which number is the standard equation for a circle centered at the origin should one increase to make the circle larger
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.
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.
Which of the following statements is true?
A
6.75 < 6.759 < 6.751 < 6.85
B
5.55 < 5.559 < 5.65 < 5.69
C
4.11 < 4.12 < 4.17 < 4.15
D
7.42 < 7.41 < 7.40 < 7.39
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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18.666667 rounded to nearest hundredth
what is 10 times as much as 700
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.
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.
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.
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
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.
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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What compound inequality represents the phrase? Graph the solutions.
all real numbers that are greater than –8 and less than 8
How do you rename 805 tens
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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How many numbers are equal to the sum of two odd one digit numbers
The mayor of a small city has proposed that a gambling casino be built in the downtown area, arguing that the construction project, resulting jobs, and tax revenue will boost the local economy. A total of 183 residents attend a public hearing on the proposal and a show of hands finds only 31 in favor of the casino. What does this vote tell the city council about public support for the project?
Determine the domain of the function. f as a function of x is equal to the square root of two minus x.
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?
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
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?
How much would $300 invested at 7% interest compounded continuously be worth after 4 years
Answer:
$396.93
Step-by-step explanation:
It asks to round to the nearest cent not dollar.
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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Determine whether it is reasonably possible that the proportion of adults from country a and the proportion of adults from country b are equal and explain your reasoning. choose the correct answer below.
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.
The solution set of 3x+4y<0 lies in which quadrant?
if ax +3=7-bx what is x expressed in terms of a and b
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
Twice x,plus 3,is the same as -6
write the equation out as given:
2x+3=-6
subtract 3 from each side
2x = -9
x=-9/2
x = -4.5