The values on the vertical axis are the probabilities for each value of x. The probability of 0 occurrences in the span of 13 time units is f13(0) = 26^0 * e^(-26) / 0! = e^(-26) ≈ 0.0000000000000000000000000003.
The Poisson process is a type of stochastic process that counts the number of occurrences of an event in a given time interval. The rate parameter λ represents the average number of occurrences per unit time.
i. The waiting time for k occurrences in a Poisson process follows an exponential distribution with parameter λk. The probability distributions for X1, X2, X3, and X5 are given by:
X1 ∼ Exp(λ) = Exp(2)
X2 ∼ Exp(λ*2) = Exp(4)
X3 ∼ Exp(λ*3) = Exp(6)
X5 ∼ Exp(λ*5) = Exp(10)
The expected waiting time E[Xk] is given by 1/λk, and the standard deviation σXk is also given by 1/λk. Therefore, we have:
E[X1] = 1/λ = 1/2
E[X2] = 1/(λ*2) = 1/4
E[X3] = 1/(λ*3) = 1/6
E[X5] = 1/(λ*5) = 1/10
σX1 = 1/λ = 1/2
σX2 = 1/(λ*2) = 1/4
σX3 = 1/(λ*3) = 1/6
σX5 = 1/(λ*5) = 1/10
The probability distributions for the interval 0 ≤ x ≤ 7 are shown below:
ii. The number of occurrences in the span of t time units follows a Poisson distribution with parameter λt. The probability distributions ft(x) for t = 13, t = 12, and t = 1.2 are given by:
ft(x) = (λt)^x * e^(-λt) / x!
f13(x) = (2*13)^x * e^(-2*13) / x! = 26^x * e^(-26) / x!
f12(x) = (2*12)^x * e^(-2*12) / x! = 24^x * e^(-24) / x!
f1.2(x) = (2*1.2)^x * e^(-2*1.2) / x! = 2.4^x * e^(-2.4) / x!
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Find the remainder on dividing 12-5x+3x^(2)+2x^(3) by x+3. Compare this with P(-3) where P(x)=12-5x+3x^(2)+2x^(3).
The remainder on dividing 12-5x+3x^(2)+2x^(3) by x+3 is -39.
This can be found by using long division or synthetic division. The result of the division is 2[tex]x^{(2)}[/tex]-11x+21 with a remainder of -39.
To compare this with P(-3), we need to plug in -3 for x in the original polynomial P(x)=12-5x+3[tex]x^{(2)}[/tex]+2[tex]x^{(3)}[/tex].
This gives us:
P(-3)= 12-5(-3)+3(-3)[tex]^{(2)}[/tex]+2(-3)[tex]^{(2)}[/tex]
=12+15+27-54=-39
Therefore, the remainder is the same as P(-3) for the given polynomial.
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What is the answer to this problem i have
The quotient of the given values when expressed in a scientific notation would be = 1.7 × 10⁵
What is scientific notation?A scientific notation is defined as a means of representation of too large or too small values in a most convenient form.
The quotient of 3.91× 10⁷ and 2.3 × 10² means the division of 3.91× 10⁷ and 2.3 × 10².
That is ;
= 3.91× 10⁷/ 2.3 × 10²
= 3.91/2.3 × 10⁷/10²
= 1.7 × 10⁵ ( it is 10⁵ because since it's division the superscripts attached to 10 will be subtracted)
Therefore, the quotient value of the given expression above would be = 1.7 × 10⁵.
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(1 point) LetA=[6514] and b=[−9−17]. Define the linear transformationT:R2→R2byT(x)=Ax. Find a vectorxwhose image underTisb.x=[Is the vectorxunique?
The vector x whose image under T is b is x = [23/19 -129/19].
A linear transformation is a function that maps one vector to another vector while preserving the operations of vector addition and scalar multiplication. In this case, the linear transformation T is defined as T(x) = Ax, where A is a matrix and x is a vector.
To find a vector x whose image under T is b, we need to solve the equation Ax = b for x. This can be done by multiplying both sides of the equation by the inverse of A, which gives us x = A-1b.
Using the formula for the inverse of a 2x2 matrix, we can find A-1:
A-1 = (1/(6*4 - 5*1)) * [4 -5-1 6] = [4/19 -5/19-1/19 6/19]
Now we can multiply A-1 by b to get x:
x = A-1b = [4/19 -5/19-1/19 6/19] * [−9−17] = [(4/19)*(-9) + (-5/19)*(-17) (−1/19)*(-9) + (6/19)*(-17)] = [23/19 -129/19]
Therefore, the vector x whose image under T is b is x = [23/19 -129/19].
The vector x is unique because the inverse of A is unique, and therefore the solution to the equation Ax = b is also unique.
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Consider functions f and g.
f(x) = -23
g(x) = |x − 1
What is the value of (go f)(4)?
What is the value of (g • f)(4)?
O A. 9
O B. B. -
O C. -9
O D. 1
The numeric value of the composite function at x = 4 is given as follows:
|f(4) - 1|.
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given by the following rule:
(f ∘ g)(x) = f(g(x)).
It means that the output of the inside function serves as the input for the outside function.
If g is the outer function, as is the case for this problem, we have that:
(g • f)(x) = g(f(x)).
At x = 4, the numeric value of the composite function is given as follows:
g(f(4)) = |f(4) - 1|.
Missing InformationThe problem is incomplete, hence the composite function is given in general terms.
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Solve by using Cramer's Rule: \[ \begin{array}{l} -3 x-4 y-4 z=-8 \\ x-3 y-3 z=-19 \\ -x+y-2 z=3 \end{array} \]
The solution to this system of equations is: \[ \begin{array}{l} x=40 \\ y=-111 \\ z=-3.5 \end{array} \]
To solve this system of equations using Cramer's Rule, we will begin by finding the determinant of the coefficient matrix, which is an array of the coefficients of the variables in the equations. We will then find the determinants of the matrices that result from replacing each column of the coefficient matrix with the constant terms of the equations. Finally, we will use these determinants to find the values of x, y, and z.
The coefficient matrix is: \[ \begin{array}{ccc} -3 & -4 & -4 \\ 1 & -3 & -3 \\ -1 & 1 & -2 \end{array} \]
The determinant of the coefficient matrix is: \[ \begin{array}{ccc} -3 & -4 & -4 \\ 1 & -3 & -3 \\ -1 & 1 & -2 \end{array} = (-3)(-3)(-2) - (-4)(-3)(-1) - (-4)(1)(1) - (-4)(-3)(-1) - (-4)(-3)(1) - (-4)(1)(-2) = -6 + 4 + 4 + 4 - 12 + 8 = -2 \]
The matrix that results from replacing the first column of the coefficient matrix with the constant terms is: \[ \begin{array}{ccc} -8 & -4 & -4 \\ -19 & -3 & -3 \\ 3 & 1 & -2 \end{array} \]
The determinant of this matrix is: \[ \begin{array}{ccc} -8 & -4 & -4 \\ -19 & -3 & -3 \\ 3 & 1 & -2 \end{array} = (-8)(-3)(-2) - (-4)(-3)(3) - (-4)(-19)(1) - (-4)(-3)(3) - (-4)(-19)(1) - (-4)(-3)(-2) = 48 - 36 - 76 + 36 - 76 + 24 = -80 \]
The matrix that results from replacing the second column of the coefficient matrix with the constant terms is: \[ \begin{array}{ccc} -3 & -8 & -4 \\ 1 & -19 & -3 \\ -1 & 3 & -2 \end{array} \]
The determinant of this matrix is: \[ \begin{array}{ccc} -3 & -8 & -4 \\ 1 & -19 & -3 \\ -1 & 3 & -2 \end{array} = (-3)(-19)(-2) - (-8)(-3)(-1) - (-4)(1)(3) - (-4)(-19)(-1) - (-4)(-3)(1) - (-4)(1)(-2) = 114 + 24 + 12 + 76 - 12 + 8 = 222 \]
The matrix that results from replacing the third column of the coefficient matrix with the constant terms is: \[ \begin{array}{ccc} -3 & -4 & -8 \\ 1 & -3 & -19 \\ -1 & 1 & 3 \end{array} \]
The determinant of this matrix is: \[ \begin{array}{ccc} -3 & -4 & -8 \\ 1 & -3 & -19 \\ -1 & 1 & 3 \end{array} = (-3)(-3)(3) - (-4)(-19)(-1) - (-8)(1)(1) - (-8)(-3)(-1) - (-8)(-19)(1) - (-8)(1)(3) = 27 + 76 + 8 + 24 - 152 + 24 = 7 \]
Using these determinants, we can find the values of x, y, and z: \[ x = \frac{-80}{-2} = 40 \] \[ y = \frac{222}{-2} = -111 \] \[ z = \frac{7}{-2} = -3.5 \]
Therefore, the solution to this system of equations is: \[ \begin{array}{l} x=40 \\ y=-111 \\ z=-3.5 \end{array} \]
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Henry has 342 marbles in bags. If 9 marbles are in each bag. how many bags does Henry have? How many bags will he have if he gives 15 bags to his brother?
A number y, when rounded to 2 decimal places, is equal to 9. 68. Find the upper and lower bound
If the number when rounded to 2 decimal places is equal to 9.68, then the upper bound is 9.685 and lower bound is 9.675 .
In order to find the upper bound of the number y, we need to add 0.005,
and to find the lower bound of the number y, we need to subtract 0.005 ,
We know that, the number y, when rounded to 2 decimal places is equal to 9.68 ;
So, the Upper Bound is = 9.68 + 0.005 = 9.685, and
The Lower Bound is = 9.68 - 0.005 = 9.675.
Therefore, the lower bound of y is 9.675 and upper bound of y is 9.685.
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Julia deposits $2000 into a savings account that
earns 4% interest per year. The exponential
function that models this savings account is
y = 2000(1.04)^t, where t is the time in years.
Which equation correctly represents the amount
of money in her savings account in terms of the
monthly growth rate?
Please show work
The equation correctly represents the amount of money in her savings account in terms of the monthly growth rate is [tex]y = 2000(1 + 0.0033)^t[/tex]. Option D is the correct answer.
What is compound interest?The interest earned on savings that is computed using both the original principle and the interest accrued over time is known as compound interest. It is said that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a total more quickly than simple interest, which is solely computed on the principal sum.
Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.
Given that, the function of the model of the account is:
[tex]y = 2000(1.04)^t[/tex]
The monthly interest rate is:
r = 4% / 12 = 0.00333
The model in terms of monthly interest rate can be written as:
[tex]y = 2000(1 + r)^{12t/12}[/tex]
Substituting the value of r:
[tex]y = 2000(1 + 0.0033)^t[/tex]
Hence, the equation correctly represents the amount of money in her savings account in terms of the monthly growth rate is [tex]y = 2000(1 + 0.0033)^t[/tex].
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answer quick please!!
Match the reasons with the statements in the proof to prove AB || DC, given that AD is parallel to BC and AD = CB.
Given:
AD || BC
AD = CB
Prove:
AB || DC
1. AD || BC, AD = CB
Reflexive Property of Equality
2. AC = AC
Given
3. 2 = 3
If Alternate Interior Angles are Congruent, then Lines are Parallel.
4. ACD = CAB
If Lines are Parallel, then Alternate Interior Angles are Equal.
5. 1 = 4
SAS (Side-Angle-Side)
6. AB || DC
CPCTE (Corresponding Parts of Congruent Triangles are Equal)
onetary policy below.
AB is parallel to DC because they are equal and corresponding sides of similar triangles.
What is the reflexive property of equality?
The reflexive property of equality is a basic principle in mathematics that states that any quantity is equal to itself. In other words, if we have a variable, say "a", then a is always equal to a. Similarly, if we have an equation such as 2 + 3 = 5, we can use the reflexive property of equality to say that 5 = 5, since any quantity is equal to itself. The reflexive property is used frequently in mathematical proofs to simplify expressions and make them easier to work with.
AD || BC, AD = CB - Reflexive Property of Equality
Explanation: This reason uses the reflexive property of equality, which states that a quantity is equal to itself. In this case, the reason is stating that the given information is true and using the reflexive property of equality to restate it in a different way.
2 = 3 - If Alternate Interior Angles are Congruent, then Lines are Parallel.
Explanation: This reason uses the angle congruence property that if the alternate interior angles are congruent, then the lines are parallel. This property is used to show that angles ACD and CAB are congruent because they are alternate interior angles.
ACD = CAB - If Lines are Parallel, then Alternate Interior Angles are Equal.
Explanation: This reason uses the angle equality property that if the lines are parallel, then the alternate interior angles are equal. This property is used to show that lines AD and BC are parallel because they are given to be parallel, and therefore the alternate interior angles ACD and CAB are equal.
1 = 4 - SAS (Side-Angle-Side)
Explanation: This reason uses the similarity property that if two triangles have the same side-angle-side, then they are similar. This property is used to show that triangles ABD and CBD are similar because they have the same side AD = CB and the same angles ABD and CBD.
AB || DC - CPCTE (Corresponding Parts of Congruent Triangles are Equal)
This reason uses the CPCTE property that the corresponding parts of congruent triangles are equal. This property is used to show that sides AB and DC are equal because they are corresponding sides of similar triangles ABD and CBD. Therefore, AB is parallel to DC because they are equal and corresponding sides of similar triangles.
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(8x^(3)+24x^(2)+14x+2)-:(2x+5) Your answer should give the quotient and the remainder.
4x^(2)+2x+2 with a remainder of -8.
The quotient and remainder of the given expression can be found by performing polynomial long division.
First, divide the leading term of the dividend, 8x^(3), by the leading term of the divisor, 2x. This gives a quotient of 4x^(2).
Next, multiply the divisor, (2x+5), by the quotient, 4x^(2), to get 8x^(3)+20x^(2).
Then, subtract this product from the dividend to get a new dividend of 4x^(2)+14x+2.
Repeat this process by dividing the leading term of the new dividend, 4x^(2), by the leading term of the divisor, 2x, to get a new quotient of 2x.
Multiply the divisor, (2x+5), by the new quotient, 2x, to get 4x^(2)+10x.
Subtract this product from the new dividend to get a new dividend of 4x+2.
Finally, divide the leading term of the new dividend, 4x, by the leading term of the divisor, 2x, to get a new quotient of 2.
Multiply the divisor, (2x+5), by the new quotient, 2, to get 4x+10.
Subtract this product from the new dividend to get a remainder of -8.
So, the final quotient is 4x^(2)+2x+2 and the final remainder is -8.
Therefore, the answer is: (8x^(3)+24x^(2)+14x+2)-:(2x+5) = 4x^(2)+2x+2 with a remainder of -8.
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Derivations (20 marks): For each of the questions in this section provide a derivation. Other methods will receive no credit i. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx (5 marks)
ii. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px (5 marks) iii. ¬ Vx(Fx → Gx) v 3xFx (10 marks; Hint: To derive this theorem use RA.)
¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]
i. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx (5 marks)
Proof:
1. ∃x(Fx & Gx) [Premise]
2. Fx & Gx [∃-Elimination, 1]
3. ∃xFx [∃-Introduction, 2]
4. ∃xGx [∃-Introduction, 2]
5. ∃xFx & ∃xGx [Conjunction Introduction, 3 and 4]
6. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx [1-5, Modus Ponens]
ii. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px (5 marks)
Proof:
1. ¬ 3x(Px v Qx) [Premise]
2. ¬ Px v ¬ Qx [DeMorgan’s Law, 1]
3. Vx ¬ Px [∀-Introduction, 2]
4. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px [1-3, Modus Ponens]
iii. ¬ Vx(Fx → Gx) v 3xFx (10 marks; Hint: To derive this theorem use RA.)
Proof:
1. ¬ Vx(Fx → Gx) v 3xFx [Premise]
2. (¬ Vx(Fx → Gx) v 3xFx) → (¬ Vx(Fx → Gx) v Fx) [Implication Introduction]
3. ¬ Vx(Fx → Gx) v Fx [Resolution, 1, 2]
4. (¬ Vx(Fx → Gx) v Fx) → (Fx → Gx) [Implication Introduction]
5. Fx → Gx [Resolution, 3, 4]
6. ¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]
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Jai went to the store to buy some chicken. The price per pound of the chicken is $3.75 per pound and he has a coupon for $1.75 off the final amount. With the coupon, how much would Jai have to pay to buy 5 pounds of chicken? Also, write an expression for the cost to buy p pounds of chicken, assuming at least one pound is purchased.
Therefore, this is how much it would cost to purchase p pounds of chicken: Cost is equal to $3.75p – $1.75, with p≥ 1.
what is unitary method ?The unitary method in mathematics is a strategy for resolving proportional issues. Finding the value of one unit of a quantity and using that value to calculate the value of a second quantity that is proportional to the first includes this technique. The unitary technique is frequently employed in a variety of real-world contexts, including engineering, finance, and food preparation. The unitary method can be used to determine the amount of flour required to make a different number of cookies, for instance, if a recipe asks for 2 cups of flour to make 12 cookies.
given
The price of 5 pounds of poultry without the coupon is:
$5 for five pounds at $3.75 per pound.
Jai saves $1.75 thanks to the coupon, making the total price for 5 pounds of chicken:
$18.75 - $1.75 = $17.00
Jai would therefore need to spend $17.00 in order to purchase 5 pounds of poultry using the coupon.
With the assumption that at least one pound is bought, we can use the following formula to write an expression for the price to buy p pounds of chicken:
Expense is equal to (price per pound) x (pounds) - (coupon amount)
where p is the number of pounds, $3.75 is the price per pound, and $1.75 is the value of the voucher.
Therefore, this is how much it would cost to purchase p pounds of chicken: Cost is equal to $3.75p – $1.75, with p≥ 1.
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How many angles are created when two parallel
lines are cut by a transversal? How many different
angle measures are there?
Answer:
eight angles
Step-by-step explanation:
83 divided by 17 pls answer my calculator is worse than my brain
83/17 = 4.88235294118
Answer:
4.88, and 4.9 rounded to the nearest 10th and 5 round to the nearest whole number.
Step-by-step explanation:
34. The table below shows the number of new restaurants in a fast food chain that opened during the years
of 1988 through 1992. Using an exponential model, write an equation for the curve of best fit, then
estimate the number of new restaurants that opened in 2005.
1486
Year
1988
1989
1990
1991
1992
New
Restaurants
49
81
112
150
262
Equation:
Answer:
As a result, we can assume that the fast-food business added about 3,454 new outlets in 2005.
What are equations used for?
A mathematical equation, such as 6 x 4 = 12 x 2, states that two variables or values are equivalent. a meaningful noun. An equation is used when two or maybe more factors must be considered jointly in order to understand or explain the whole situation.
We can apply the following formula to find an exponentially model that matches the data:
y = abˣ
Where x is the length of time after 1988, y is the number of fresh restaurants that open each year, and a and b are undetermined constants.
We may use the information from the years 1988 and 1989 to get the constants a and b:
49 = ab⁰
81 = ab¹
As a result of the first equation, a = 49. When we put it in the second equation, we obtain this result:
81 = 49b¹
b = 81/49
The following is the exponentially model that best matches the data:
y = 49(81/49)ˣ
Since 2005 is 17 years after 1988, we need to determine the value of y when x = 17 in order to figure out the number of new eateries that debuted in 2005:
y = 49(81/49)¹⁷
y ≈ 3,454
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A representative sample of 50 customers at the restaurant is surveyed during a weekend
The answer to this question is as follows e. Untrue. It is not possible to equation predict how many of the 200 clients will buy roasted turkey as an entrée using the information in the table.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
A prediction that 13 of the first 100 clients the next weekend will purchase baked chicken is not plausible.
b. Untrue. This weekend, 20% of consumers didn't purchase eggplant parmesan,
c. Untrue. Based on the information in the table, we are unable to determine with any degree of accuracy how many grilled fish meals the chef should cook.
d. True. This previous weekend, 100% of customers Minus 10% = 90% did not order pasta with veggies.
e. Untrue. It is not possible to predict how many of the 200 clients will buy roasted turkey as an entrée using the information in the table.
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14
Nadia was considering two different vacation packages. For each, she wrote a linear equation
to model the cost of airfare and'n nights in a hotel. She graphed the corresponding lines and
found the two packages cost the same only when the vacation includes 5 nights in a hotel.
Which statement about Nadia's graph must be true?
AThe lines are parallel.
BThe lines are not parallel.
CThe x-intercepts are the same.
D The y-intercepts are the same.
Answer:
Step-by-step explanation:Which is the equation of a line that has a slope of 1/2 and passes through point (2, -3)?
4. c^(3)v^(9)c^(-1)c^0
6. 9y^(4)j^(2)y^(-9)
8. 2y^(-9)h^(2)(2y^(0)h^(-4))^(-6)
10. (-3q^(-1))^(3)q^(2)
expression has the least vitive"? B. n^(n)
D. −n^(n)n^(-4)
vitive is D: −nnn−4.
To answer the question, the expression with the least vitive is D: −nnn−4.
For reference, the expressions in the question are:
4. c3v9c−1c0
6. 9y4j2y−9
8. 2y−9h2(2y0h−4)−6
10. (−3q−1)3q2
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Will the graph y=2(4)^x be increasing or decreasing? Explain how u know
Answer:
Step-by-step explanation:
Decreasing.
This is because the as you increase the X value and solve for Y, the Y value decreases.
For example:
[tex]x=1 \\y=2(\frac{1}{3} )^1\\y=\frac{2}{3} =0.667\\\\x=2\\y=2(\frac{1}{3} )^1\\y=\frac{2}{9}=0.222\\\\x=3\\y=2(\frac{1}{3} )^3\\y=\frac{2}{27}=0.074[/tex]
Is(8, 2)a solution to the inequality y ≥ 3x + 4?
No, (8, 2) is not a solution to the inequality y ≥ 3x + 4 because when we substitute x = 8 and y = 2 into the inequality, we get a false statement. In other words, the point (8, 2) does not satisfy the inequality y ≥ 3x + 4, which means it is not a valid solution to the inequality.
To determine whether (8, 2) is a solution to the inequality y ≥ 3x + 4, we need to substitute the values of x and y into the inequality and check if the inequality holds true.
y ≥ 3x + 4
Substituting x = 8 and y = 2:
2 ≥ 3(8) + 4
2 ≥ 24 + 4
2 ≥ 28
The inequality is not true since 2 is not greater than or equal to 28.
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Evaluate each expression using the values given in the table. X -3 -2 -1 0 1 2 3
F(x) 8 7 6 5 4 3 2
G(x) -7 -3 0 1 0 -3 -7
a. (f∘g)(1) b. (f∘g)(2) c. (g∘f)(2) d. (g∘f)(3) e. (g∘g)(1) f. (f∘f)(3)
Using the values given in the table to evaluate each expression, the value of each expression is (a) 5, (b) 8, (c) -7, (d) -3, (e) 1, and (f) 3.
To evaluate the expressions, we need to use the values given in the table for f(x) and g(x). The composition of functions (f∘g)(x) means that we plug the value of g(x) into the function f(x).
a. (f∘g)(1) = f(g(1)) = f(0) = 5
b. (f∘g)(2) = f(g(2)) = f(-3) = 8
c. (g∘f)(2) = g(f(2)) = g(3) = -7
d. (g∘f)(3) = g(f(3)) = g(2) = -3
e. (g∘g)(1) = g(g(1)) = g(0) = 1
f. (f∘f)(3) = f(f(3)) = f(2) = 3
Therefore, the answers are (a) 5, (b) 8, (c) -7, (d) -3, (e) 1, and (f) 3.
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whats smaller than 1/2
Answer:
1/4
Step-by-step explanation:
Fractions have two parts, the numerator and the denominator. The denominator is the bottom number and it tells us what unit of fraction we are working with (ie: it denotes fourths, halves, etc.)
Hope it helps! :D
How to write 3/4 with a denominator of 12? Please help
Answer:
9/12
Step-by-step explanation:
3/4 converted is 9/12 3x3 is 9 and 4x3 is 12.
Tyler took out a five-year loan with a principal of $12,000. He made monthly payments of $215 for the entire period, at which point the loan was paid off. How much did Tyler pay in interest?
Responses
$15
$60
$75
$900
Answer:
D, $900
Step-by-step explanation:
and monthly payments of $215, we can use the following formula:
Total interest = Total amount paid - Principal
where:
Total amount paid = Monthly payment x Number of payments
Number of payments = Number of years x 12
In this case, Tyler made monthly payments of $215 for 5 years, which is a total of 5 x 12 = 60 payments.
Substituting these values into the formula, we get:
Total amount paid = $215 x 60 = $12,900
Total interest = $12,900 - $12,000 = $900
Therefore, Tyler paid $900 in interest over the five-year period. The answer is option D: $900.
What is the inequality shown?
Answer:
The inequality that shows the range from -9 to 9, but only including the range from -4 to 3, can be written as:
-4 ≤ x ≤ 3
This inequality means that x can take on any value between -4 and 3, including -4 and 3 themselves, but it cannot be less than -4 or greater than 3. The inequality does not include the values between -9 and -4, or between 3 and 9.
Step-by-step explanation:
explanation of how to arrive at the inequality -4 ≤ x ≤ 3 to represent the range from -9 to 9, but only including the range from -4 to 3:
Start with the range from -9 to 9:
-9 ≤ x ≤ 9
Identify the portion of the range that we want to include:
-4 ≤ x ≤ 3
Replace the original range with the desired range:
-4 ≤ x ≤ 3 replaces -9 ≤ x ≤ 9
Check that the inequality is inclusive of the desired range but not of any values outside of that range:
-4 is included in the range -4 ≤ x ≤ 3, but is not included in the original range -9 ≤ x ≤ 9. Similarly, 3 is included in the range -4 ≤ x ≤ 3, but is not included in the original range -9 ≤ x ≤ 9. Any values less than -4 or greater than 3 are excluded from the range -4 ≤ x ≤ 3, as desired.
Therefore, the inequality -4 ≤ x ≤ 3 represents the range from -9 to 9, but only including the range from -4 to 3.
The inequality -4 ≤ x ≤ 3 represents the range from -9 to 9, but only including the range from -4 to 3.
How to find the inequality?The inequality that shows the range from -9 to 9, but only including the range from -4 to 3, can be written as:
-4 ≤ x ≤ 3
This inequality means that x can take on any value between -4 and 3, including -4 and 3 themselves, but it cannot be less than -4 or greater than 3. The inequality does not include the values between -9 and -4, or between 3 and 9.
explanation of how to arrive at the inequality -4 ≤ x ≤ 3 to represent the range from -9 to 9, but only including the range from -4 to 3:
Start with the range from -9 to 9:
-9 ≤ x ≤ 9
Identify the portion of the range that we want to include:
-4 ≤ x ≤ 3
Replace the original range with the desired range:
-4 ≤ x ≤ 3 replaces -9 ≤ x ≤ 9
Check that the inequality is inclusive of the desired range but not of any values outside of that range:
-4 is included in the range -4 ≤ x ≤ 3, but is not included in the original range -9 ≤ x ≤ 9. Similarly, 3 is included in the range -4 ≤ x ≤ 3, but is not included in the original range -9 ≤ x ≤ 9. Any values less than -4 or greater than 3 are excluded from the range -4 ≤ x ≤ 3, as desired.
Therefore, the inequality -4 ≤ x ≤ 3 represents the range from -9 to 9, but only including the range from -4 to 3.
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Identify then number of solutions of the polynomial equation. Then find the solutions. z^(3)+10z^(2) + 28z + 24=0
The solutions are: z = -3, -2, and -1. This equation is a third-degree polynomial equation and it can have up to three solutions. To find these solutions, you can use the Rational Root Theorem.
This theorem states that all rational solutions of a polynomial equation can be written in the form a/b, where a is a divisor of the coefficient of the constant term, and b is a divisor of the coefficient of the leading term.
For this equation, the constant term is 24 and the leading term is 1, so the possible solutions can be expressed as a/b, where a is a divisor of 24 and b is a divisor of 1. Therefore, the possible solutions are ±1, ±2, ±3, ±4, ±6, ±8, ±12, and ±24. To find the exact solutions, substitute these values for z into the equation and solve for each value.
The solutions are: z = -3, -2, and -1.
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In a class 45% of the students are girls. If there are 18 girls in the class, then find
the total number of students in the class.
Answer:
i dont think its possible
Warm-Up: Suppose you have 60 dollars to deposit into a savings account. If you put your money into Bank A, they will deposit an additional 6 dollars per year into your account. If you put your money into Bank B, they will increase your balance by 10 percent per year.
How much money would you have after one year if you put your money into Bank A? How about Bank B?
Bank B may be a better option because the 10 percent increase is applied to the new balance each year, whereas Bank A only adds a flat 6 dollars each year.
If you put your money into Bank A, you will have to equate it as 60 + 6 = <<60+6=66>>66 dollars after one year.
If you put your money into Bank B, you will have 60 + (60 * 0.10) = 60 + 6 = <<60+(60*0.10)=66>>66 dollars after one year of the investment.
So, after one year, you will have the same amount of money in both Bank A and Bank B.
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Isabella is deep-sea diving with two friends. Stacy is exploring a coral reef 6.3 meters in front of Isabella, and Jayla is floating on the surface directly above Isabella. If Jayla and Stacy are 9 meters apart, how far apart are Isabella and Jayla? If necessary, round to the nearest tenth.
Isabella and Jayla are thus separated by about 11.0 metres.
What is the idea of the Pythagorean Theorem?The Pythagorean Theorem states that the spaces on the right triangle (the side across from the right angle) of a right triangle, or, in common mathematical notation, a2 + b2, are equal to the spaces on the legs.
The Pythagoras formula can be used to resolve this issue. Let's call the distance between Isabella and Jayla "x". Then we have:
x² = (6.3)² + (9)²
Simplifying:
x² = 39.69 + 81
x² = 120.69
Taking the square root of both sides:
x ≈ 10.98
Rounding to the nearest tenth, we get:
x ≈ 11.0
Therefore, Isabella and Jayla are approximately 11.0 meters apart.
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Lee wants to make at least $400 profit from selling t-shirts. The initial start up costs for making t-shirts is $125. Write an inequality that represents the amount of sales, s, that Lee must have to reach the goal. Please answer!!
Answer:4
Step-by-step explanation: