"to find x in part a, you would need" to solve the equation x 2 – 25 =0. wh
explain why counting by tens might be faster than counting by ones
how to solve x^2-4y^2=7
540 less than the product of 54 and a number is 918
20.301_____ 20.31 is this equal or greater
a baseball team plays 83 games in a season. if the team won 17 more than twice as many as they lost how many times did the did lose?
Final answer:
By creating an equation based on the information provided and solving for L, which represents the number of games lost, it was determined that the baseball team lost 22 games during the season.
Explanation:
To determine how many games the baseball team lost during the season, let us denote the number of lost games as L. The problem states that the baseball team won 17 more than twice the number of games they lost, which can be expressed as 2L + 17. Since the team played a total of 83 games in the season, we have the following equation to represent the total number of games played:
L + (2L + 17) = 83.
Combining like terms, we get:
3L + 17 = 83.
Now, subtract 17 from both sides of the equation:
3L = 66.
Then, we divide both sides of the equation by 3:
L = 22.
So, the baseball team lost 22 games during the season.
To find the number of times the team lost, set up an equation using the given information. The team won 17 more than twice the number of times they lost. The team lost 22 times.
Explanation:To find the number of times the team lost, we can set up an equation using the given information.
Let's assume the number of times the team lost is x.
According to the given information, the team won 17 more than twice the number of times they lost. So, the number of times the team won is 2x + 17.
The total number of games played is 83, which is the sum of the number of games won and lost.
So we have the equation 83 = x + (2x + 17).
Simplifying this equation, we get 83 = 3x + 17.
Subtracting 17 from both sides, we have 66 = 3x.
Dividing both sides by 3, we get x = 22.
Therefore, the team lost 22 times.
Lesley raised $25 for the food bank last year and she raised 8 times as much money this year how much money did she raise this year
Estimate the area of the irregular shape. Explain your method and show your work. Can someone explain this to me?
Answer:
Approximate area: 27.5 square units
Step-by-step explanation:
The irregular shape is very similar to a trapezium with coordinates (-3,3), (2, 2), (2, -2) and (-3, -4).
Area of a trapezium: [(a+ b)/2]*h
where a and b refer to the two parallel sides and h is the distance between them. From the above coordinates: a = 7 length units, b = 4 length units and h = 5 length units. Therefore, approximate area = [(7+ 4)/2]*5 = 27.5 square units
Becky bought 4 pounds of grapes for $8.24.How much did the grapes cost per pound?
A right triangle has sides 5.0 m, 12 m, and 13 m. the smallest angle of this triangle is nearest:
Final answer:
To find the smallest angle in a right triangle with side lengths of 5.0 m, 12 m, and 13 m, we use the inverse tangent function with the shortest leg over the adjacent leg, yielding an angle of approximately 22.6 degrees.
Explanation:
The subject of the question is mathematics, and it pertains to high school level geometry. The question is asking to determine the smallest angle in a right triangle with sides measuring 5.0 m, 12 m, and 13 m. To find the smallest angle, we can use trigonometry, specifically the inverse tangent function.
Step-by-Step Explanation
Identify the sides of the triangle. In this case, we know that the sides are 5.0 m, 12 m (which could be interpreted as legs), and 13 m (the hypotenuse).
Because we are looking for the smallest angle, we will use the smallest leg, which is 5.0 m, and the next largest leg, which is 12 m.
Use the tangent function, which relates the opposite side to the adjacent side in a right triangle. The smallest angle, which we will call θ, will have the opposite side of 5.0 m and an adjacent side of 12 m.
Calculate θ using the inverse tangent function (also known as arctangent). θ = tan-1(5.0/12).
Perform the calculation using a calculator to find the nearest degree. θ = tan-1(5.0/12) ≈ 22.6°.
Therefore, the smallest angle in the triangle is approximately 22.6 degrees.
nearly 4 of 5 people choose vanilla as their favorite ice cream flavor. if 120 people attend an ice cream social, how many would you expect to choose vanilla?
A bag contains 1 gold marbles, 6 silver marbles, and 30 black marbles. Someone offers to play this game: You randomly select on marble from the bag. If it is gold, you win $4. If it is silver, you win $2. If it is black, you lose $1. You can expect to lose an average of ________ cents every time you play. (round to the nearest cent)
Jim has half a pizza left over from dinner. If he eats of this for breakfast, what fractional part did he eat for breakfast
Find the reference angle when o= 420 degrees
A) 30 degrees
B) 45 degrees
C) 50 degrees
D) 120 degrees
Find the perimeter of the following rectangle. Write your answer as a mixed number in simplest form. Be sure to include the correct unit in your answer. length is 7/10 and 2 1/4
From a sample of 500 items, 30 were found to be defective. the point estimate of the population proportion defective will be
Final answer:
The point estimate of the population proportion defective, given 30 defects in a 500 item sample, is 0.06 or 6%.
Explanation:
The point estimate of the population proportion defective can be calculated by dividing the number of defective items in the sample by the total number of items in the sample.
In this case, there are 30 defective items out of a sample of 500 items.
So the point estimate of the population proportion defective is:
Point estimate = Number of defective items / Total number of items
Point estimate = 30 / 500 = 0.06
Divide then check using multiplcation
1056÷37=
Seven weightlifters are competing in the dead-lift competition. In how many ways can the weightlifters finish first, second, and third ( no ties)?
The _______ form of a quadratic equation is written y = a(x - h)2 + k
Answer:
Correct Answer: vertex form
Step-by-step explanation:
F=9/5C+32 What Does C And F represent
Suppose that factory a produces 12 tables and 6 chairs an hour while factory b produces 8 tables and 4 chairs and hour. how many hours should each factory work to produce 48 tables and 24 chairs? how many different solutions are there to this problem?
Factory A should work for 4 hours, while factory B should work for 6 hours to produce 48 tables and 24 chairs
The rates of both factories are given as:
Factory A = 12 tables and 6 chairs in an hour
Factory B = 8 tables and 4 chairs in an hour
To produce 48 tables and 24 chairs, we make use of the following equation
[tex]h = \frac{Produce}{Rate}[/tex]
Where h represents time (in hours)
So, we have:
Factory A
[tex]h = \frac{48\ tables, 24\ chairs}{12\ tables, 6\ chairs}[/tex]
[tex]h = 4[/tex]
Factory A
[tex]h = \frac{48\ tables, 24\ chairs}{8\ tables, 4\ chairs}[/tex]
[tex]h = 6[/tex]
Hence, factory A should work for 4 hours, while factory B should work for 6 hours to produce 48 tables and 24 chairs
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Factory A should work for 0 hours and Factory B should work for 6 hours to produce 48 tables and 24 chairs. There is only one solution to this problem.
Explanation:To find out how many hours each factory should work to produce 48 tables and 24 chairs, we can set up a system of equations. Let's say that factory A works for x hours and factory B works for y hours. From the information given, we can write the following equations:
12x + 8y = 48 (equation 1, for tables)
6x + 4y = 24 (equation 2, for chairs)
We can solve this system of equations using substitution or elimination method. Let's solve it using the substitution method:
From equation 1, we can isolate x by subtracting 8y from both sides:
12x = 48 - 8y
x = (48 - 8y) / 12
Substituting this value of x in equation 2:
6((48 - 8y) / 12) + 4y = 24
Simplifying the equation:
3(48 - 8y) + 4y = 24
144 - 24y + 4y = 24
-20y = -120
y = (-120) / (-20)
y = 6
Substituting the value of y in equation 1:
12x + 8(6) = 48
12x + 48 = 48
12x = 0
x = 0
Therefore, factory A should work for 0 hours and factory B should work for 6 hours to produce 48 tables and 24 chairs. There is only one solution to this problem.
Factor 27x+9y
using the GCF.
The greatest common factor for the expression 27x+9y will be 9.
What is the greatest common factor?The highest number that is a factor of all the numbers is known as the greatest common factor of two or more numbers. The largest factor that splits both numbers is said to be the greatest common factor.
List the prime factors of each integer before calculating the greatest common factor.
It is given that the expression is,
27x+9y
We can take out 9 commons in the expression because it does not affect the expression,
The greatest common factor is,
9( 3x + y)
We obtain 9 as the value that we can take commonly from the complete expression. As a result, it is the greatest common factor.
Thus, the greatest common factor for the expression 27x+9y will be 9.
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Forty percent of all registered voters in a national election are female. a random sample of 5 voters is selected. the probability that there are no females in the sample is
To calculate the probability of selecting no female voters in a sample of 5, given that 40% of the registered voters are female, we multiply the probability of selecting a male voter (60%) five times, which equals to (0.6)⁵ or 7.776% probability.
The question involves calculating the probability that none of the five randomly selected voters are female, given that 40% of registered voters are female. To find this probability, we need to use the complementary probability, which is the probability of the opposite event occurring (that is, selecting a male voter).
The probability of selecting one male voter randomly is 60% (or 0.6), as females account for 40% of the registered voters. When we select 5 voters independently, we multiply the individual probabilities together because the events are independent. Therefore, the probability of selecting no female voters in 5 trials is calculated as:
(0.6) × (0.6) × (0.6) × (0.6) × (0.6) = (0.6)⁵ = 0.07776 or 7.776%.
This is the probability that a random sample of 5 voters will contain no females.
A college professor noted that the grades of his students in an introductory statistics class were normally distributed with a mean of 76.5 and a standard deviation of 9. if 67.36% of his students received grades of c or above, what is the minimum score of those students receiving a grade of at least a c?
Using the properties of normal distribution and the Z-score related to the given percentile, it can be inferred that the minimum grade for a 'C' in this college statistics class is approximately 72.
Explanation:In this scenario, the professor's grades reflect a normal distribution, therefore, we can utilize the properties of normal distribution to answer your question. The probability given, 67.36%, corresponds to a Z-score of -0.45 (you can find this in standard statistical tables).
We'll utilize the formula Z = (X - μ) / σ, Z is the Z-score, X is the data point, μ is the mean, and σ is the standard deviation. Therefore, if we rearrange the formula to find X (the data point,or in this case, the lowest grades for students receiving a C or above), it will be X = Z * σ + μ. Substituting the given values in the equation gives X = -0.45 * 9 + 76.5. This results in a minimum score approximately equal to 72.45, or 72 if we consider only whole marks. Hence, our conclusion that the minimum grade for a 'C' is 72.
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The minimum score required to receive at least a grade of C in this normally distributed class is approximately 72.54.
To determine the minimum score that students need to receive at least a grade of C in a class where grades are normally distributed, we analyze the problem with a mean [tex](\mu)[/tex] of 76.5 and a standard deviation [tex](\sigma)[/tex] of 9.
We know that 67.36% of the students received a grade of C or above.
This corresponds to the top 67.36% of the distribution.
The bottom 32.64% of the distribution received less than a C.
The z-score associated with the 32.64th percentile can be found using z-tables or a standard normal distribution calculator:
z = -0.44
Next, we convert this z-score to the actual score using the formula:
[tex]X = \mu + z\cdot \sigma[/tex]
Substituting the given values:
X = 76.5 + (-0.44 * 9) = 76.5 - 3.96 = 72.54
Thus, the minimum score required for a grade of at least C is approximately 72.54.
Find the thirtieth term of the following sequence.
-6, -4, -2, 0, ...
Answer: 52
Step-by-step explanation:
To find the 30th number sequence with the given values of: -6,-4,-2,0.
Multiply 30 by 2 because we add 2 to the sequence every time we go up.
30*2 gives us 60, then we subtract however many 2's were in the given sequence.
From -6 to -4 to -2 to 0, we get 8.
60-8 = 52.
Thank you and I hope this helps. Even if my math is wrong somewhere, I got the answer right on my assignment so this is 100% correct.
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Which are the solutions of the quadratic equation?
x2 = 9x + 6
The solutions of the quadratic equation x^2 = 9x + 6 are (9 + sqrt(105))/2 and (9 - sqrt(105))/2.
Explanation:To find the solutions of the quadratic equation x^2 = 9x + 6, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b +- sqrt(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -9, and c = -6. Plugging in these values, we get:
x = (-(-9) +- sqrt((-9)^2 - 4(1)(-6))) / (2(1))
Simplifying further:
x = (9 +- sqrt(81 + 24)) / 2
x = (9 +- sqrt(105)) / 2
So the solutions of the quadratic equation x^2 = 9x + 6 are:
x = (9 + sqrt(105)) / 2
x = (9 - sqrt(105)) / 2
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The solutions to the quadratic equation x² = 9x + 6 are x = 3 and x = 6. This is done by rearranging the equation and then factoring into two binomials (x - 3) and (x - 6) equals 0, then set each binomial equal to zero.
Explanation:The given quadratic equation is x² = 9x + 6. To find the solutions of the quadratic equation, we first move all the terms to one side. This gives us: x² - 9x - 6 = 0. This is now a standard quadratic equation, and can be solved by either factoring or using the Quadratic Formula.
If we opt to solve via factoring, we're looking to factorize the original expression into two binomial expressions, essentially looking for two numbers which both add up to -9 and multiply to -6. These two numbers are -3 and 6. Therefore, the quadratic equation can be factored as follows: (x - 3)(x - 6) = 0. Setting each factor equal to 0 gives the possible solutions for x, in this case, x = 3 and x = 6.
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Draw cubes to show the number. Write the number different ways. Love has seven ones Nick has 5 ones they put all their once together what number did they make
A publishing company has a weekly cost equation of C=96,000+20x and a weekly revenue equation of R=26x, where x is the number of books produced and sold in a week. The company loses money when R
To find when a publisher makes or loses money, compare the cost function C=96,000+20x to the revenue function R=26x. The break-even point is at x=16,000 books produced and sold weekly. Below this, the company incurs losses.
When determining when a publishing company makes or loses money, we investigate the relationship between cost and revenue functions. The cost function given is C=96,000+20x and the revenue function is R=26x, with x representing the number of books produced and sold per week. A company loses money when costs exceed revenues, that is when C > R.
To find the quantity of books where this happens, we equate the two equations:
C = R96,000 + 20x = 26x96,000 = 26x - 20x96,000 = 6xx = 96,000 / 6x = 16,000Therefore, at the production and sale of 16,000 books, the company will break even. Producing fewer than 16,000 books would result in a loss because the cost would be higher than the revenue generated.
Find the dimensions of a triangle given the following information. The perimeter is equal to 36cm, side 1 is 4 less than side 2 and side 3 is twice the length of side 2.
You are scheduled to receive $16,500 in three years. when you receive it, you will invest it for nine more years at 9.5 percent per year. how much will you have in twelve years?
The total amount you will have in twelve years is calculated by multiplying your initial amount of $16,500 with (1 + 0.095) raised to the power of 9 (years of investment). This is a demonstration of the future value concept in finance.
Explanation:This question is about the concept of future value in finance. First, you receive $16,500 after three years. Following this, you invest this amount at an interest rate of 9.5% for nine more years. To calculate the future value of an investment, you can use the formula: Future Value = Present Value * (1 + Interest rate)^numbers of years. In this case, it would be $16,500 * (1 + 0.095)^9. This calculation will give you the total amount you will have in twelve years after the investment.
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