2 = 26.
c) There are 50 states, and each state has 2 senators. So, there are a total of 100 pairs of senators.
The probability that a randomly chosen pair of senators both belong to the same state is 50/100 * 49/99
= 1/11.
The expected number of states such that both of the state's senators are on the committee is 100 * 1/11 = 9.09.
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Jerry pays $1.40 per gallon for premium gasoline. He spends $16.80 and wants
to know how many gallons he bought. Which equation models this situation?
Answer:
let x be the total amount of gallons he bought
$16.80÷$1.40 = x
16.80÷1.40=12
x=12
Step-by-step explanation:
There are 18 boys and 12 girls in a math class . What is the ratio of girls to total students
Answer:
The ratio of girls to total students is 12:30, which can be simplified to 2:5.
Step-by-step explanation:
You can express the ratio in different ways by using the same numbers, for example, you could say that for every 2 girls, there are 5 total students, or that for every 5 total students, 2 of them are girls.
g how many times would you expect a person selected at random to have to take the test until (s)he passes it? (if necessary, round your answer to 2 decimal places.)
The probability that a person selected at random to have the test until (s)he passes the test is, 0.03125
Given, a test occurred 5 times in a class.
we have to find that how many times a person selected at random to have the test until (s)he passes it.
the probability of getting pass in the exam be, 1/2
and similarly the probability of getting fail in the exam also be, 1/2
so, the probability that a person selected at random to have the test until (s)he passes the test is,
(1/2)^5
= 1/32
= 0.03125
Hence, the probability that a person selected at random to have the test until (s)he passes the test is, 0.03125
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Compute the surface area of revolution of y=(4−x^3/2)^2/3 about the x-axis over the interval [0,1]. SA=
Since the integral can be quite complex to solve analytically, we can approximate the surface area using numerical methods or use software tools like Mathematica or Wolfram Alpha to compute the integral.
To compute the surface area of revolution for the given curve y = (4 - x^(3/2))^(2/3) about the x-axis over the interval [0, 1], we can use the formula for the surface area of revolution:
SA = 2π ∫[a,b] y√(1 + (dy/dx)^2) dx
In this case, a = 0 and b = 1.
First, let's find dy/dx by taking the derivative of y with respect to x:
dy/dx = (2/3)(4 - x^(3/2))^(-1/3)(-3/2)x^(1/2)
= -(2/3)(3/2)x^(1/2)(4 - x^(3/2))^(-1/3)
= -x^(1/2)(3/4 - x^(3/2))^(1/3)
Now, let's compute the integral using the given formula:
SA = 2π ∫[0,1] (4 - x^(3/2))^(2/3) √(1 + (-x^(1/2)(3/4 - x^(3/2))^(1/3))^2) dx
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Solve: 64-3x-3 x64+22=38
Answer:
X = -48
Step-by-step explanation:
Find the area of the rectangle and the triangle independently. What is the ratio comparing the area of the triangle to the area of the rectangle? (Must be in Reduced Form)
Answer:
hello your question is incomplete attached below is the complete question
answer : 2
Step-by-step explanation:
Area of rectangle = \((\frac{b}{h}) (\frac{h}{2})\)
Area of triangle = \(\frac{1}{2}bh\)
therefore the ratio of the area of the triangle to the area of the rectangle
= \(\frac{\frac{1}{2} bh}{\frac{b}{2}*\frac{h}{2} }\) = 2
The Mid-High JV Team is playing in the state championship for football. In order
to beat their all-time points in a season record, they need to score more than 60
points in the game.
Considering a field goal (f) scores 3 points, a touchdown (t) scores 6 points, and a
touchdown with an extra point (p) scores 7 points, which inequality best represents
the possible ways the team can score more than 60 points.
The inequality best represents the possible ways the team can score more than 60 points.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
Given that, the Mid-High JV Team is playing in the state championship for football.
In order to beat their all-time points in a season record, they need to score more than 60 points in the game.
Considering a field goal (f) scores 3 points, a touchdown (t) scores 6 points, and a touchdown with an extra point (p) scores 7 points.
We need to find the inequality best represents the possible ways the team can score more than 60 points.
3f+6t+7p>60
Hence, 3f+6t+7p>60 is the inequality best represents the possible ways the team can score more than 60 points.
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According to the situational theory of leadership, a leader with a _____ provides little direction or support because complete responsibility for decisions and their implementation is turned over to followers.
According to the situational theory of leadership, a leader with a "Delegating style" provides little direction or support because complete responsibility for decisions and their implementation is turned over to followers.
Situational Leadership Theory (SLT) is a leadership theory that prioritizes the context and individuals involved in leadership over a universal leadership style. Leadership behavior and style, in this theory, should be driven by the context of the situation, and the leader must have a proper understanding of their own leadership style and its impact on followers.
The situational leadership theory suggests that the leadership style can be changed based on the situation and the abilities of the followers. The four leadership styles in situational leadership theory are: Directing, Coaching, Supporting, and Delegating.
The Delegating style of leadership is one where the leader allows the followers to make decisions. In this style, the leader turns over complete responsibility for decisions and their implementation to followers. This style is effective when followers are capable of making informed decisions.
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When Dylan checks his school lunch account, the balance is $56.
After buying 8 lunches, the balance is $40.
How much (in dollars) does the balance change with each lunch bought? Show whether the change is positive or negative.
What's 11,000lb in tons
Step-by-step explanation:
What's 11,000lb in tons
it 5.5 us tone