The confidence interval for the population mean has the following structure:
\(\lbrack\bar{x}\pm Z_{1-\frac{\alpha}{2}}\cdot\frac{\sigma}{\sqrt[]{n}}\rbrack\)You have to add/subtract the margin of error to the point estimation.
The point estimation of the population mean is the sample mean, in this case, the sample mean is 300.
The margin of error is the second term of the formula:
\(Z_{1-\frac{\alpha}{2}}\cdot\frac{\sigma}{\sqrt[]{n}}\)-First, you have to determine the z-value to use for the confidence interval. To do so you have to use the confidence level:
\(1-\alpha=0.95\)Determine the value of 1-α/2
\(\begin{gathered} \alpha=1-0.95 \\ \alpha=0.05 \\ \frac{\alpha}{2}=0.025 \\ 1-\frac{\alpha}{2}=1-0.025=0.975 \end{gathered}\)You have to use the Z-value that accumulates 0.975 of probability, that is:
\(Z_{0.975}=1.96\)Next, calculate the margin of error:
\(\begin{gathered} Z_{1-\frac{\alpha}{2}}\frac{\sigma}{\sqrt[]{n}} \\ 1.96\cdot\frac{47}{\sqrt[]{50}}=13.0277 \end{gathered}\)The margin of error rounded to the nearest hundredth is 13.03.
Subtract the margin of error from the mean to determine the lower bound:
\(\begin{gathered} \bar{x}-Z_{1-\frac{a}{2}}\cdot\frac{\sigma}{\sqrt[]{n}} \\ 300-13.03=286.97 \end{gathered}\)Add the margin of error to determine the upper bound:
\(\begin{gathered} \bar{x}+Z_{1-\frac{\alpha}{2}}\cdot\frac{\sigma}{\sqrt[]{n}} \\ 300+13.03=313.03 \end{gathered}\)The 95% confidence interval is [286.97;313.03]
The confidence level of a confidence interval indicates the probability that the confidence interval will contain the true value of the estimated parameter. So if you were to construct 100 intervals, you would expect 95 of them to include the population parameter.
In terms of the exercise, you can interpret the calculated interval, with a 95% confidence level, you expect the interval [286.97;313.03] to contain the true value of the average GRE scores.
In the EAI sampling problem, the population mean is $51,800 and the population standard deviation is $4,000. When the sample size is n = 30, there is a .5034 probability of obtaining a sample mean within +/- $500 of the population mean. A. What is the probability that the sample mean is within $500 of the population mean if a sample of size 60 is used (to 4 decimals)?
B. What is the probability that the sample mean is within $500 of the population mean if a sample of size 120 is used (to 4 decimals)?
A) The probability that the sample mean is within $500 of the population mean for a sample of size 60 is 0.6611
B) The probability that the sample mean is within $500 of the population mean for a sample of size 120 is 0.7362
The EAI (Error of the Estimate) sampling problem is a specific case of the Central Limit Theorem, which states that the distribution of sample means from a population with a finite variance will be approximately normally distributed as the sample size increases.
The formula for calculating the standard error of the mean is
SE = σ/√n
where SE is the standard error, σ is the population standard deviation, and n is the sample size.
For n = 30, SE = 4,000/√30 = 729.16
A. For a sample size of n = 60, SE = 4,000/√60 = 516.40
To find the probability that the sample mean is within $500 of the population mean, we need to calculate the z-score for a range of +/- $500
z = (x - μ) / SE
where x is the sample mean, μ is the population mean, and SE is the standard error.
For a range of +/- $500, the z-scores are
z = ($51,300 - $51,800) / 516.40 = -0.969
z = ($52,300 - $51,800) / 516.40 = 0.969
Using a standard normal distribution table, the area between z = -0.969 and z = 0.969 is 0.6611.
B. For a sample size of n = 120, SE = 4,000/√120 = 368.93
Following the same steps as above, the z-scores for a range of +/- $500 are
z = ($51,300 - $51,800) / 368.93 = -1.364
z = ($52,300 - $51,800) / 368.93 = 1.364
Using the standard normal distribution table, the area between z = -1.364 and z = 1.364 is 0.7362.
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On January 1st you bought 100 shares of Ford Motor Company (F) for $8 per share . On October 2nd the stock price is $10 per share. You sell the 100 shares at $10 per share. How much did you make or lose (\$) ? What was your return on investment (ROl) ?
Answer:
$200; $800
Step-by-step explanation:
100 x8 =800
100 x10=1000
1000-800= $200 (what you earn)
the money that you pay back is the return on investment so $800
The amount of profit made by the shares is given by A = $ 200
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
The cost of 1 share on January 1st = $ 8
The number of shares = 100
So , the total cost of 100 shares = $ 800
And , the cost of 1 share on October 2nd = $ 10
The number of shares = 100
So , the total selling price of 100 shares = $ 1,000
And , the profit A = total selling price of 100 shares - cost of 100 shares
On simplifying the equation , we get
The profit made A = $ 1,000 - $ 800
The profit made A = $ 200
Hence , the equation is A = $ 200
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Toms age minus bobs age is 2 bobs age is 82 less than three times toms age how old is Tom age how old is Tom and bob
Answer:
Tom is 164 years old and Bob is 3*164-82=246 years old.
Step-by-step explanation:
Let X be Tom's age.
Bob's age is 3X-82.
The difference in their ages is X-(3X-82)=2(3X-82)
Solving for X, we get X=164.
Tom is 164 years old and Bob is 3*164-82=246 years old.
Find values of p for which the integral
∫10xpln(x)dx
converges and calculate the value of the integral for these values of p.
The integral ∫10x^p * ln(x) dx converges for all values of p except p = -1.
To determine the values of p for which the integral ∫10x^p * ln(x) dx converges, we need to consider the convergence of the integrand for different values of p. The integral will converge if the integrand is well-behaved and does not exhibit any divergence.
Let's analyze the integrand in two separate cases:
Case 1: p ≠ -1
When p ≠ -1, the integrand is well-defined for all x > 0. We can proceed with evaluating the integral.
∫10x^p * ln(x) dx = [x^(p+1) * ln(x)] / (p+1) + C
To calculate the value of the integral for a specific value of p, we can substitute the limits of integration into the antiderivative expression and evaluate the resulting expression.
Case 2: p = -1
When p = -1, the integrand becomes 10x^(-1) * ln(x), which poses a potential issue at x = 0. To determine if the integral converges for this case, we need to examine the behavior of the integrand near x = 0.
As x approaches 0, the expression ln(x) approaches negative infinity, which would cause the integrand to diverge. Therefore, for p = -1, the integral does not converge.
In summary, the integral ∫10x^p * ln(x) dx converges for all values of p except p = -1.
Please note that when evaluating the definite integral for specific limits of integration, you should substitute the limits into the antiderivative expression and then calculate the difference of the resulting expressions evaluated at the upper and lower limits.
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Which number line shows the solution to the inequality? y minus 2 less-than negative 5 A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded. A number line going from negative 8 to positive 2. A closed circle is at negative 3. Everything to the left of the circle is shaded. A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the right of the circle is shaded. A number line going from negative 8 to positive 2. An open circle is at negative 7. Everything to the left of the circle is shaded.\\
The number line that shows the solution to the inequality y - 2 < -5 is:
A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded.
What is inequality?
In mathematics, an inequality is a statement that compares two values, expressing that one value is less than, greater than, or less than or equal to, greater than or equal to, or not equal to another value.
The inequality is y - 2 < -5.
To graph the solution on a number line, we start by marking the point where y - 2 equals -5, which is y = -3. Then, since the inequality is less-than, we use an open circle to represent the point y = -3.
Next, we shade all the values of y that make the inequality y - 2 < -5 true. Since y is less than -3, we shade everything to the left of the open circle.
Therefore, the number line that shows the solution to the inequality y - 2 < -5 is:
A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded.
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Henry bought a new car for $22,568
The car had a sales tax of 4%
What is the sales tax for the car in dollars and cents?
A) $843.63
B) $865.21
C) $881.52
D) $402.72
E) $924.53
F) None of the above
Answer:
The answer is F) none of the above. The correct sales tax is $902.72
Step-by-step explanation:
Mr. Milstein needs a larger kitchen table. The top of his current kitchen table measures 17 1_2square feet. Mr. Milstein has decided to build a new table with a width of 5 feet.
Therefore, Mr. Milstein needs to build a table with a length of 7/2 feet, or 3 1/2 feet, to achieve an area of 17 1/2 square feet with a width of 5 feet.
What is area?Area is a measurement of the size of a two-dimensional surface or region, typically measured in square units, such as square meters or square feet. It is a measure of how much space is contained within the boundaries of a flat shape or object. The formula for calculating the area of a shape varies depending on the type of shape, but generally involves multiplying the length of one side or dimension by another. For example, the area of a rectangle can be found by multiplying its length by its width, while the area of a circle can be found by multiplying pi (approximately equal to 3.14159) by the radius squared.
Here,
To determine the length of the new table that Mr. Milstein needs to build, we can use the formula for the area of a rectangle, which is:
Area = Length x Width
We know that Mr. Milstein's current table has an area of 17 1/2 square feet. To find the length of his new table, we can rearrange the formula as follows:
Length = Area / Width
Substituting the given values, we get:
Length = 17 1/2 / 5
To simplify the calculation, we can convert the mixed number 17 1/2 to an improper fraction:
17 1/2 = 35/2
Then, we can divide the numerator by the denominator:
Length = (35/2) / 5
Length = 35/10
Simplifying the fraction by dividing both the numerator and denominator by their greatest common factor, we get:
Length = 7/2 feet
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I have stopped going to school due to my mental break downs because of school so my teachers started sending me my work i have missed but the only thing i was not at school to learn how to do it so please help me....!!
Answer:
1. C.
2. A.
3. B.
i just know those im sorry-
Answer:
1 - c 6.4 ×10^6
2 - a 6.4 ×10
3- b 6.04 ×10^5
4) 5.21× 10^8 × 1.6km
=8.33×10^8 km
5) 10,000,000,000 = 1 ×10^10
BRAINLIST PLS
The L shape is reflected in the y axis. Which one of the following shows the correct image
Answer:
B
Step-by-step explanation:
The image gets flipped across the y-axis.
It might help if you think about it like flipping a piece of paper cut into that shape horizontally.
also (x, y) -> (-x, y)
Answer:
B
Step-by-step explanation:
What is the area of the trapezoid?
Answer:
26 this is because 4x5=20 then add the triangle which is 3x4 ÷ 2 equalling 26
Answer:
Step-by-step explanation:
(5+8)/2 = 13/2 = 6.5
6.5*4 = 26m²
The formula for the area of a trapezoid is the same as a trapezium :
(a+b)/2 *h = Area
If events A and B are independent, what must be true?
P(A|B) = P(B)
P(A|B) = P(A)
P(A) = P(B)
P(A|B) = P(B|A)
Answer:
P(A|B) = P(A)
Step-by-step explanation:
If events A and B are independent, then we have:
P(A) x P(B) = P(A⋂B)
As the conditional probability formula states:
P(A⋂B) = P(A|B) x P(B) = P(B|A) x P(A)
=> P(A) x P(B) = P(A|B) x P(B) = P(B|A) x P(A)
or
P(A) = P(A|B)
or
P(B) = P(B|A)
Answer:
B
Step-by-step explanation:
ANSWER IF YOU ARE GOOD AT WRITING ESSAYS AND WANT 1,600 POINTS!!
Why is [3, ∞) the range of the function.
The interval [3, ∞) represents the range of the function as it is the interval containing the output values, which are the values of y on the graph of the function.
How to obtain the domain and range of a function?The domain of a function is defined as the set containing all the values assumed by the independent variable x of the function, which are also all the input values assumed by the function.The range of a function is defined as the set containing all the values assumed by the dependent variable y of the function, which are also all the output values assumed by the function.For this problem, we have that the values of y on the graph of the function are of 3 or higher, hence the interval representing the range is given as follows:
[3, ∞)
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let a=2-3j and c=-9-2j
c) polar representation of a
d) polar representation of c
e) a+c*
f) a* (complex conjugate)
g) |a|
h) angle(a)
i) angle(c)
The angle of c, denoted as angle(c), is the angle formed between the positive real axis and the line connecting the origin to c. To find the angle, we can use the arctan function: angle(c) = arctan(-2/(-9)).
c) The polar representation of a is r_a * e^(i * theta_a), where r_a is the modulus (magnitude) of a and theta_a is the argument (angle) of a.
d) The polar representation of c is r_c * e^(i * theta_c), where r_c is the modulus (magnitude) of c and theta_c is the argument (angle) of c.
e) To find the sum of a and the complex conjugate of c (c*), we add the real parts and imaginary parts separately. The sum is (a + c*) = (2 - 3j) + (-9 + 2j) = (-7 - j).
f) The complex conjugate of a (a*) is obtained by changing the sign of the imaginary part. So, a* = 2 + 3j.
g) The modulus (magnitude) of a, denoted as |a|, is the distance of a from the origin in the complex plane. |a| = sqrt((2^2) + (-3^2)) = sqrt(4 + 9) = sqrt(13).
h) The angle of a, denoted as angle(a), is the angle formed between the positive real axis and the line connecting the origin to a. To find the angle, we can use the arctan function: angle(a) = arctan(-3/2).
i) The angle of c, denoted as angle(c), is the angle formed between the positive real axis and the line connecting the origin to c. To find the angle, we can use the arctan function: angle(c) = arctan(-2/(-9)).
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Please answer correctly !!!!!!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!!
A+22°=90° (SUM OF COMPLEMENTRY ANGLES )
A=90°-22°
A=68° ANSWER.
If 2 times the sum of two consecutive even numbers is greater than 94, what is the smallest possible value of the larger number?
Answer:
26
Step-by-step explanation:
Define the variables:
2n = first even number2n + 2 = consecutive even numberGiven information:
2 times the sum of two consecutive even numbers is greater than 94Create an inequality from the defined variables and the given information:
⇒ 2(2n + 2n + 2) > 94
Solve the inequality:
⇒ 2(4n + 2) > 94
⇒ 8n + 4 > 94
⇒ 8n > 90
⇒ n > 11.25
Therefore:
2n > 22.52n + 2 > 24.5As 2n and 2n+2 are even numbers:
smaller number (2n) ≥ 24larger number (2n + 2) ≥ 26Therefore, the smallest possible value of the larger number is 26.
your price for chicken parmesan is $11.99. your food cost for this item is $4.31. you change you menu prices to be 30% of food cost. by what percentage will the price of chicken parmesan increase?
The percentage by which the price of chicken parmesan will increase is 153.76%.
Food cost is defined as the cost of ingredients and raw materials that are required to make a dish. Food cost is also known as menu cost or recipe cost.
Menu pricing strategy determines the selling price of a dish or menu item. To price the menu, the food cost is usually divided by the desired percentage of profit. Let's solve the problem using the following formula:
Menu Price = (Food Cost ÷ Desired Percentage Markup) + Food Cost
Given, Price for chicken parmesan = $11.99
Food cost for this item = $4.31
New menu price will be 30% of the food cost.
Menu Price = (30% × 4.31) + 4.31= 1.293 + 4.31= 5.6033 ≈ $5.60
The percentage increase in the price of chicken parmesan is given by the following formula:
Percentage increase = (New Price - Old Price) / Old Price × 100%
Percentage increase = (5.60 - 11.99) / 11.99 × 100%
Percentage increase ≈ -53.76%
This is a negative value which implies that the price is decreased instead of increasing. So we have to add the absolute value of the percentage increase to 100% to get the actual percentage increase.
Percentage increase = 53.76% + 100%
Percentage increase = 153.76%
So, the percentage by which the price of chicken parmesan will increase is 153.76% rounded to two decimal places .
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In a basketball tournament, Team A scored 5 less than twice as many points as Team B. Team C scored 80 more points than Team B. The combined score for all three teams was 983 points. Let the variable b represent Team B’s total points. The equation representing this scenario is (2b – 5) + b + (b + 80) = 983. Team B scored 227 total points.
Answer: Let us assume number of points scored by Team B = b points.
Number of points scored by Team A 5 fewer than twice as many points as Team B, that is "5 less than 2b" = (2b-5) points .
Team C scored 80 more points than Team B, that is " 80 more than b" = (b+80) points.
Total number of points scored by all teams = 983 points.
Therefore, we can setup an equation:
(2b-5) + b + (b+80) = 983.
Therefore, an equation to represent this scenario using the variable b to represent Team B’s total points is (2b-5) + b + (b+80) = 983.
Team A= 2b-5
Team B= b
Team C= b+80
The equation representing this scenario is (2b-5)+ b + (b+80)= 983
Answer:
b=227
Step-by-step explanation:
how is 15×3/5 = 9
the slash is for the fraction
Answer:15x3 /=divide 5 = 9
Step-by-step explanation:
because if you do 15x3 it is 45 then you divide it by 5 and get 9 as your answer!
If a quadrilateral is inscribed in a circle then opposite angles are:.
Answer:
Step-by-step explanation:
Theorem
An inscribed quadrilateral is one where all four angles touch the circumference of the circle containing those 4 angles.
The opposite angles can be shown to be supplementary (that is equal to 180 degrees)
Answer: Supplementary
Draw triangle LMN with vertices L(2,-2), M(6,-4) and(5,4). Find the coordinates of the vertices after 90degrees rotation about the origin and about each of the point of L,M,and N
The coordinates of the vertices after rotation depend on the point around which rotation is done.
Rotation of a shape around the origin (0,0) means that each point in the shape has to be moved around the origin by a certain angle. This is done by using the equation x'=xcosθ-ysinθ and y'=xsinθ+ycosθ, where x and y are the coordinates of the point before rotation and x' and y' are the coordinates of the point after rotation. In this case, the angle of rotation is 90 degrees. When we rotate triangle LMN by 90 degrees around the origin, the coordinates of the vertices become L'(2,2), M'(-4,6) and N'(4,-5).When we rotate the triangle around any of the points of L, M, or N, the coordinates of the vertices will change accordingly. For example, if we rotate the triangle around point L, the coordinates of the vertices become L'(2,-2), M'(-2,4) and N'(-6,0). Similarly, if we rotate the triangle around point M, the coordinates of the vertices become L'(2,-2), M'(6,-4) and N'(0,6). Lastly, if we rotate the triangle around point N, the coordinates of the vertices become L'(2,-2), M'(4,5) and N'(5,4).
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This year a herd of bison had a 10 percent decrease in population; if there are 550 bison now how many bison are there?
The total amount of kinetic and potential energy in a system is called
The total amount of kinetic and potential energy in a system is called mechanical energy.
Mechanical energy is the sum of kinetic energy and potential energy within a system. Kinetic energy (KE) is the energy possessed by an object due to its motion, and it is calculated using the formula KE = (1/2)mv², where m is the mass of the object and v is its velocity. Potential energy (PE) is the energy possessed by an object due to its position or condition, and it can be gravitational potential energy, elastic potential energy, or other forms. The total mechanical energy (ME) is obtained by adding the kinetic and potential energy together, so ME = KE + PE.
In summary, the total amount of kinetic and potential energy in a system is referred to as mechanical energy. This energy accounts for both the motion and position-related energies within the system. The calculation of mechanical energy involves summing the kinetic energy, which depends on the mass and velocity of the objects, with the potential energy, which can arise from factors such as gravity or elasticity. Understanding and analyzing the mechanical energy in a system can provide insights into its overall energy distribution and behavior.
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Write an equation in point-slope form for the line that passes through the point with the given slope.
Answer:
Slope: 3
Equation: y + 2 = 3(x + 1)
Step-by-step explanation:
Find the slope using (-1, -2) and (0, 1):
\( slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - (-2)}{0 - (-1)} = \frac{3}{1} = 3 \)
Slope (m) = 3
The equation can be represented in point-slope form, y - b = m(x - a)
Where,
(-1, -2) = (a, b)
m = 3
Plug in the values into y - b = m(x - a)
y - (-2) = 3(x - (-1))
y + 2 = 3(x + 1)
HELP QUICK NEED DONE BEFORE MIDNIGHT
Answer:
52 square units
Step-by-step explanation:
The big area (include red squares) is: \(6\cdot 11=66\) square units
The small area (only red squares) is: \(2\cdot 7=14\) square units
The area shaded in yellow is obtained by subtracting the small area from the big area: \(66-14=52\) square units
whats the volume of this shape
r-11cm
h-16 cm
Answer:
you know who else like the shape my mom
Find the installment price of a recliner bought on the installment plan with a down payment of \( \$ 90 \) and six payments of \( \$ 107.72 \). The installment price is \( \$ \)
The installment price of the recliner bought on the installment plan with a down payment of $ 90 and six payments of $ 107.72 is $736.32.
The installment price of the recliner, we need to calculate the total amount paid over the installment plan, including the down payment and the six payments.
Down payment: $90
Six payments: $107.72 each
Total amount paid = Down payment + (Number of payments × Payment amount)
Total amount paid = $90 + (6 × $107.72)
Total amount paid = $90 + $646.32
Total amount paid = $736.32
Therefore, the installment price of the recliner is $736.32.
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Which transformation is a translation?
A.
B.
田田田
由田中
c.
D.
Answer:
A, B, and C are rotations so it must be D
Step-by-step explanation:
What would be the cost of a Big Mac in Azerbaijan in US dollars (convert the price in bolivar to US dollars)?
= 4.7/1.7
= $2.76 would be the cost of a Big Mac
he cost of a Big Mac in the US is $5.15. If the law of one price holds for the Big Mac in the United States and Azerbaijan, what would be the exchange rate between the manat and the dollar?
=4.7/1.7
= $.91 manat/dollar
c. Compare the actual exchange rate between the bolivar and the dollar of 1.7 manat/$1 to the exchange rate suggested by the law of one price in part b. Is the manat overvalued or undervalued according to our application of the law of one price? (6 points)
The cost of a Big Mac in Azerbaijan in US dollars would be $2.76 and The exchange rate between the Azerbaijani manat and the US dollar would be approximately 0.91 manat per dollar.
To calculate the cost of a Big Mac in US dollars in Azerbaijan, we need to convert the price in Azerbaijani manat (AZN) to US dollars (USD) using the exchange rate. If the price of a Big Mac in Azerbaijan is 4.7 AZN and the exchange rate is 1.7 AZN/USD, we can calculate the cost in US dollars as follows:
Cost in USD = Price in AZN / Exchange rate
= 4.7 AZN / 1.7 AZN/USD
≈ $2.76 USD
Therefore, the cost of a Big Mac in Azerbaijan in US dollars would be approximately $2.76.
Given that the cost of a Big Mac in the US is $5.15, we can use the law of one price to determine the exchange rate between the Azerbaijani manat (AZN) and the US dollar (USD). By equating the cost of a Big Mac in both countries, we can set up the following equation:
Price in Azerbaijan (in AZN) = Price in the US (in USD)
4.7 AZN = $5.15 USD
To find the exchange rate, we can rearrange the equation as follows:
Exchange rate = Price in Azerbaijan / Price in the US
= 4.7 AZN / $5.15 USD
≈ 0.91 AZN/USD
Therefore, the exchange rate between the Azerbaijani manat and the US dollar would be approximately 0.91 manat per dollar.
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What is 2x+5g+7y+1.52x+32.6+5.1g+11.1+9y simplified?
Answer:
10.1g+3.52x+16y+43.7
Step-by-step explanation: