The bench costs $375, and the garden table costs $295. Together, they amount to $670, with the table being $80 cheaper than the bench.
Let the cost of the bench be x. Then the cost of the garden table is x-80. The sum of the costs of both items is $670. So we have the equation: x + (x-80) = $670.
Simplifying this, we get 2x - 80 = $670 + 80 2x = $750 x = $375. So the cost of the bench is $375. The garden table costs $375 - $80 = $295. A garden table and a bench cost $670 combined.
The garden table costs $80 less than the bench. To find the cost of the bench, we can use algebraic equations. Let the cost of the bench be x. Then, the cost of the garden table is x - 80.
The sum of both costs is $670. Using this information, we can form an equation: x + (x - 80) = $670. Simplifying, we get 2x - 80 = $670 + 80. Solving for x, we get x = $375.
Therefore, the cost of the bench is $375, and the cost of the garden table is $295.
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The manager of a diner is evaluating their egg costs via their current food service contract. They are currently buying organic free-range eggs at $4.75 a dozen. Currently the average price of eggs of the same quality is $5 per dozen and the population standard deviation is $0.75. The prices are normally distributed. They decide to sample 5 vendors that sell similar quality eggs, collect the prices, and compute the mean price for the sample. Should they renegotiate their egg prices with their vendor based on the likelihood that the sample mean will be higher than their current price? Justify your answer using the probability of the sample mean.
Given statement solution is :-The decision to renegotiate the egg prices should be based on the calculated probability (P) obtained from the z-score calculation.
To determine whether the diner should renegotiate their egg prices with their vendor, we need to assess the likelihood that the sample mean price will be higher than their current price of $4.75 per dozen. We can use the concept of the sampling distribution of the sample mean to make this assessment.
Given that the population standard deviation is known ($0.75) and the sample size is small (n = 5), we can assume the sampling distribution of the sample mean will be approximately normally distributed. The mean of the sampling distribution will be equal to the population mean ($5 per dozen), and the standard deviation of the sampling distribution (also known as the standard error) can be calculated by dividing the population standard deviation by the square root of the sample size.
Standard error (SE) = population standard deviation / √(sample size)
SE = 0.75 / √(5)
SE ≈ 0.3354
Now, we can calculate the probability that the sample mean price will be higher than $4.75 by standardizing the sample mean using the z-score formula:
z = (sample mean - population mean) / standard error
z = ($4.75 - $5) / 0.3354
z ≈ -0.445
Using a standard normal distribution table or calculator, we can find the probability corresponding to a z-score of -0.445. Let's assume this probability is P.
If P is sufficiently small (typically less than 0.05), it indicates that the sample mean being higher than $4.75 is unlikely to occur by chance. In such a case, it would suggest that the diner should consider renegotiating their egg prices with their vendor.
However, if P is relatively large (greater than or equal to 0.05), it suggests that the sample mean being higher than $4.75 is reasonably likely to occur by chance. In this scenario, there may not be sufficient evidence to justify renegotiating the egg prices based solely on the sample mean.
Therefore, the decision to renegotiate the egg prices should be based on the calculated probability (P) obtained from the z-score calculation.
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Simplify and show your work. [tex](6i)(-2i)(-6-4i)[/tex]
Answer:
- 72 - 48i
Step-by-step explanation:
note that i² = - 1
(6i)(- 2i)(- 6 - 4i)
= - 12i²(- 6 - 4i)
= - 12(- 1)(- 6 - 4i)
= 12(- 6 - 4i) ← distribute parenthesis by 12
= - 72 - 48i
Solve the following quadratic inequality x^2+x-6>0
Answer:
x < -3 or x > 2
Step-by-step explanation:
x² + x - 6 > 0
Convert the inequality to an equation.
x² + x - 6 = 0
Factor using the AC method and get:
(x - 2) (x + 3) = 0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
x - 2 = 0
x = 2
x + 3 = 0
x = -3
So, the solution is x < -3 or x > 2
3(8+2) is the same as
Answer:
3(8 + 2) = 3(8) + 3(2) = 3(10) = 30
p(-2,6),q(-8,4),r(1,2) what is the y value of p’
Answer:
OK, here is your answer
Step-by-step explanation:
AI-generated answer
We are given three points, p(-2, 6), q(-8, 4), and r(1, 2), and we are asked to find the y-value of p'. Since we are not given any information about p', we can assume that it is the reflection of p across the x-axis.To find the reflection of p across the x-axis, we need to negate the y-coordinate of p. Therefore, the y-value of p' is equal to the negative of the y-coordinate of p.
So, the y-value of p' is -6.
Hence, the coordinates of p' are (-2, -6).
mark me as brainliestwhat needs to be demonstrated to show quadrilateral DEFG is a parallelogram? (select all the correct answers) ILL MARK AS BRAINLIEST PLEASE HELP ASAP.
For quadrilateral DEFG to be shown to be a parallelogram, we need to demonstrate that: a. EF║GD; b. DE = FG = EF = GD; e. DE║FG; f. DE = FG
What is a parallelogram?A parallelogram is a four-sided polygon with opposite sides that are parallel and equal in length.
To demonstrate that quadrilateral DEFG is a parallelogram, the following conditions need to be satisfied:
a. EF║GD (Opposite sides are parallel)
b. DE = FG = EF = GD (Opposite sides are congruent)
e. DE║FG (Opposite sides are parallel)
f. DE = FG (Opposite sides are congruent)
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Simplify i) ( x-y )( x−y )( x−y )
The simplified expression for ( x - y ) ( x - y ) ( x - y ) is x³ - x²y - xy² + y³.
To simplify ( x - y ) ( x - y ) ( x - y ), we can expand the expression using the distributive property of multiplication. We can also simplify the expression by combining like terms.
In using the distributive property of multiplication, we multiply each term in the first set of parentheses by each term in the second set of parentheses. This gives us:( x - y ) ( x - y ) ( x - y ) = ( x(x - y) - y(x - y) ) ( x - y )= ( x² - xy - xy + y² ) ( x - y )= ( x² - 2xy + y² ) ( x - y )
Now we can further simplify the expression by combining like terms. We can use the difference of squares formula to simplify the second set of parentheses.( x² - 2xy + y² ) ( x - y ) = ( x - y ) ( x - y )²= ( x - y ) ( x² - 2xy + y² )= x³ - x²y - 2xy² + xy² - xy² + y³= x³ - x²y - xy² + y³
Therefore, the simplified expression is x³ - x²y - xy² + y³.
Summary: To simplify ( x - y ) ( x - y ) ( x - y ), we expand the expression using the distributive property of multiplication. We simplify the expression by combining like terms. We use the difference of squares formula to simplify the second set of parentheses. Finally, we simplify the expression further by combining like terms. The simplified expression is x³ - x²y - xy² + y³.
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Find the function value.
cos (-305.3)°
Answer:
Step-by-step explanation:
Answer:
The function value.of cos (-305.3)° is 0.5921
Explanation:
To find the value of cos (-305.3)°, we can use the periodicity property of the cosine function. Since cos (x) is a periodic function with a period of 360 degrees, we can add or subtract multiples of 360 degrees from the angle without changing the value of the cosine.
Step 1: Convert -305.3° to an equivalent angle within period one (0 to 360 degrees).
-305.3° + 360° = 54.7°
Step 2: Calculate the cosine of the equivalent angle.
cos (54.7°)
Step 3: Use a scientific calculator or trigonometric table to find the cosine value.
cos (54.7°) ≈ 0.5921
Therefore, the value of cos(-305.3)° is approximately 0.5921
Need help with question 1 please
A. The initial value of the linear formula is $40,500
The growth rate of the function is $950
B. The value of the car in 2020 is $69,000
C. The year in which the car is worth $61,400 is 2012.
What is the initial and growth rate value of the linear formula?.A. V = 40,500 + 950n
Where,
V = value in dollars
n = number of years since 1990
The initial value of the linear formula is $40,500
The growth rate of the function is $950
B. The value of the car in 2020;
When n = 30
V = 40,500 + 950n
= 40,500 + 950(30)
= 40,500 + 28,500
= $69,000
C. The year in which the car is worth $61,400
V = 40,500 + 950n
61,400 = 40,500 + 950n
subtract 40,500 from both sides
61,400 - 40,500 = 950n
20,900 = 950n
divide both sides by 950
n = 22 years
Therefore, 22 years after 1990 is 2012
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