For the following function, factor, then use case OR interval solutions (full marks only given to clear solutions showing multiple steps), to find when f(x)>0 and THEN by graphing. Make a closing statement about your solution and preferance for methods. f(x) = x4 – 6x3 + 9x2 + 4x – 12
Answers
To find the intervals where the function f(x) = x^4 - 6x^3 + 9x^2 + 4x - 12 is greater than zero (f(x) > 0), we can follow the steps like factorizing and determining the critical point
Step 1: Factor the polynomial if possible.
Unfortunately, the given function does not factor easily, so we will proceed with finding the intervals using other methods.
Step 2: Determine the critical points.
To find the critical points, we need to find the values of x where f(x) = 0 or where the derivative f'(x) = 0.
Finding f(x) = 0:
x^4 - 6x^3 + 9x^2 + 4x - 12 = 0
At this point, we can either use numerical methods or graph the function to estimate the approximate values of the roots. Alternatively, we can use a computer algebra system or calculator to find the roots, which are approximately x = -1.56, x = 0.26, x = 1.67, and x = 4.63.
Next, we find the derivative f'(x):
f'(x) = 4x^3 - 18x^2 + 18x + 4
Setting f'(x) = 0 and solving for x:
4x^3 - 18x^2 + 18x + 4 = 0
Again, we can use numerical methods or a calculator to find the approximate solutions. The solutions are approximately x = -0.52, x = 0.38, and x = 3.14.
Step 3: Create a sign chart.
We create a sign chart using the critical points and test intervals to determine where f(x) > 0.
Interval 1: (-∞, -1.56)
We choose a test value, for example, x = -2, and substitute it into the function:
f(-2) = (-2)^4 - 6(-2)^3 + 9(-2)^2 + 4(-2) - 12 = 68
Since the value is positive, f(x) > 0 in this interval.
Interval 2: (-1.56, -0.52)
Choosing a test value, for example, x = -1, we substitute it into the function:
f(-1) = (-1)^4 - 6(-1)^3 + 9(-1)^2 + 4(-1) - 12 = -6
Since the value is negative, f(x) < 0 in this interval.
Interval 3: (-0.52, 0.26)
Choosing a test value, for example, x = 0, we substitute it into the function:
f(0) = (0)^4 - 6(0)^3 + 9(0)^2 + 4(0) - 12 = -12
Since the value is negative, f(x) < 0 in this interval.
Interval 4: (0.26, 0.38)
Choosing a test value, for example, x = 0.3, we substitute it into the function:
f(0.3) = (0.3)^4 - 6(0.3)^3 + 9(0.3)^2 + 4(0.3) - 12 ≈ -11.08
Since the value is negative, f(x) < 0 in this interval.
Interval 5: (0.38, 1.67)
Choosing a test value, for example, x = 1, we substitute it into the function:
f(1) = (1)^4 - 6(1)^3 + 9(1)^2 + 4(1) - 12 = -4
Since the value is negative, f(x) < 0 in this interval.
Interval 6: (1.67, 3.14)
Choosing a test value, for example, x = 2, we substitute it into the function:
f(2) = (2)^4 - 6(2)^3 + 9(2)^2 + 4(2) - 12 = 12
Since the value is positive, f(x) > 0 in this interval.
Interval 7: (3.14, 4.63)
Choosing a test value, for example, x = 4, we substitute it into the function:
f(4) = (4)^4 - 6(4)^3 + 9(4)^2 + 4(4) - 12 = 140
Since the value is positive, f(x) > 0 in this interval.
Interval 8: (4.63, ∞)
Choosing a test value, for example, x = 5, we substitute it into the function:
f(5) = (5)^4 - 6(5)^3 + 9(5)^2 + 4(5) - 12 = 140
Since the value is positive, f(x) > 0 in this interval.
Step 4: Graphing the function.
By graphing the function f(x) = x^4 - 6x^3 + 9x^2 + 4x - 12, we can visually confirm the intervals where f(x) > 0. The graph will show the points where the function is above the x-axis.
Closing statement:
The analysis and solution indicate that the function f(x) = x^4 - 6x^3 + 9x^2 + 4x - 12 is positive (greater than zero) in the intervals (-∞, -1.56), (1.67, 3.14), and (4.63, ∞). By using either case analysis or interval solutions, we have identified the regions where the function is positive.
Regarding the preference for methods, both case analysis and interval solutions are valid approaches for finding intervals where a function is positive. The choice of method can depend on personal preference, the complexity of the function, and the available resources. In this case, we used both methods to showcase their effectiveness.
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Related Questions
a baker is deciding how many batches of muffins to make to sell in his bakery. he wants to make enough to sell to everyone and no fewer. through observation, the baker has established a probability distribution. what is the probability the baker will sell exactly one batch? (find p(x
Answers
Form the given probability distribution, the probability of selling exactly one batch by baker is equal to 0.10.
As given in the question,
Probability distribution established by baker :
x : 1 2 3 4
P(x) : 0.10 0.30 0.40 0.20
As it is give that number of batches made by baker to sell muffins .
For selling 1 batch x = 1.
For selling 2 batch x = 2.
For selling 3batch x = 3.
For selling 4 batch x = 4
Probability of selling exactly one batch by baker is given by when x =1
Probability of x = 1 is given by :
P( x = 1 ) = 0.10
Therefore, form the given probability distribution, the probability of selling exactly one batch by baker is equal to 0.10.
The complete question is :
A baker is deciding how many batches of muffins to make to sell in his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established a probability distribution. x P(x) 1 0.10 2 0.30 3 0.40 4 0.20 What is the probability the baker will sell exactly one batch.
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11/12 = 4h solve for h
(With explanations please.)
Answers
Answer:
h = 11/48
Step-by-step explanation:
We need to isolate the variable h to solve for the value of h
11/12 = 4h
If we divide both sides by 4, we can get the value of h. When we divide, we need to multiply by the reciprocal of 4 with 11/12. The reciprocal of 4 is 1/4.
11/12(1/4) = h
h = 11/48
A bag contains 14 green marbles and 10 purple marbles. You select one marble at random form the bag. What is the probability that you select a green marble?
Write your answer in SIMPLEST/REDUCED FORM.
Answers
Answer:
The bag contains 24 marbles total. If there are 14 green marbles, you have a 14 in 23 chance of selecting a green marble. This is because you avoid counting the marble you just picked while counting the total interpreted as a denominator.
14/23
Because the numerator and denominator do not share any GCFs, the fraction is already in its simplest form.
What is the quotient 2x3 − 3x − 10 x − 2 )?.
Answers
After solving the quotient (2x^3 - 3x - 10) ÷ (x - 2) is 2x^2 + 4x + 5.
In the given question, we have to find the quotient (2x^3 - 3x - 10) ÷ (x - 2).
The given expression is (2x^3 - 3x - 10) ÷ (x - 2).
We must use the synthetic division approach to determine the quotient.
By artificial division,
1) Identify the term's coefficients.
2) Decrease the initial coefficient, which is 2.
3) Putting 4 under the second coefficient 0 (2×2 = 4) now. Together, we get 4.
4) We take 4 and double it by 2, which gives us 8. Put 8 under coefficient 3 in the third place. Together, we get 5.
5) Next, divide 5 by 2. We get 10. Under the fourth coefficient, put 10. Together, we get 0.
x-2 ) 2x^3 - 3x - 10 ( 2x^2 + 4x + 5
2x^3 - 4x^2
- -
___________
4x^2 - 3x
4x^2 - 8x
- -
______________
5x - 10
5x - 10
- -
____________
0
Hence, after solving the quotient (2x^3 - 3x - 10) ÷ (x - 2) is 2x^2 + 4x + 5.
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The complete question is:
What is the quotient (2x^3 - 3x - 10) ÷ (x - 2)?
(1 ÷ 2 3 ⁄ 4 ) + (1 ÷ 3 1 ⁄ 2 ) = _____.
Answers
Answer:
50/77
Step-by-step explanation:
(1÷2 3/4)+(1÷3 1/2)
2 3/4 is same as 11/44
1/2 is same as 7/2
so to divide fraction you have to flip the second number and multiply
so 1 times 4/11=4/11
and 1 times 2/7=2/7
4/11 +2/7=28/77+22/77=50/77
The Exponential distribution "rate" parameter λ has probability density function f(t)=λe −λt
for t>0 (and f(t)=0 for t≤0 ). Suppose the rate parameter is not a fixed number, but rather is itself a random variable Λ, say, having an Exponential distribution with rate 1 . Thus, we assume Λ has pdf f Λ
(λ)=e −λ
for λ>0, and the conditional density for T given Λ is f T∣Λ
(t∣λ)=λe −λt
for t>0. (a) Find the cumulative distribution function F T
(t). Here are some tips: - You can use the law of total probability (LTP) in a form applied to continuous distributions, which I'll explain here. If Λ were a discrete random variable having possible values λ 1
,…,λ m
, then the LTP would tell us that P{T≤t}=∑ i=1
m
P{Λ=λ i
}P{T≤t∣Λ=λ i
}=∑ i=1
m
f Λ
(λ i
)P{T≤t∣Λ=λ i
} where f Λ
is the probability mass function f Λ
(λ i
)=P{Λ=λ i
}. The analogous statement for a continuous rv Λ replaces summation by integration, and for f Λ
uses the pdf of Λ, so that P{T≤t}=∫f Λ
(λ)P{T≤t∣Λ=λ}dλ. - In case you'd like an answer check: for t=1 and t=9, I get F T
(1)=0.5 and F T
(9)=0.9. But you don't really need me to tell you this, because in part (c) you will do simulations that check your answers to this part. (b) Find the probability density function f T
(t). (c) Perform a simulation corresponding to part (a) of this problem. You can use rexp to generate a vector Lambdas containing many random values of Λ drawn from an Exp(1) distribution, and then use rexp again together with your Lambdas vector to generate a vector Ts of many random values for T. Then use R to calculate what fraction of the values in Ts are ≤1 and what fraction are ≤9 (and of course if everything is correct you should find that your answers are close to 0.5 and 0.9-wow, another self-checking homework problem!).
Answers
The values of f1 and f2 should be close to 0.5 and 0.9, respectively.
(a)The conditional probability density function of T given Lambda is given by:
f_{T|\Lambda}(t|\lambda) = \lambda e^{-\lambda t} \quad t > 0
The cumulative distribution function of T is given by:
F_T(t) = P(T \le t) = \int_{0}^{\infty} P(T \le t | \Lambda = \lambda) f_{\Lambda}(\lambda) d\lambda
Substituting the conditional probability density function of T given
Lambda and the probability density function of Lambda into the above equation, we have:
F_T(t) = \int_{0}^{\infty} \lambda e^{-\lambda t} e^{-\lambda} d\lambda
= \int_{0}^{\infty} \lambda e^{-\lambda(t+1)} d\lambda
= \frac{1}{(t+1)^2} \int_{0}^{\infty} u e^{-u} du
where u = \lambda(t+1)
= \frac{1}{(t+1)^2}
= \frac{1}{t+1} - \frac{1}{(t+1)^2} for t > 0
Thus, the cumulative distribution function of T
is given by:
F_T(t) = \begin{cases} 0 &\mbox{if } t \le 0 \\ 1 - \frac{1}{t+1} &\mbox{if } t > 0 \end{cases}
(b) The probability density function of T is the derivative of the cumulative distribution function of T.
Thus, f_T(t) = \frac{d}{dt}F_T(t)
= \frac{1}{(t+1)^2}, for t > 0
(c) Simulation code:
# Generate a vector of lambdas
Lambdas <- rexp(100000, 1)
# Generate a vector of Ts
Ts <- rexp(100000, Lambdas)
# Calculate fraction of Ts <= 1 and Ts <= 9f1 <- mean(Ts <= 1)f2 <- mean(Ts <= 9)
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Function f(x) is an exponential function on the continuous interval -∞o < x <∞o, and is represented by the
table of values shown below. Function g(x)
-3
-2
-1
1
3
f(x)
-2.999
-2.99
-2.9
-2
7
97
997
Answers
Therefore , the solution of the given problem of function comes out to be f(x) = -4.5199 * (1.5546)ˣ
Function : what is it?The mathematics class covers a broad variety of subjects, such as mathematics, numbers and their subsets, as well as expressions building, construction, and both real and imagined geographic locations. The relationships between various components that all cooperate to create the same outcome are covered by a work. A utility is comprised of several unique parts that work together to produce unique outcomes for each input.
Here,
We can see from the table that:
When x = -3, f(x) = -2.999.
f(x) equals -2.99 when x is two.
At x = 1, f(x) equals -2.9.
If x = 1, then f(x) = 7.
F(x) = 97 when x = 3.
x = 5 when f(x) = 997.
We can write: since f(x) is an exponential function.
f(x) = a + bˣ
Using the specified numbers for x and f(x), we obtain:
=> -2.999 = a * b⁻³
=> -2.99 = a * b⁻²
=> -2.9 = a * b⁻¹
=> 7 = a * b¹
=> 97 = a * b³
=> 997 = a * b⁵
Any two sets of the aforementioned equations can be used to find the values of a and b. By splitting the fourth equation by the third equation, for instance, we obtain:
7 / (-2.9) = (a * b^(1)) / (a * b⁻¹)
-2.4138 = b²
=> b ≈ -1.5546 or b ≈ 1.5546
Using b = 1.5546 as a replacement in the third equation, we obtain:
=> -2.9 = a * (1.5546)⁻¹
=> a ≈ -4.5199
Consequently, the exponential function's general form is as follows:
=> f(x) = -4.5199 * (1.5546)ˣ
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How can you write the value of 6 hundred thousandths?
Answers
We can write the value of 6 hundred thousandths by using multiplication and the required value is 6,00,000.
This problem can be done by using multiplication. Like 6 hundred can be multiplied with the thousand then the value gets. We can write the value of 6 hundred thousandths by using multiplication and the required value is 6lakhs.
In mathematics, the number has ones place, tens place and hundreds place, thousands place. So, by that we can conclude the required value.
The value can be get by multiplying the given terms
Given 600 and multiplied by thousandths
600 * 1000 = 6,00,000
So, the required value is 6 lakhs or 6,00,000.
Therefore, this problem can be done by using multiplication. Like 6 hundred can be multiplied with the thousand then the value gets. We can write the value of 6 hundred thousandths by using multiplication and the required value is 6lakhs.
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You areplanning a Partyon a limited budgetIn order to do so youwilldeterminecost (total) to rent a space and per person for meals if the rental space is $780 and the price is $9.75 how much will it cost to host 50 peopleIf the budget is only $1500, how many guests can I invite to the party?
Answers
Let p be the number of people we want to host, then we can set the following equation:
\(C=780+9.75p\text{.}\)Where C is the total cost. Therefore, if p=50 we get:
\(C=780+9.75(50)=1267.5\text{.}\)If the budget is $1500, setting C=1500 and solving for p we get:
\(\begin{gathered} 1500=780+9.75p, \\ 1500-780=9.75p, \\ 720=9.75p, \\ \frac{720}{9.75}=p, \\ p=73.84. \end{gathered}\)Therefore, you can invite 73 people.
Answer: The total cost to host 50 people is $1267.5. If the budget is $1500, you can invite 73 people.
What is the length of side bc of the triangle? enter your answer in the box. Units.
Answers
The length of the side BC Iis equal to 28 units which we get by using congruency.
What is congruency?In other words, if the lengths of the sides and angles are the same for two shapes, they are congruent (the same in shape and size). When two triangles are congruent, it is frequently useful to know.
* In triangle ABC
∵ Angles B and C comes to be congruent
∴ m∠B = m∠C
* In any triangle if two angles are equal in measure, then the triangle is isosceles means the two sides which opposite to the congruent angles are equal in length
∴ AB = AC
∵ AB = 4x - 7
∵ AC = 2x + 7
∴ 4x - 7 = 2x + 7 ⇒ collect same terms
∴ 4x - 2x = 7 + 7
∴ 2x = 14 ⇒ divide both the sides by 2
∴ x = 14 ÷ 2 = 7
* Now we can find the length of side BC
∵ The length of side BC = 4x ⇒ substituting the value of x
∴ The length of side BC = 4 × 7 = 28 units
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Correct QuestionWhat is the length of side BC of the triangle? Enter your answer in the box. units Triangle A B C with horizontal side B C. Vertex A lies above side B C. Angle B and angle C are marked congruent. The length of side A C is labeled as 2 x plus 7. The length of side A B is labeled as 4 x minus 7. The length of side B C is labeled as 4 x.
Which of the points below lies on the curve y = x®?
(-1, 1)
(-2,-6)
(**)
3
A
B
C
D
Answers
Answer:
The answer is option d.
Hope this helps.
what statements are true about f(x)=49(1/7)
Answers
Answer:
f(x)=7
Step-by-step explanation:
A bakery sells 6 bagels for $2.99. What is the cost, in dollars, for 48 bagels?
A. $10.76
B. $13.16
C. $23.92
D. $37.08
Answers
Answer: $23.92
Step-by-step explanation:
First, we know that 6 bagels is $2.99.
48/6=8
This means that 6 is a multiple of 48, which makes it easier to solve.
$2.99 x 8 = 23.92
= $23.92
6 bagels for 2.99: 2.99/6
48 bagels for x cost: x/48
2.99/6 and x/48
2.99(48)=143.52
6(x)=6x
6x=143.52
/6 /6
x=23.92
The total cost is C: $23.92.
50 points and brainliest help pls
Answers
Answer:
Large bucket
Step-by-step explanation:
Sugar water isnt a real life factor in dye. It just makes it sweeter.
But, since it has triple the dye, it has more and therefore darker.
Hope this helps plz hit the crown ;D
Let f(x)= ax^2+bx+c and g(x)= ax^2-bx+c. If f(1) = g(1)+2 and f(2)=2, find g(2).
Answers
Answer:
first lets calculate f(1)=g(1)+2
a+b+c=a-b+c+2 so b=1
next lets calculate f(2)=2 remembering that we found b=1
4a+2*1+c=2 so c=-4a
Now lets find g(2)
g(2)=4a-2b+c= -c-2+c=-2 this is the final response
Which relation is a function?
Answers
Answer:
C
Step-by-step explanation:
if you don't have from same x different outcomes is a function
think that x is a day you count votes, you can not get for the same day different y number of votes ( something is fishy then)
A. not a function because (6, -3) and (6, 3)
B. not a function because (4,7) and (4,2)
C. is a function
D. not a function because (2, -1) (2,1) (2,3)
Find 3 rational number between: 1) -5 and -6 2)
Answers
Answer:
3 rational numbers between -5 and -6 include -5.6, -5.7, and -5.1.
Step-by-step explanation:
Answer:
-5.2, -5.6, and -5.8.
Step-by-step explanation:
3 rational numbers between -5 and -6.
-5 > x > -6
Where x is a rational number, that can be expressed in p/q form.
The numbers can be -5.2, -5.6, and -5.8.
-5.2 = -26/5
-5.6 = -28/5
-5.8 = -29/5
The numbers can be expressed in p/q form, so they are rational.
Find the slope of the line passing through the points(3,8) and (7,-7)
Answers
Answer:
\(-\frac{15}{4}\)
Step-by-step explanation:
Substituting into the slope formula,
\(m=\frac{-7-8}{7-3}=-\frac{15}{4}\)
1. Let the distribution of X be the normal distribution N (μ, σ2) and let Y = aX + b. Prove that Y is distributed as N (aμ + b, a2σ2).
2. Let X and Y be two independent random variables with E|X| < [infinity], E|Y| < [infinity] and E|XY| < [infinity]. Prove that E[XY] = E[X]E[Y].
Answers
1 Y is distributed as N(aμ + b, a^2σ^2), as desired.
2 We have shown that under these conditions, E[XY] = E[X]E[Y].
To prove that Y is distributed as N(aμ + b, a^2σ^2), we need to show that the mean and variance of Y match those of a normal distribution with parameters aμ + b and a^2σ^2, respectively.
First, let's find the mean of Y:
E(Y) = E(aX + b) = aE(X) + b = aμ + b
Next, let's find the variance of Y:
Var(Y) = Var(aX + b) = a^2Var(X) = a^2σ^2
Therefore, Y is distributed as N(aμ + b, a^2σ^2), as desired.
We can use the definition of covariance to prove that E[XY] = E[X]E[Y]. By the properties of expected value, we know that:
E[XY] = ∫∫ xy f(x,y) dxdy
where f(x,y) is the joint probability density function of X and Y.
Then, we can use the fact that X and Y are independent to simplify the expression:
E[XY] = ∫∫ xy f(x) f(y) dxdy
= ∫ x f(x) dx ∫ y f(y) dy
= E[X]E[Y]
where f(x) and f(y) are the marginal probability density functions of X and Y, respectively.
Therefore, we have shown that under these conditions, E[XY] = E[X]E[Y].
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z scores that fall below the mean are ______. a. 0 b. negative c. either positive or negative d. positive
Answers
The correct answer to the question "z scores that fall below the mean are" is "negative". Z-scores are measures of relative standing that can be used to make comparisons among the scores in the distribution by transforming raw data into standardized units.
The formula for z-score is:z = (X-μ)/σz-scores can be negative, zero, or positive numbers. A negative z-score tells us that the corresponding score is below the mean and vice versa.In addition to this, the mean of all z-scores is always zero. If the mean of all z-scores is zero, that means that z-scores are measuring deviation from the mean. If a z-score is below the mean, it means that the corresponding raw score is below the mean, which results in a negative z-score.
Z-scores that fall below the mean are negative. Z-scores are statistical values that allow analysts to transform raw data into standardized units that make comparisons possible among scores in the distribution. The formula for calculating the z-score is: z = (X-μ)/σThe z-score can be either negative, zero, or positive, depending on whether the value is below, equal to, or above the mean, respectively. Because the mean of all z-scores is always zero, z-scores can be used to measure deviation from the mean, with a negative z-score indicating that the corresponding raw score is below the mean. Z-scores allow us to compare the scores in the distribution by converting them into standard units. Negative z-scores are associated with scores that are below the mean. Conversely, positive z-scores are associated with scores that are above the mean.
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PQ= RQ and PS= RS a=?
Answers
The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.
What are interior angles?In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.
Given:
The length of the segment PQ is equal to the length of the segment RQ.The length of the segment PS is equal to the length of the segment RS.The following steps can be used in order to determine the measure of angle a:
Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.
Step 2 - Apply the sum of interior angle property on triangle PQR.
\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)
\(\angle\text{Q}+2\angle\text{R}=180\)
\(2\angle\text{R}=180-60\)
\(\angle\text{R}=60^\circ\)
Step 3 - Now, apply the sum of interior angle property on triangle PSR.
\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)
\(\angle\text{S}+2\angle\text{R}=180\)
\(2\angle\text{R}=180-90\)
\(\angle\text{R}=45^\circ\)
Step 4 - Now, the measure of angle a is calculated as:
\(\angle\text{a}=60-45\)
\(\angle\text{a}=15\)
The measure of angle a is 15 degrees.
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Write a word problem using the equation y = -2x+10 with a domain of { 0<_x<_5} and a range of
{0<_y<_10}
Answers
Answer:0,10
Step-by-step explanation:
x|y
0|10
1|8
Periodic Deposit: $? at the end of each monthRate: 7.5% compounded monthlyTime: 3 yearsFinancial Goal: $35,000O A. $2,628; $31,536 from deposits and $3,464 from interestB. $776; $27,936 from deposits and $7,064 from interestO c. $933; $33,588 from deposits and $1,412 from interestOD. $870; $31,320 from deposits and $3,680 from interest
Answers
Answer:
D. $870; $31,320 from deposits and $3,680 from interest
Explanation:
In order to calculate the monthly payment, we use the formula below:
\(P=\frac{A\mleft(\frac{r}{n}\mright)}{\mleft[\mleft(1+\frac{r}{n}\mright)^{nt}-1\mright]}\)Given:
• The Financial Goal, A= $35,000
,• Rate = 7.5% = 0.075
,• Number of compounding period = 12 (Monthly)
,• Time, t = 3 years
Substitute into the given formula:
\(\begin{gathered} P=\frac{35000\mleft(\frac{0.075}{12}\mright)}{\mleft[\mleft(1+\frac{0.075}{12}\mright)^{12\times3}-1\mright]} \\ P\approx\$870 \end{gathered}\)The monthly payment is $870.
\(\begin{gathered} \text{Total deposit}=870\times36=31,320 \\ \text{Interests}=35,000-31,320=3680 \end{gathered}\)Option D is correct.
Plz help me this is due in 45mins
Answers
in ... are the exponents
Answer:
2, 2 7
Step-by-step explanation:
\(252 = 4 \times 9 \times 7 \\ = \boxed{{2}}^{ 2} \times {3}^{ \boxed{2}} \times \boxed{7}\)
What is the answer to 2937682+28373938
Answers
Answer: 31311620
Step-by-step explanation: Calculator
You are choosing between two health clubs. club a offers a membership for a fee of $40
Answers
After 5 months the total cost at each health club be the same.
Given that, club A offers membership for a fee of $40 plus a monthly fee of $25.
Let the number of months be x.
Membership fee of club A = 40+25x ------(i)
Club B offers a membership fee of $15 plus a monthly fee of $30.
Membership fee of club B = 15+30x
The total cost at each health club be the same
40+25x = 15+30x
30x-25x=40-15
5x=25
x=25/5
x=5
Therefore, after 5 months the total cost at each health club be the same.
To learn more about an equation visit:
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"Your question is incomplete, probably the complete question/missing part is:"
You are choosing between two health clubs. Club A offers membership for a fee of $40 plus a monthly fee of $25. Club B offers a membership fee of $15 plus a monthly fee of $30.
Using variables of your choice, set-up an equation for each club’s membership cost. Make sure your variables are defined clearly.
After how many months will the total cost at each health club be the same?
Find the Surface area of the trapezoid
please help
show work
Answers
Answer:
259.5
Step-by-step explanation:
8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5
Maurice buys a dozen of donuts on sale for $7.99 before tax.
The sales tax is 4%.
What is the total price Maurice pays for the dozen donuts?
Answers
Answer:
$8.30
Step-by-step explanation:
7.99 + 4% = 8.30
The bucket is 30% full. when half way empty it is 15% full. how full is the bucket when 250% full?
Answers
Answer:
125%
Step-by-step explanation:
divide 250% by 2
100:30 (the bucket is completely full)
50:15 (the bucket is half empty)
250 = 100 + 100 + 50
So the ratio would be 250: 150, making the bucket 150% full.
(6,11) and (5,9) on a line in standard form
Answers
Answer:
2x - y = 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (6, 11) and (x₂, y₂ ) = (5, 9)
m = \(\frac{9-11}{5-6}\) = \(\frac{-2}{-1}\) = 2 , thus
y = 2x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (5, 9) , then
9 = 10 + c ⇒ c = 9 - 10 = - 1
y = 2x - 1 ← in slope- intercept form
The equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
From y = 2x - 1 ( subtract y and add 1 to both sides )
2x - y = 1 ← equation in standard form