Subtract 8-4 1/2. A. 3 B. 4 C. 4 1/2 D. 3 1/2
Subtraction of 8-4 1/2 is 3 1/2.
The correct option is D.
To subtract 8 - 4 1/2, we need to convert the mixed number 4 1/2 into an improper fraction.
To do this, we multiply the whole number (4) by the denominator (2), which gives us 8. Then we add the numerator (1) to get 9. So, 4 1/2 is equivalent to the improper fraction 9/2.
Now, we can subtract 8 from 9/2. To subtract fractions, the denominators must be the same. We can rewrite 8 as 8/1 to have a common denominator with 9/2.
Subtracting 8/1 from 9/2 gives us (8 - 9/2).
To subtract fractions, we need a common denominator, which is 2 in this case.
Converting 8/1 to have a denominator of 2, we get 16/2.
Now we can subtract the fractions: (16- 9)/2 = 7/2.
Therefore, the answer is 7/2, which can also be expressed as 3 1/2.
So the correct answer is D. 3 1/2.
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Gambler is deciding whether or not to take a bet. she must pay $40 to take the bet, but if she wins, she willprofit$225.theprobability that she wins the bet is ¼. what is the player’s expected value in this situation
what is the meaning os slpoe in math and please give an example for
y=2x-1;(-2,2)
Slope in math is the difference in y-values divided by x-values.
The slope helps determine the steepness of a line. Y-intercept is the y-value when x=0. The formula for slope, denoted as m, is (y2-y1)/(x2-x1).
Example: For the equation y = 2x - 1, if we have the point (-2, 2), we can calculate the slope by substituting the values into the formula: m = (2-(-1))/(-2-0) = 3/-2 = -1.5.
Y-intercept is the y-value when x=0, or where the graph crosses the y-axis.
You are driving 70 miles per hour, starting at mile marker 255. How many hours will it take you to reach mile marker 115?
255-115 = 140 miles
140/70 = 2 hours
How do you rename 805 tens
a House sits on a 5/8 acre lot and 1/2 of the lot is lawn. 2/3 of lawn was mowed. how much was mowed?
5/8 x 1/2 = 5/16 acre is lawn
5/16 x 2/3 = 10/48 reduces to 5/24 of the lawn was mowed
Write the standard form of the line that passes through the given points.
4, 7) and (0, 7)
The equation of the line would be y = 7 which passes through the points (4, 7) and (0, 7).
What is the slope of the line?The slope of a line is defined as the gradient of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Given that line passes through points (4, 7) and (0, 7)
Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = 4, y₁ = 7
x₂ = 0, y₂ = 7
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Substitute values in the equation, we get
⇒ y - 7 = (7 - 7)/(0- 4)[x -4]
⇒ y - 7 = (0)/(-10 )[x -4]
⇒ y - 7 = 0(x -4)
⇒ y - 7 = 0
⇒ y = 7
Therefore, the equation of the line would be y = 7 which passes through the points (4, 7) and (0, 7).
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Consider H0: μ = 45 versus H1: μ < 45. A random sample of 25 observations produced a sample mean of 41.8. Using α = .025 and the population is known to be normally distributed with σ = 6.
A taxi company charges passengers $1.75 for a ride, no matter how long the ride is, and an additional $0.40 for each mile traveled. The rule mc014-1.jpg describes the relationship between the number of miles m and the total cost of the ride c. What is the charge for a 2.7-mile ride?
18.666667 rounded to nearest hundredth
Find the area. ABCD∼EFGHABCD∼EFGH The area of rectangle ABCD is 72 inches2 and a diagonal is 12 inches. The diagonal of rectangle EFGH is 22 inches. Find the area of rectangle EFGH. Round to the nearest inch2 if necessary.
Which of the followings explains the difference between a regular subquery and a correlated subquery?
A regular subquery is a standalone query that can be executed independently of the outer query and passes its result to the outer query. Conversely, a correlated subquery is linked with the outer query, executes for each row processed by the outer query, and may be slower due to these repeated executions.
The primary difference between a regular subquery and a correlated subquery resides in the way they operate and when they execute the control flow. A regular subquery is a standalone query, which means it can be executed independently of the outer query. Once it executes, it passes its result to the outer query.
On the other hand, a correlated subquery, as its name suggests, is 'correlated' with the outer query. It cannot be executed independently and must be run for each row processed by the outer query.
For example, if you use a correlated subquery to determine whether a record exists in another table, the subquery will run once for each record in the primary query. This can potentially be slower than a regular subquery due to the repeated executions.
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The question probable may be:
What distinguishes a regular subquery from a correlated subquery in terms of execution and operation? How does the control flow differ, and why might a correlated subquery be slower than a regular subquery in certain scenarios?
Raul received a score of 72 on a history test for which the class mean was 70 with a standard deviation of 9. he received a score of 71 on a biology test for which the class mean was 70 with standard deviation 7. on which test did he do better relative to the rest of the class?
Final answer:
Raul did better on the history test relative to his classmates, as indicated by a higher z-score of approximately 0.22, compared to 0.14 for the biology test.
Explanation:
To determine on which test Raul did better relative to the rest of the class, we need to calculate the z-scores for Raul's history and biology test results. A z-score is a statistical measurement that describes a value's relationship to the mean of a group of values, measured in terms of standard deviations from the mean. The formula for calculating a z-score is:
z = (X - μ) / σ
where X is the score, μ is the mean, and σ is the standard deviation. Let's apply this to Raul's scores:
For the history test:
z = (72 - 70) / 9 = 2 / 9 ≈ 0.22
For the biology test:
z = (71 - 70) / 7 = 1 / 7 ≈ 0.14
Comparing the two z-scores, we can see that Raul's z-score for history is higher than his z-score for biology. Hence, Raul did better on the history test relative to the rest of the class.
A ball is launched from 8 feet off the ground at an initial vertical speed of 64 feet per second. It is aimed across a field at a target also 8 feet off the ground. The height of the ball at time, t, in seconds, is given by the function, h = –16t 2 + 64t + 8.
How many numbers are equal to the sum of two odd one digit numbers
HELP PLZ!!!! A courtyard in the shape of a right triangle is set in the middle of three square office buildings, with one office building along each side. Which statement is true about the three office buildings?
Five times the sum of a number and 27 ig greater than or equal to six times the sum of that number and 26 . What is the solution set of this problem
Given
5(x + 27) ≥ 6(x + 26)
Find
The solution set of x
Solution
Eliminate parenthses.
... 5x + 135 ≥ 6x + 156
Subtract 5x+156
... -21 ≥ x
The solution set is all real numbers less than or equal to -21.
The present value of an ordinary annuity of $350 each year for five years, assuming an opportunity cost of 4 percent, is ________.
The present value of an ordinary annuity of $350 each year for five years with a 4 percent opportunity cost is $1,551.88, calculated using the present value formula for annuities.
To find the present value of an ordinary annuity, you can use the formula for the present value of an annuity:
[tex]\[ PV = Pmt \times \frac{{1 - (1 + r)^{-n}}}{{r}} \][/tex]
Where:
- PV is the present value of the annuity,
- Pmt is the annual payment (in this case, $350),
- r is the interest rate per period (in decimal form),
- n is the number of periods (in this case, 5 years).
Given that the opportunity cost (interest rate) is 4%, or 0.04 in decimal form, and there are 5 years of payments, we can plug these values into the formula:
[tex]\[ PV = 350 \times \frac{{1 - (1 + 0.04)^{-5}}}{{0.04}} \][/tex]
Let's calculate:
[tex]\[ PV = 350 \times \frac{{1 - (1.04)^{-5}}}{{0.04}} \][/tex]
[tex]\[ PV = 350 \times \frac{{1 - (0.8227)}}{{0.04}} \][/tex]
[tex]\[ PV = 350 \times \frac{{0.1773}}{{0.04}} \][/tex]
[tex]\[ PV \approx 350 \times 4.4325 \][/tex]
PV = $1551.88 (Approximately)
So, the present value of the annuity, assuming an opportunity cost of 4%, is approximately $1551.88.
On two investments totaling $11,500, Peter lost 3% on one and earned 4% on the other. If his net annual receipts were $201, how much was each investment?
Final answer:
Peter invested $3,700 at a 3% loss and $7,800 at a 4% gain. By setting up a system of equations and solving them, we determined the amount invested in each.
Explanation:
To solve the problem of how much was invested by Peter in each investment, we need to set up a system of equations. Let's call the amount invested at 3% loss x, and the amount invested at 4% gain y. The total amount invested is $11,500, so we have x + y = $11,500.
Peter's net annual receipts were $201, which comes from a loss of 3% on investment x and a gain of 4% on investment y. The equation for this would be -0.03x + 0.04y = $201.
Now we have a system of two equations:
-0.03x + 0.04y = $201
Adding (1) and (2) gives us:
0.03y + 0.04y = $546
Combining like terms, we get:
0.07y = $546
Dividing both sides by 0.07, we find that:
y = $7,800
Substituting y back into the first equation, we get:
x = $11,500 - $7,800 = $3,700
So, Peter invested $3,700 in the investment with a 3% loss and $7,800 in the investment with a 4% gain.
The solution set of 3x+4y<0 lies in which quadrant?
A university found that 10% of its students withdraw without completing the introductory statistics course. assume that 20 students registered for the course.
What compound inequality represents the phrase? Graph the solutions.
all real numbers that are greater than –8 and less than 8
On may 31, the cash account of bottle's r us had a normal balance of $5,000. during may, the account was debited for a total of $12,200 and credited for a total of $11,500. what was the balance in the cash account at the beginning of may?
The balance in the cash account at the beginning of May was -$6,500.
Explanation:The balance in the cash account at the beginning of May can be calculated by adding up the debits and credits for the month and subtracting them from the normal balance at the end of May.
In this case, the total debits for May were $12,200 and the total credits were $11,500.
To find the beginning balance, subtract the total credits from the normal balance:
Beginning balance = Normal balance - Total credits
Beginning balance = $5,000 - $11,500 = $-6,500
Therefore, the balance in the cash account at the beginning of May was -$6,500.
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The area of a rectangle is 52ft ^2 and the length of the rectangle is 5ft less than twice the width. Find the dimensions of the rectangle.
Determine the domain of the function. f as a function of x is equal to the square root of two minus x.
Write four hundred seven trillion six million one hundred five thousand twenty eight in standard form
The standard form of four hundred seven trillion six million one hundred five thousand twenty-eight is 407,000,006,105,028.
As we know that,
In trillion, there are 12 zeros.In billion, there are 9 zeros.In million, there are 6 zeros, In thousand, there are 3 zeros.In hundred there are 2 zeros.In tens, there is 1 zero. In ones, there is no zero.So, it should be presented below.
Trillion Billion Million Thousand Hundred Tens Ones
407 , 000 , 006 , 105 , 0 2 8
Therefore we can conclude that the standard form of four hundred seven trillion six million one hundred five thousand twenty-eight is 407,000,006,105,028.
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if ax +3=7-bx what is x expressed in terms of a and b
The volume of a pyramid varies jointly with the base area of the pyramid and its height. The volume of one pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches. What is the volume of a pyramid with a base area of 10 square inches and a height of 9 inches?
The volume of a pyramid with a base area of 10 square inches and a height of 9 inches will be 30 cubic inches.
What is the volume of the pyramid?Suppose the base of the pyramid has length = L units and width = W units, slant height = K units, and the height of the pyramid is of H units.
Then the volume of the pyramid will be
V = (L × B × H) / 3
V = (Base area x H) / 3
The volume of a pyramid varies jointly with the base area of the pyramid and its height.
The volume of one pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches.
Then the volume of a pyramid with a base area of 10 square inches and a height of 9 inches will be
V = (10 x 9) / 3
V = 30 cubic inches
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The volume of a pyramid is obtained from the joint variation relationship with its base area and height. Given a certain pyramid's dimensions, we can determine the volume of another pyramid if we know its base area and height. The volume of the second pyramid is 30 cubic inches.
Explanation:The student's question pertains to joint variation, a concept in mathematics, specifically applied here to understand how the volume of a pyramid relates to its base area and height. For a pyramid, this relationship can be expressed as V = k * A * H, where V is volume, A is base area, H is height, and k is the constant of variation.
First, we find the value of 'k' using the given pyramid's measurements; so 24 = k * 24 * 3 gives us k = 1/3.
Then, we use this constant to find the volume of the other pyramid whose base area is 10 square inches and height is 9 inches. Therefore, V = 1/3 * 10 * 9, which simplifies to V = 30 cubic inches.
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what is 10 times as much as 700
solve for w.
-3w+2=-10w+30
-3w+2=-10w+30
add 3 w to each side
2=-7w+30
subtract 30 from each side
-28 = -7w
divide both sides by -7
w = 4
double check
-3(4) +2 = -10
-10(4) +30 = -10
so w = 4