Using a calculator, the critical value for the t-distribution, with a confidence level of 99%, a sample size n = 20 and a two-tailed test is of Tc = 2.8609.
How to find the critical value of the t-distribution?It is found using a calculator, with three inputs, which are given by:
The confidence level.The number of degrees of freedom, which is one less than the sample size.The tail.In this problem, the inputs are given as follows:
Confidence level of 99%, as 1 - 0.01 = 0.99 = 99%.19 df, as 20 - 1 = 19.Two-tailed test, as stated in this problem.Hence, using a calculator, the critical value is of is of Tc = 2.8609.
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What number should come next in the sequence? 0.8, 0.35, -0.1, -0.55, ... FASTTTTT
Answer:
-1
Step-by-step explanation:
0.35 - 0.8 = -0.45
-0.1 - 0.35 = -0.45
-0.55 - 0.45 = -1
Fill in the P(X=x) values to give a legitimate probability distribution for the discrete random variable , whose possible values are 0, 1, 3, 4, and 5.
For a probability distribution to be represented, it is needed that P(X = 0) + P(X = 1) = 0.44. Hence one possible example is:
P(X = 0) = 0.40.P(X = 1) = 0.04.What is needed for a discrete random variable to represent a probability distribution?The sum of all the probabilities must be of 1, hence:
P(X = 0) + P(X = 1) + P(X = 3) + P(X = 4) + P(X = 5) = 1.
Then, considering the table:
P(X = 0) + P(X = 1) + 0.15 + 0.17 + 0.24 = 1
P(X = 0) + P(X = 1) + 0.56 = 1
P(X = 0) + P(X = 1) = 0.44.
Hence one possible example is:
P(X = 0) = 0.40.P(X = 1) = 0.04.More can be learned about probability distributions at https://brainly.com/question/24802582
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Absolute value of sqrt(5) - 2.2
0.03607
Step-by-step explanation:Absolute value is the distance of a number from zero. Since distance is always positive, the absolute value is the same number but positive.
Please note, for this problem I have rounded to 5 decimal points because the answer is irrational.
Subtracting
There are 2 different ways to approach this problem. You can either estimate the square root of 5 or plug this question straight into a calculator.
First, we can estimate [tex]\sqrt{5}[/tex] and round to 5 decimal places.
[tex]\sqrt{5}[/tex] ≈ 2.23607Then, take this value and subtract.
2.23607 - 2.2 = 0.03607Absolute Value
Now that we have solved the subtraction problem we have to find the absolute value. As stated above, the easiest way to find absolute value is to simply make the number positive. Since the answer is already positive, this is the final answer.
|0.03607| = 0.03607(3x) (4x) =
A. – x
B. 7x
C. 12x
D. 12x²
E. none of these
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textbf{Equation: }[/tex]
[tex]\large\textsf{(3x)(4x)}[/tex]
[tex]\large\textbf{Solving:}[/tex]
[tex]\large\textsf{(3x)(4x)}[/tex]
[tex]\large\textsf{= 3x} * \large\textsf{4x}[/tex]
[tex]\large\textbf{Combine the like terms:}[/tex]
[tex]\large\textsf{(3x * 4x)}[/tex]
[tex]\large\textsf{= 3x * 4x}[/tex]
[tex]\large\textsf{= 12x}^2[/tex]
[tex]\large\textbf{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\frak{Option\ D. 12\mathsf{x}^2}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Find the measures of x and y
Answer:
x = 159; y = 140
Step-by-step explanation:
a = 40
a + y = 180
y = 180 - 40
y = 140
b = 61
b = (180 - x) + a
61 = 180 - x + 40
x = 159
Answer:
m∠x = 159°
m∠y = 140°
Step-by-step explanation:
PART I: Find the measure of yGiven information
∠a = 40°
Given formula
∠a + ∠y = 180° (Supplementary angles)
Substitute values into the formula
40 + ∠y = 180
∠y = 180 - 40
[tex]\Large\boxed{\angle y=140^\circ}[/tex]
PART II: Find the measure of xGiven information
∠b = 61°
∠c = Supplementary angle of ∠b
Given formula
∠b + ∠c = 180°
Substitute values into the formula
61 + ∠c = 180
∠c = 180 - 61
∠c = 119°
Determine the value of ∠x
∠x = ∠a + ∠c (Exterior angle theorem)
∠x = (40) + (119)
[tex]\Large\boxed{\angle x=159^\circ}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
A binomial experiment is given. Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, find the mean and standard
deviation. If you cannot, explain why.
A survey of adults found that 66% have used a multivitamin in the past 12 months. You randomly select 40 adults and ask them if they have used a multivitamin in the
past 12 months.
Select the correct answer below and, if necessary, fill in the answer boxes within your choice.
OA. No, because np < 5.
B. No, because nq <5.
OC. Yes, the mean is_______
(Round to two decimal places as needed.)
and the standard deviation is _____
Yes, the mean is 26.4 and the standard deviation is 3
How to find the mean in binomial experiment?We are given;
n = 40, p = 66% = 0.66, and q = 1 – 0.66 = 0.34
If np ≥ 5 and np ≥ 5, then the binomial random variable, x is approximately normally distributed, then;
Mean; µ = np
Standard deviation; σ = √npq
where;
n is the sample size.
p is the population proportion.
q = 1 – p.
Calculating np and nq gives;
np = (40)(0.66) = 26.4
nq = (40)(0.34) = 13.6
Both np and nq are greater than 5, the normal distribution can be used to approximate the binomial distribution.
Thus, µ = np
µ = 40(0.66) = 26.4
Standard deviation;
σ = √(40 * 0.66 * 0.34)
σ = 3
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In conducting a goodness-of-fit test, a requirement is that ________. Question content area bottom Part 1 A. the expected frequency must be at least five for each category B. the expected frequency must be at least ten for each category C. the observed frequency must be at least ten for each category D. the observed frequency must be at least five for each category
In conducting a goodness of fit test, a requirement is that the expected frequency must be at least ten for each category.
What is a goodness of fit test?In relation to the statistical model, the test tells how well it fits a set of observations.
The measures of the goodness of fit summarize the discrepancy between observed values and the values expected under the model in question.
Also, when conducting a goodness of fit test, a requirement is that the expected frequency must be at least ten for each category.
Therefore, the Option B is correct,
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Solve for x.
2x² = 18x+20
Find equations of the following. y = x^2 − z^2, (6, 32, 2) (a) the tangent plane (b) the normal line
The equation for the tangent plane is 12x - y + 4z - 56 = 0 and the equation for normal line is (x - 6)/12 = (32 - y) = (z - 2)/4
Finding the Equations for Tangent Plane and Normal Line:
The given function is,
f(x, y, z) = x² - y - z² = 0
∂f/ ∂x = 2x
∂f/ ∂y = -1
∂f/ ∂z = 2z
At given point (6, 32, 2),
∂f/ ∂x = 12
∂f/ ∂y = -1
∂f/ ∂z = 4
(a) The equation of tangent plane is given as follows,
(∂f/ ∂x)(x-x₁) + (∂f/ ∂y)(y-y₁) + (∂f/ ∂z)(z-z₁) = 0
12(x - 6) - 1(y - 32) + 4(z - 4) = 0
12x - 72 - y + 32 + 4z - 16 = 0
The required tangent plane is,
12x - y + 4z - 56 = 0
(b) The equation for normal line is given as,
(x-x₁) / (∂f/ ∂x) = (y-y₁) / (y-y₁) = (z-z₁) / (∂f/ ∂z)
(x - 6)/12 = (y - 32)/(-1) = (z - 2)/4
Thus, the required equation of normal line is,
(x - 6)/12 = (32 - y) = (z - 2)/4
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Joey had eight pencils in the morning. He gave some pencils away to friends who needed them. To determine the number of pencils he has left, ___ the number of pencils he gave away. count difference subtract add
What does ! mean in a math problem?
Divide each number in sequence from that number to 1.
Add each number in sequence from that number to 1.
Multiply each number in sequence from that number to 1.
Subtract each number in sequence from that number to 1.
It is an exciting problem.
! is shorthand for the factorial function. If [tex]n[/tex] is a non-negative integer, then
[tex]n! = n\times(n-1)\times(n-2)\times\cdots3\times2\times1[/tex]
with [tex]0! = 1[/tex].
So how to compute [tex]n![/tex] ?
Multiply each number in sequence from that number to 1.
b) The diameter of a circular coin is 1.14 cm. How many coins of the same size are required to place in a straight row to cover 2.85 m length (without leaving any gap between each coin)
Answer:
250.
Step-by-step explanation:
if one coin covers 1.14 cm, then the required number can be calculated according the equality:
required_number=(given_length/given_diameter);
Then:
[tex]number=\frac{2.85*100}{1.14} =\frac{285}{1.14} =250[coins].[/tex]
P.S. note, the given length is in [meter], the diameter is in [cm].
A study was conducted to determine whether there were significant differences between medical students admitted through special programs (such as retention incentive and guaranteed placement programs) and medical students admitted through the regular admissions criteria. It was found that the graduation rate was 92.5% for the medical students admitted through special programs. Round your answers to 4 decimal places. If 12 of the students from the special programs are randomly selected, find the probability that at least 11 of them graduated.
The probability that at least 11 of them graduated is 0.7739 if graduation rate is 92.5%.
Given that graduation rate is 95.2%.
We are required to find the probability that out of 12 selected candidates atleast 11 should be graduated.
Probability is basically the chance of happening an event among all the events possible. It cannot be negative. It lies between 0 and 1.
Probability=Number of items/ Total items.
Probability that atleast 11 will be graduated out of 12 selected candidates is as under:
It will be a binomial distribution.
So,
P(X>=11)=[tex]12C_{11}(0.925)^{11} (0.075)^{1} +12C_{12}(0.925)^{12} (0.075)^{0}[/tex]
=12*0.4241*0.075+1*0.3923
=0.3816+0.3923
=0.7739
Hence the probability that at least 11 of them graduated is 0.7739 if graduation rate is 92.5%.
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. A community theater sold 63 tickets to the afternoon performance for a total of 444 Birr. An adult ticket cost 8 Birr, a child ticket cost 4 Birr, and a senior ticket cost 6 Birr. If twice as many tickets were sold to adults as to children and seniors combined, how many of each ticket were sold? (Use Gaussian Elimination Method)
The number of tickets sold are:
30 children tickets were sold33 adult tickets were soldHow to determine the number of tickets sold to children and seniors?From the question, we have the following parameters:
Number of tickets = 63Total amount = 444 BirrAdult ticket = 8 Birr per adultChildren ticket = 6 Birr per adultRepresent the children tickets with x and adults ticket with y.
So, we have the following system of equations
x + y = 63
6x + 8y = 444
Express the equations as a matrix
x y
1 1 63
6 8 444
Apply the following transformation
R2 = R2 - 6R1
This gives
x y
1 1 63
0 2 66
Apply the following transformation
R2 = 1/2R2
x y
1 1 63
0 1 33
From the above matrix, we have the following system of equations
x + y = 63
y = 33
Substitute y = 33 in x + y = 63
x + 33 = 63
Subtract 33 from both sides of the above equation
x = 30
Hence, 30 children tickets were sold and 33 adult tickets were sold
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Perform the operation and
simplify.
3
x - 3
5
x + 2
-2x + 21
x² + [ ? ]x + [
Answer: -1
Step-by-step explanation:
Here, we are subtracting two fractions; therefore, we must make the denominators the same by finding the least common multiple. Since we have x - 3 for one denominator and x + 2 for the other, we don't have any common factors. Hence, the least common multiple would be their product.
[tex](x-3)(x+2)\\x(x-3)+2(x-3)\\x^2-3x+2x-6\\x^2-x-6[/tex]
The question is looking for the coefficient of the second term. Since there is just a negative sign in front of the x, the "?" can be filled with either a negative sign or a -1.
Consider the parametric equations below.
x = t^2 − 3, y = t + 2, −3 ≤ t ≤ 3
Eliminate the parameter to find a Cartesian equation of the curve.
for
−1 ≤ y ≤ 5
Solve the second equation for [tex]t[/tex], then substitute it into the first equation.
[tex]y = t + 2 \implies t = y-2[/tex]
[tex]x = t^2 - 3 \implies \boxed{x = (y-2)^2 - 3}[/tex]
I’m really confused on this problem., pls help me!
Answer:
Domain: All Real Numbers
Range: All Real Numbers
Step-by-step explanation:
So the domain of a function can be defined as an interval of x-values, which you can input into the function and get real numbers as an output. Since we have a cube root here, or more specifically an odd nth root, the domain is all real numbers, since cbrt(negative number) will just be a negative number since (negative number * negative number * negative number) = negative number, so there does exist a solution, unlike even nth roots like square root, which is restricted to only positive values inside the radical, otherwise you get non-real solutions.
Now let's look at the range of the function, which can be defined as an interval of y-values which can possibly be outputted by the function.
Since as mentioned before, the cube root isn't limited to a certain interval, and rather all real numbers, the range is also similar, since whenever you have a negative number in the radical, the output will be a negative number, so the range is all real numbers
The answer is A.
As any number can be inputted in place of x and the result, y, will be directly proportional to the inputting value, the domain and range of the function is All Real Numbers.
A bird flies 50km everyday to collect food for his offspring and 20km to drink water. To fly this distance takes him 1 hour and 40 minutes. What’s his average speed during flight?
Answer:
Step-by-step explanation:
speed = 50 km / hr.
distance = 20 km
time = distance / speed.
time = ( / 50) hr.
speed = 2 km/hrs
Fatima purchased a new mattress when it was on sale. The sale price was 20% less than the regular price. If the sale price was $358, what was the original price? (Round your answer to the nearest dollar).
well, the regular price is really "x", which oddly enough is 100%, but we also know that $358 is really the discounted price by 20%, namely 100% - 20% = 80%, so we know that 358 is really just 80% of "x", so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 358& 80 \end{array} \implies \cfrac{x}{358}~~=~~\cfrac{100}{80} \\\\\\ \cfrac{x}{358}=\cfrac{5}{4}\implies 4x=1790\implies x=\cfrac{1790}{4}\implies x\approx 448[/tex]
Given AD is the median of △ABC find x, CD, and DB. i need step by step
Applying the definition of the median of a triangle: x = 9; CD = 28; DB = 28.
What is the Median of a Triangle?The median of a triangle can be defined as a line segment in a triangle that joins the vertex of a triangle to the midpoint of the side of the triangle that is opposite the vertex.
Given triangle ABC, where AD is the median and D is the midpoint of side AB, therefore:
Side CD equals side DB.
Side CD = 5x - 17
Side DB = 3x + 1
Make both segments equal to each other. Therefore, we would have the equation:
5x - 17 = 3x + 1
Solve for x
Add both sides by 17
5x - 17 + 17 = 3x + 1 + 17
5x = 3x + 18
Subtract 3x from both sides
5x - 3x = 3x + 18 - 3x
2x = 18
Divide both sides by 2
2x/2 = 18/2
x = 9
CD = 5x - 17
Plug in the value of x
CD = 5(9) - 17
CD = 45 - 17
CD = 28 units.
DB = 3x + 1
Plug in the value of x
DB = 3(9) + 1
DB = 27 + 1
DB = 28 units.
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Find the measure of angles a and b
Find the missing segment in the image below
Answer:
42
Step-by-step explanation:
similar triangles
24/x = (24+8)/x+14
that looks complicated so we do
8/24 = 14/x
or
24/8 = x/14
3 = x/14
x = 3*14
x = 42
we test it with the first equation
24/42 = 32/56
simplify
4/7 = 4/7
true so 42 is correct
Identify the discrete data.
A. the length of a caterpillar during a week
B. the number of dogs you take for a walk each day
C. the wind speed during a particular day
D. the temperature of the water in the local river during the day
Discrete data exists as a numerical kind of data that contains total, concrete numbers with clear and fixed data values specified by counting.
Therefore, the correct answer is option B. the number of dogs you take for a walk each day.
What is discrete data?Discrete data exists as a numerical kind of data that contains total, concrete numbers with clear and fixed data values specified by counting. Discrete data exists a count that involves integers only a limited number of values exists possible. This kind of data cannot be subdivided into distinct parts. Discrete data contains discrete variables that exist in finite, numeric, countable, and non-negative integers.
Therefore, the correct answer is option B. the number of dogs you take for a walk each day.
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Juan and Ari went to the farmers market to buy fruit. Juan’s bag of apples that he bought weighed StartFraction 31 over 7 EndFraction pounds. Ari’s bag of oranges that he bought weighed StartFraction 19 over 3 EndFraction pounds. Using compatible fractions, estimate how much heavier Ari’s bag is compared to Juan’s bag.
Answer:
approximately 2 lb
Step-by-step explanation:
Juan: 31/7
Ari: 19/3
Juan's fraction is close to 32/8 = 4
Ari's fraction is close to 18/3 = 6
6 - 4 = 2
Answer: approximately 2 lb
Number lineWhich of these numbers represents the difference between -3 and -2
The number which represents the difference between the numbers given -3 and -2 as in the task content is; 1.
Which number represents the difference between -3 and -2 in the task content?It follows from the task content that the difference between the given numbers -3 and -2 is to be determined by means of the number line.
On this note, since, it follows that the difference between two numbers in the number line is given by the absolute value of their arithmetic difference.
It follows that the number which is required in this scenario is; |-3-(-2)| = |-1| = 1.
This follows from the fact that the absolute value big any number is that number with a positive polarity.
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Which pair of functions are inverses of each other? O A. F(a) = I - 9 and g(2) = 2*9 O B. Ax) = 5x - 11 and g(a) = 2+11 O C. F(a) = V2m and g(2) = (3) ° O D. f(a) = ; + 8 and g(x) = 6x - 8 SUBMIT
The pair of functions that are inverses of each other is (a) f(x) = 5x - 11 and g(x) = (x + 11)/5
How to determine the function and the inverse?The complete question is added as an attachment
Function 1
f(x) = 5x - 11 and g(x) = (x + 11)/5
Represent 5x - 11 with y in f(x) = 5x - 11
y = 5x - 11
Swap x and y
x = 5y - 11
Add 11 to both sides
x + 11 = 5y
Divide by 5
y = (x + 11)/5
Express as a function
g(x) = (x + 11)/5
From the question, we have:
f(x) = 5x - 11 and g(x) = (x + 11)/5
This means that the function g(x) is an inverse of the function f(x)
Hence, the pair of functions that are inverses of each other is (a) f(x) = 5x - 11 and g(x) = (x + 11)/5
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Solve for exponential the value of X
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The two triangles are right angled Triangles and they have one common angle. so the two triangles are similar to each other.
By using similarity, ratio of their corresponding sides must be equal as well~
[tex]\qquad \sf \dashrightarrow \: \cfrac{1}{2 + 1} = \cfrac{3}{x} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{1}{3} = \cfrac{3}{x} [/tex]
[tex]\qquad \sf \dashrightarrow \: x = 3 \times 3[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 9 \: \: units[/tex]
NO LINKS! Please help me with this problem
Answer:
f(x) = x³ -4x² +9x +164
Step-by-step explanation:
When a function has a zero at x=p, it has a factor (x-p). When a polynomial function with real coefficients has a complex zero, its conjugate is also a zero.
Factored formGiven the two zeros and the one we can infer, we can factor our 3rd-degree polynomial function as ...
f(x) = a(x -(-4))·(x -(4+5i))·(x -(4-5i))
Real factorsUsing the factoring of the difference of squares, we can combine the complex factors to make a real factor.
f(x) = a(x +4)((x -4)² -(5i)²) = a(x +4)(x² -8x +16 +25)
Finding the scale factorThe value of this at x=1 is ...
f(1) = a(1 +4)(1 -8 +41) = 170a
We want f(1) = 170, so ...
170 = 170a ⇒ a=1
The factored polynomial function is ...
f(x) = (x +4)(x² -8x +41)
Standard formExpanding this expression, we have ...
f(x) = x(x² -8x +41) +4(x² -8x +41) = x³ -8x² +41x +4x² -32x +164
f(x) = x³ -4x² +9x +164
Graph
The attached graph verifies the real zero (x=-4) and the value at x=1. It also shows that the factor with complex roots has vertex form (x -4)² +25, exactly as it should be.
Answer:
[tex]f(x) = (x+4)(x^2-8x+41)[/tex]
Step-by-step explanation:
Ok, so there are a couple of things to note here. The first thing is that there is a complex solution
Complex Conjugate Root Theorem:
if [tex]a-bi[/tex] is a solution then [tex]a+bi[/tex] is a solution and vice versa
Fundamental Theorem Of Algebra:
Any polynomial with a degree "n", will have "n" solutions. Those solutions can be real and imaginary numbers
So since we're given the root: [tex]4+5i[/tex], we can use the Complex Conjugate Root Theorem to assert that: [tex]4-5i[/tex] is also a solution.
So now we know 3 solutions/zeroes, and since n=3 (the degree), we can know for a fact that we have all the solutions due to the Fundamental Theorem of Algebra.
So using these roots, we can express the polynomial as it's factors. When you express a polynomial as factors it'll look something like so: [tex]f(x) = a(x-b)(x-c)(x-d)...[/tex] where a, b, and d are zeroes of the polynomial. Also notice the "a" value? This will affect the stretch/compression of the polynomial.
So let's express the polynomial in factored form:
[tex]f(x) = a(x-(-4))(x-(4+5i))(x-(4-5i))[/tex]
Simplify the x-(-4)
[tex]f(x) = a(x+4)(x-(4+5i))(x-(4-5i))[/tex]
Now let's distribute the negative sign to the complex roots
[tex]f(x) = a(x+4)(x-4-5i)(x-4+5i))[/tex]
Now let's rewrite the two factors (x-4-5i) and (x-4+5i) so the (x-4) is grouped together
[tex]f(x) = a(x+4)((x-4)-5i)((x-4)+5i))[/tex]
If you look at the two complex factors, this looks very similar to the difference of squares: [tex](a-b)(a+b) = a^2-b^2[/tex]
In this case a=(x-4) and b=5i. So let's use this identity to rewrite the two factors
[tex]f(x) = a(x+4)((x-4)^2-(5i)^2)[/tex]
Let's expand out the (x-4)^2
[tex]f(x) = a(x+4)(x^2+2(-4)(x)+(-4)^2-(5i)^2)[/tex]
Simplify
[tex]f(x) = a(x+4)(x^2-8x+16-(5i)^2)[/tex]
Now simplify the (5i)^2 = 5^2 * i^2
[tex]f(x) = a(x+4)(x^2-8x+16-(-25))[/tex]
Simplify the subtraction (cancels out to addition)
[tex]f(x) = a(x+4)(x^2-8x+41)[/tex]
So just to check for the value of "a", we can substitute 1 as x, and set the equation equal to 170
[tex]170 = a(1+4)(1^2-8(1)+41)\\170 = a(5)(1-8+41)\\170 = a(5)(34)\\170 = 170a\\a=1[/tex]
In this case it's just 1, so the polynomial can just be expressed as:
[tex]f(x) = (x+4)(x^2-8x+41)[/tex]
how many decimal places does 22.22105 have
Answer:
5
Step-by-step explanation:
where there is the decimal point,you count the numbers after the decimal point
I need help! DUE IN 2 HOURS WILL MARK BRAINLIEST!!!
The exponential model for the data is: [tex]y = 693(1.5)^x[/tex]
When the cost is of $6000, the weight is of approximately 5.3 carats.
What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex]
In which:
a is the initial value.b is the rate of change.From the table, the rate of change is given by:
b = 4980/3210 = 3210/2140 = 2140/1430 = 1.5.
When x = 1, y = 1040, hence the initial value is found as follows:
1.5a = 1040.
a = 1040/1.5
a = 693.
So the model is:
[tex]y = 693(1.5)^x[/tex]
When the cost is of $6000, the weight is found as follows:
[tex]693(1.5)^x = 6000[/tex]
[tex](1.5)^x = \frac{6000}{693}[/tex]
[tex]1.5^x = 8.658[/tex]
[tex]\log{1.5^x} = \log{8.658}[/tex]
x log(1.5) = log(8.658)
x = log(8.658)/log(1.5)
x = 5.3
When the cost is of $6000, the weight is of approximately 5.3 carats.
More can be learned about exponential functions at https://brainly.com/question/25537936
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