The correct order of operations for simplifying the expression (x+3)^2 - [tex](x^2+9)/2x^2[/tex] is as follows:
1. Square the binomial (x+3) to get x^2 + 6x + 9.
2. Divide each term in (x^2+9) by [tex]2x^2[/tex] to get [tex]1/2 + 9/2x^2[/tex].
3. Substitute the simplified expressions back into the original expression: [tex]x^2 + 6x + 9 - (1/2 + 9/2x^2).[/tex]
The correct order of operations for simplifying the expression (x+3)^2 - (x^2+9)/2x^2 is as follows:
1. Start by simplifying the expression within the parentheses: (x+3)^2. This means squaring the binomial (x+3). To do this, you multiply the binomial by itself: (x+3) * (x+3). This results in [tex]x^2 + 6x + 9.[/tex]
2. Next, simplify the expression within the second set of parentheses: (x^2+9).
3. Now, divide [tex](x^2+9)[/tex] by 2x^2. To do this, divide each term in (x^2+9) by 2x^2. This gives us [tex](x^2/2x^2)[/tex] [tex]+ (9/2x^2)[/tex]. Simplifying further, we get 1/2 + [tex]9/2x^2[/tex].
4. Finally, substitute the simplified expressions back into the original expression: [tex]x^2 + 6x + 9 - (1/2 + 9/2x^2).[/tex]
A rhombus has diagonals 500 yd and 800 yd in length. Find the area in square miles.
To find the area of a rhombus with diagonals of 500 yards and 800 yards, use the formula (d1 * d2) / 2 and convert the result to square miles.
Given: The diagonals of the rhombus are 500 yards and 800 yards.
Formula: The area of a rhombus can be calculated using the formula: Area = (d1 * d2) / 2, where d1 and d2 are the diagonals of the rhombus.
Calculation: Area = (500 * 800) / 2 = 200,000 square yards.
Conversion: To convert square yards to square miles, divide the area by 3,097,600 (number of square yards in a square mile).
Final Result: The area of the rhombus is approximately 0.0646 square miles.
How could the relationship of the data be classified? scatter plot with points scattered going up to the right
A fairly strong positive correlation
A fairly strong negative correlation
A fairly weak negative correlation
Answer:
The correct answer is A. A fairly strong positive correlation
Step-by-step explanation:
Scatter Plot : A graph of plotted points that show the relationship between two sets of data.
Now, the points of the scatter plot are going up this shows the increase in the data points so we can say the correlation is positive.
Now, the direction of the scatter plots is to the right. So, we can say that the correlation is strong correlation.
Hence, the correct answer is A. A fairly strong positive correlation
Answer:
the Correct Option is A : fairly strong positive correlation
Step-by-step explanation:
Scatter Plot is a graph that is graphed using points and which shows the relationship between two sets of data. Only used to show correlation.
As given the points of the scatter plot are going up this implies the increment in one set of data with respect to other so we can say here correlation is positive. And the direction of the scattered points is to the right. So, it reflects that the correlation is strong correlation.
Thus, the Correct Option is A : fairly strong positive correlation
Choosing a 4-letter password using only 5 letters that may each be used more than once. How do you do this??
Challenger Elementary School has 8 0 0 800800 students. Every Wednesday, 1 2 % 12%12, percent of the students stay after school for Chess Club. How many students attend Chess Club on Wednesdays?
Given the following functions f(x) and g(x), solve f over g(−4) and select the correct answer below:
f(x) = 4x − 4
g(x) = x − 1
You have decided to buy a new home and the bank offers you a 10 year fixed loan at 5.0% on a balance of $275,325. Use the table provided to determine the monthly payments.a.$183,147c.$185,350b.$184,789d.$186,523
Answer:
ita A
Step-by-step explanation:
You can calculate the monthly payments for a 10-year fixed loan at 5.0% on a balance of $275,325 by plugging the values into the amortization formula: M = P [r(1+r)^n] / [(1+r)^n – 1]. Perform the calculations and compare the result to the answer choices.
Explanation:This question falls under the category of financial mathematics, specifically loan repayment calculations. When calculating a fixed loan, we typically use an amortization formula to find our monthly payment. The formula we use is: M = P [r(1+r)^n] / [(1+r)^n – 1], where M is our monthly payment, P is the principal loan amount (in this case $275,325), r is our monthly interest rate (annual rate of 5% divided by 12), and n is the number of payments (or the number of months, in this case, 10 years or 120 months).
Plugging in these numbers, we get M = $275,325[0.004167(1+0.004167)^120] / [(1+0.004167)^120 – 1].
After performing these calculations, you will get the monthly payment for this 10-year fixed loan. Compare this number to the choices given to get your answer.
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Huixian needs to pack 171 pens 63 pencils and 27 erasers into identical gift bags so that each item is equally distributed among gift bags.find the largest number of gift bags can be packed
Answer:
The largest number of gift bags that can be packed is:
9
Step-by-step explanation:
To find The largest number of gift bags that can be packed, we need to find the greatest common divisor of these numbers.
Listing the prime factorization's for each number:
171 = 3 x 3 x 19
63 = 3 x 3 x 7
27 = 3 x 3 x 3
As we can clearly see from the prime factorization the greatest common factor of these numbers is 9(3×3)
The largest number of gift bags that can be packed is:
9
In 2010, a city's population was 1,405,233 and it was decreasing at a rate of 1.1%. At this rate when will the city's population fall below 1,200,000?
a. 2024
b. 2027
c. 2036
d. 2049
The correct answer is: a. The population will fall below 1,200,000 around the year 2024.
To determine when the city's population will fall below 1,200,000, we need to use the formula for exponential decay:
[tex]P(t) = P_0 \cdot (1 - r)^t[/tex]
where:
- P(t) is the population at time t .
- P₀ is the initial population.
- r is the rate of decrease (expressed as a decimal).
- t is the number of years.
Given:
- Initial population, P₀ = 1,405,233
- Rate of decrease, r = 1.1% = 0.011
- Final population, P(t) = 1,200,000
We need to find t such that:
[tex]1,200,000 = 1,405,233 \cdot (1 - 0.011)^t[/tex]
First, we divide both sides by 1,405,233:
[tex]\frac{1,200,000}{1,405,233} = (0.989)^t[/tex]
Next, we calculate the left-hand side:
[tex]\frac{1,200,000}{1,405,233} \approx 0.854[/tex]
So we have:
[tex]0.854 = (0.989)^t[/tex]
To solve for t , we take the natural logarithm of both sides:
[tex]\ln(0.854) = \ln((0.989)^t)[/tex]
Using the properties of logarithms, we can bring down the exponent:
[tex]\ln(0.854) = t \cdot \ln(0.989)[/tex]
Now, solve for t :
[tex]t = \frac{\ln(0.854)}{\ln(0.989)}[/tex]
Let's calculate this:
[tex]\ln(0.854) \approx -0.157 \\\\ \ln(0.989) \approx -0.011 \\\\ t = \frac{-0.157}{-0.011} \approx 14.27[/tex]
Since 14.27 years from 2010 is approximately in 2024:
[tex]2010 + 14.27 \approx 2024[/tex]
So the population will fall below 1,200,000 around the year 2024.
The correct answer is: a. 2024
The width of a rectangular poster is 16 in its length is twice its width find the perimeter
The data list shows the scores of ten students in Mr. Smith's math class. 61, 67, 81, 83, 87, 88, 89, 90, 98, 100 What is the standard deviation, to the nearest tenth, of the data if the scores represent a sample of Mr. Smith's students? a0 What is the standard deviation, to the nearest tenth, of the data if the scores represent the entire population of Mr. Smith's students? a1
Answer: The standard deviation of the sample will be 11.6.
The standard deviation of the population will be 12.31.
Step-by-step explanation:
Mr Smith's math class scores : 61, 67, 81, 83, 87, 88, 89, 90, 98, 100
Number of terms,N = 10
[tex]Mean=\mu =\frac{\text{sum of all the terms}}{\text{total number of terms}}[/tex]
[tex]\mu =\frac{61+67+81+83+87+88+89+90+98+100}{10}=\frac{844}{10}=84.4[/tex]
Standard deviation of the sample:
[tex]\sigma=\sqrt{\frac{1}{N}\sum_{i=1}^n(x_i-\mu )^2}=\sqrt{\frac{1}{10}(1364.4)}=11.68[/tex]
Standard deviation for the population:
[tex]\sigma=\sqrt{\frac{1}{N-1}\sum_{i=1}^n(x_i-\mu )^2}=\sqrt{\frac{1}{9}(1364.4)}=12.31[/tex]
The standard deviation of the sample will be 11.6.
The standard deviation of the population will be 12.31.
A helicopter hovers 950 over......
Which image of figure WXYZ is under the composition T 2,7 . D 0,2?
A.figure A
B. figure B
C.figure C
D.figure D
Answer:
A. Figure A
Step-by-step explanation:
We are given the figure WXYZ.
It is required to find the final figure after [tex]T_{2,7}D_{0,2}[/tex].
Now, [tex]D_{0,2}[/tex] means to dilate the figure by 2 units and [tex]T_{2,7}[/tex] means to translate it by 2 units to the left/right and seven units up/down.
As we have to apply [tex]T_{2,7}D_{0,2}[/tex] to the figure.
This means that first dilation is applied and then translation.
Since, the all the figures are dilated. We focus on the translations.
We can see that, only figure A is translated 2 units to the right and 7 units upwards.
So, option A is correct.
Mike saw 4 times and Many birds as Gigi. Mike saw 28 birds. Which equation can be used to find how many birds Gigi saw? a. 4x28=n b. 28-4=n c. 4+28=n d. 28+4=n
I really need this answer to be correct
Solve this application using logarithms.
How long will money in savings take to double at 5% interest compounded annually? Round the answer to the nearest hundredth of a year.
Answer:
14.21
Step-by-step explanation:
What is the value of x
Solve using the quadratic formula
Answer:
x = - 16, x = 9
Step-by-step explanation:
[tex]x=\frac{-b±\sqrt{b^{2} -4ac} }{2a}[/tex]
Ignore the "A" ^
v² + 7v - 144 = 0
a = 1, b = 7, c = - 144
[tex]x=\frac{-7±\sqrt{7^{2} -4(1)(-144)} }{2(1)}[/tex]
[tex]x=\frac{-7±\sqrt{49 +576} }{2}[/tex]
[tex]x=\frac{-7±\sqrt{625} }{2}[/tex]
[tex]x=\frac{-7+25}{2}[/tex] and [tex]x=\frac{-7-25}{2}[/tex]
[tex]x=\frac{18}{2}[/tex] and [tex]x=\frac{-32}{2}[/tex]
x = 9 and x = - 16
For a circle with a diameter of 6 meters, what is the measurement of a central angle (in degrees) subtended by an arc with a length of 7 3 π meters? A) 35° B) 50° C) 70° D) 140°
Answer:
the answer is (D)
Step-by-step explanation:
Find the slope of the line on the graph
ABCD is a square. Given only the choices below, which properties would you use to prove AEB ≅ DEC by SAS? The diagonals are ⊥ to each other. Opposite sides are | |. The diagonals bisect each other. All sides are congruent.
Which answer best describes the shape of this distribution?
the bottle of water contains 32 fluid ounces of water. How many cups of water are in a bottle.
There are 4 cups of water in a bottle containing 32 fluid ounces.
We have,
The number of cups in a bottle of water depends on the conversion rate from fluid ounces to cups.
1 cup is equivalent to 8 fluid ounces.
To find the number of cups in a bottle containing 32 fluid ounces of water, we can divide the total number of fluid ounces by the conversion rate:
So,
= 32 fluid ounces / 8 fluid ounces per cup
= 4 cups
Therefore,
There are 4 cups of water in a bottle containing 32 fluid ounces.
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$80 is divided Between two men such that 1/4 of one persons share is equal to 1/6 Of the other how much will each man receive
Final answer:
To divide $80 between two men so that 1/4 of one person's share equals 1/6 of the other's share, each man will receive $40 and $60, respectively.
Explanation:
To divide $80 between two men so that 1/4 of one person's share equals 1/6 of the other's share:
Let x be one person's share and y be the other person's share.
Set up the given ratio: 1/4x = 1/6y.
Solve the ratio equation to find x and y: 1/4x = 1/6y can be simplified to x = $40 and y = $60.
which of the following equations can be used to solve for the radius
Given a possible triangle ABC with a=5, b=11, and A=23 degrees, find a possible value for angle b. Round to the nearest tenth. A. 10.2° B. 11.2° C. 59.3° D. no solution Please select the best answer from the choices provided
Find the balance after 8 years
Explain the process of solving the following equation: 4^x - 2 = 20
Juan Ramirez sells suits in a major department store on weekends. He earns a commission of 5% on the first 10 suits he sells. If he sells more than 10, he earns another 3% on the additional suits. Last weekend Juan sold 13 suits priced at $250 each. What was his commission?
A. $185.00
B. $260.00
C. $147.50
D. $210.40
Someone please help me?
Below are the heights of the players on the University of Maryland women's basketball team for the 2017-2018 season and the heights of the players on the women's field hockey team for the 2018 season.
Note: it is typical for a women's field hockey team to have more players than a women's basketball team would.
Field Hockey Player Heights (inches) Basketball Player Heights (inches)
Field Hockey Player Heights (inches) Field Hockey Player Heights (inches) Field Hockey Player Heights (inches) Field Hockey Player Heights (inches) Basketball Player Heights (inches)
66 in. 60 in. 67 in. 68 in. 75 in. 72 in.
68 in. 64 in. 63 in. 63 in. 72 in. 74 in.
67 in. 69 in. 66 in. 66 in. 68 in. 75 in.
65 in. 64 in. 65 in. 70 in. 73 in.
66 in. 68 in. 66 in. 68 in. 72 in.
60 in. 66 in. 65 in. 69 in.
64 in. 66 in. 67 in. 72 in.
1. Field Hockey Players:
Find the Measures of Center and Variability for Field Hockey Players Heights.
Mean (Round to Nearest Whole Number):
Mode:
Median:
Range:
2. Basketball Players:
Find the Measures of Center and Variability for Basketball Players Heights.
Mean (Round to Nearest Whole Number):
Mode:
Median:
Range:
3. a. How many of the 10 basketball players are shorter than the tallest field hockey player?
b. List the heights that overlap in the dot plot?
Answer:
for the first and second questions the answers are
Field hockey players basketball players
mean:66 mean:72
mode:66 mode:72
median: 66 median:72
range:10 range:7
Step-by-step explanation:
1. For the Field Hockey Players
The mean height is 68 inches, the mode is 66 inches, the median is 66 inches, and the range is 15 inches.
2. For the Basketball Players:
The mean is approximately 67 inches, the median is 67 inches, the modes are 63 inches and 72 inches, and the range of the heights is 11 inches
3. All 10 basketball players are shorter than the tallest field hockey player.
3b. the overlapping heights are: 60 in., 64 in., 65 in., 66 in., 67 in., 68 in., 69 in., 72 in., and 74 in.
Field Hockey Players:
The data is sort as follows
60, 60, 64, 64, 65, 65, 65, 66, 66, 66, 66, 66, 66, 66, 67, 67, 67, 68, 68, 68, 68, 69, 69, 70, 72, 72, 72, 73, 75, 75.
Now let's calculate the measures of center and variability:
Mean (Average): Add up all the heights and divide by the total number of heights. We then round the answer to the nearest whole number.
Mean
= (60 + 60 + 64 + 64 + 65 + 65 + 65 + 66 + 66 + 66 + 66 + 66 + 66 + 66 + 67 + 67 + 67 + 68 + 68 + 68 + 68 + 69 + 69 + 70 + 72 + 72 + 72 + 73 + 75 + 75) / 30
= 2040 / 30
= 68 inches (rounded to the nearest whole number).
Mode: This is the height that occurs most frequently.
From the sorted list, we can see that 66 inches appears 8 times, which is more than any other height, so Mode = 66 inches.
Median: This is the middle height when all the heights are listed in ascending order. If there is an even number of heights, as in this case, the median is the average of the two middle heights.
Here, the 15th and 16th heights are both 66 inches, so Median = (66 + 66) / 2 = 66 inches.
Range: This is the difference between the tallest (maximum) and shortest (minimum) players.
Range = Maximum - Minimum = 75 inches - 60 inches = 15 inches.
So, for the field hockey players, the mean height is 68 inches, the mode is 66 inches, the median is 66 inches, and the range is 15 inches.
Basketball Player Heights
The data is sort as follows
63, 63, 64, 64, 66, 67, 68, 72, 72, 74.
Mean (Average): The mean is calculated by adding all the numbers together and then dividing by the number of numbers.
Mean
= (63 + 63 + 64 + 64 + 66 + 67 + 68 + 72 + 72 + 74) / 10
= 673 / 10
= 67.3 inches.
Median: The median is the middle number in a sorted, ascending list. If there are an even number of observations, the median is the average of the two middle numbers.
In our list, since we have 10 numbers, an even number, the median is the average of the 5th and 6th numbers.
Median = (66 + 67) / 2 = 66.5 inches.
Mode: The mode is the number that appears most frequently in a data set.
From our list, we can see that the numbers 63 and 72 both appear the most (2 times each). So, this data set has two modes: 63 inches and 72 inches.
The range is calculated by subtracting the smallest number in a set from the largest number.
In your data set, the smallest number (the minimum) is 63 inches and the largest number (the maximum) is 74 inches.
So, Range = Maximum - Minimum = 74 - 63 = 11 inches.
So, for this data set, the mean is approximately 67.3 inches, the median is 66.5 inches, the modes are 63 inches and 72 inches, and the range of the heights is 11 inches.
3. First, let's identify the tallest field hockey player. Considering all heights given for field hockey players, the tallest field hockey player is 75 inches.
Now, let's look at the basketball player heights. We have 10 basketball player heights in total: 68 in., 64 in., 63 in., 63 in., 72 in., 74 in., 60 in., 66 in., 65 in., and 69 in.
From this, we can see that all 10 basketball players are shorter than 75 inches. So, all 10 basketball players are shorter than the tallest field hockey player.
3b. The overlapping heights are those that appear in both basketball and field hockey teams. Looking at both sets, the overlapping heights are: 60 in., 64 in., 65 in., 66 in., 67 in., 68 in., 69 in., 72 in., and 74 in.
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