Original number = $\frac{3}{4}$. The original number expressed as a common fraction is $\frac{3}{4}$.
1. Reciprocal: This is the result of switching the numerator and denominator of a fraction (or dividing 1 by a whole number).
2. Original number: This is the number we're trying to find.
3. Common fraction: This is a fraction where the numerator and denominator are both integers (whole numbers).
Step 1: Set up the equation using the given information.
One more than the reciprocal of the original number is $\frac{7}{3}$. We can express this as an equation:
Reciprocal of the original number + 1 = $\frac{7}{3}$
Step 2: Solve for the reciprocal of the original number.
Reciprocal of the original number = $\frac{7}{3}$ - 1
Step 3: Simplify the equation.
Reciprocal of the original number = $\frac{7}{3}$ - $\frac{3}{3}$
Reciprocal of the original number = $\frac{4}{3}$
Step 4: Find the original number.
Since we have the reciprocal of the original number, we can find the original number by taking the reciprocal of this value:
Original number = $\frac{1}{(\frac{4}{3})}$
Step 5: Simplify the expression.
Original number = $\frac{1}{1} \times \frac{3}{4}$
Original number = $\frac{3}{4}$
The original number expressed as a common fraction is $\frac{3}{4}$.
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!!PLEASE HELPPP MEEE!!!!
The balance of the account after all the deposits is given as follows:
B = 800.25 + x + y + b.
What is the balance of the account?The balance of an account refers to the amount of money that is currently in the account, taking into account all the transactions that have been made on the account, that is, adding all the money that has been deposited on the account.
Considering the initial balance of the account of b dollars, plus all the deposits listed on the problem, the expression is given as follows:
B = 750.25 + x + y + 100 + b
B = 800.25 + x + y + b.
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Which statement is true?
Please help
You select a marble without looking and then put it back. If you do this 24 times, what is the
best prediction possible for the number of times you will pick a marble that is not orange?
times
Step-by-step explanation:
24 times, as there are no orange marbles in the set.
so, every pull will produce a marble that is not orange with 100% certainty.
in general, we have 12 marbles.
let's change the problem description into picking a marbles that is not blue.
we have 6 blue marbles.
the chance to pick a blue marble is therefore 6/12 = 1/2.
and the probability to not pick a blue marbles is 1 - 1/2 = 1/2.
so, in 24 pulls, we expect 24× 1/2 = 12 times to get a marble that is not blue.
or change it to "not green" marbles.
5 green marbles.
the probability to pick a green marble is 5/12.
the probabilty to not pick a green marble = 1 - 5/12 = 7/12.
in 24 pulls we expect 24 × 7/12 = 14 times to get a marble that is not green.
it change it to "not purple" marbles.
1 purple marble.
the probability to pick a purple marble is 1/12.
the probabilty to not pick a purple marble = 1 - 1/12 = 11/12.
in 24 pulls we expect 24 × 11/12 = 22 times to get a marble that is not purple.
In a triangle PQR,the sides PQ, QR and PR measure 15 in, 20 in and 25 in respectively.
Triangle PQR's perimeter is **60 inches**.
What is the triangle's perimeter?The lengths of a triangle's sides added together form its perimeter.
Pythagorean triplet: what is it?The Pythagorean theorem asserts that in a right-angled triangle, the square of the hypotenuse's length (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides 1. A Pythagorean triplet is a group of three positive integers that satisfies this condition.
Triangle PQR has sides PQ = 15 inches, QR = 20 inches, and PR = 25 inches.
A triangle's perimeter is equal to the sum of its sides. Triangle PQR's perimeter is 15 + 20 + 25= **60 inches**. as a result.
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what is the probability that abby, barry, and sylvia win the first, second, and third prizes, respectively, in a drawing if 200 people enter a contest and winning more than one prize is allowed?
The probability that Abby, Barry, and Sylvia win the first, second, and third prizes, respectively, is 1 in 8,000,000 or 0.0000125%
How to calculate the probability?Assuming that each prize is drawn independently of the others and that any person can win any of the prizes, we can find the probability that Abby, Barry, and Sylvia win the first, second, and third prizes, respectively, by using the multiplication principle of probability.
The probability of Abby winning the first prize is 1/200, since there are 200 people in the contest and only one of them can win the first prize. Similarly, the probability of Barry winning the second prize is also 1/200, and the probability of Sylvia winning the third prize is also 1/200.
Since winning more than one prize is allowed, the probability of all three of these events occurring simultaneously is simply the product of their individual probabilities:
P(Abby wins 1st prize AND Barry wins 2nd prize AND Sylvia wins 3rd prize) = (1/200) * (1/200) * (1/200) = 1/8,000,000
Therefore, the probability that Abby, Barry, and Sylvia win the first, second, and third prizes, respectively, is 1 in 8,000,000 or 0.0000125%
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a fair coin is tossed 26 times. in how many outcomes does at least 1 head occur?
There are 67,108,863 outcomes in which at least one head occurs if a fair coin is tossed 26 times.
The probability of getting tails on any given toss is 1/2, so the probability of getting tails on all 26 tosses is (1/2)^26. Therefore, the probability of getting at least one head is
1 - (1/2)^26 ≈ 0.999999999996
So there are almost 100% chance of getting at least one head in 26 coin tosses. To find the number of outcomes that satisfy this condition, we can use the formula for combinations
ⁿCₓ = n! / (x! * (n-x)!)
where n is the total number of trials (26 in this case), x is the number of successes (at least 1 head), and ! denotes the factorial function (e.g., 5! = 54321).
Using this formula, we get
26C1 + 26C2 + ... + 26C26
which simplifies to
2^26 - 1 = 67,108,863
So there are 67,108,863 outcomes in which at least one head occurs in 26 coin tosses.
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A pancake company uses the
function f(x) = 1.5x² to calculate
the number of calories in a
pancake with a diameter of x cm.
What is the average rate of change
for the function over the interval
10
A.) 150 calories per cm of diameter
B.) 33 calories per cm of diameter
C.) 65calories per cm of diameter
D.) 215 calories per cm of diameter
Answer:
To find the average rate of change of the function f(x) = 1.5x² over the interval [10, 11], we need to calculate the change in f(x) over the interval, and divide by the change in x.
The change in f(x) over the interval [10, 11] is:
f(11) - f(10) = (1.511^2) - (1.510^2) = 165 - 150 = 15
The change in x over the interval [10, 11] is:
11 - 10 = 1
Therefore, the average rate of change of the function over the interval [10, 11] is:
(15/1) = 15
This means that for every 1 cm increase in diameter (i.e., for every 1 unit increase in x), the number of calories in the pancake increases by an average of 15 calories per cm of diameter.
Therefore, the answer is (A) 150 calories per cm of diameter.
these four geometry questions i’m not quite sure how to do and have been struggling in them for a while and it’s due tomorrow!!!!
The total areas of each composite shape are:
1) 121 in²
2) 150m²
3) 14.03 ft²
4) 538.36 cm²
How to find the area of the composite figure?1) Formula for area of a rectangle is:
Area = Length * width
Thus:
Area of composite shape = (9 * 8) + (7 * 7)
= 121 in²
2) Formula for area of rectangle is:
Area = Length * width
Area = 12 * 5 = 60 m²
Area of triangle = ¹/₂ * base * height
Area = ¹/₂ * 12 * 15
Area = 90 m²
Area of composite shape = 60 + 90 = 150m²
3) Area of triangle = ¹/₂ * 3 * 7 = 10.5 ft²
Area of semi circle = ¹/₂ * πr²
= ¹/₂ * π * 1.5²
= 3.53 ft²
Total composite area = 10.5 ft² + 3.53 ft²
Total composite area = 14.03 ft²
4) Total composite area = (¹/₂ * π * 7.5²) + (30 * 15)
= 538.36 cm²
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. imagine you had a research question in which you wanted to compare a sample mean to the mean of a population. under these circumstances you would either do a z-test or a one-sample t-test. what key piece of information would be missing if you needed to do a one-sample t-test?
Sample size and sample standard deviation are the key information needed for a single-sample t-test.
In the event that you need to compare the test cruel with the populace cruel, and you perform a single-sample t-test rather than a z-test, the vital piece of data that will be lost is the populace standard deviation.
Within the z-test, the populace standard deviation is known and the standard mistake of the cruel is calculated utilizing the populace standard deviation.
In a single-sample t-test, the populace standard deviation is obscure, and the standard mistake of the cruel is evaluated from the test standard deviation.
Therefore, sample size and sample standard deviation are the key information needed for a single-sample t-test.
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armer needs a fenced-in 1 square kilometer rectangular region. on one of the four sides, she decides to use fencing that costs three times as much as the fencing on the other three sides. what dimensions will minimize the cost of the fence?
The dimensions will minimize the cost of fence 3555C, armer needs a fenced-in 1 square kilometer rectangular region.
Let the length of the rectangular region be 'l' and the width be 'w'. The area of the rectangular region is given by:
A = lw = 1 sq. km = 1000 x 1000 sq. m
We need to minimize the cost of the fence, which consists of three sides with fencing of cost C and one side with fencing of cost 3C. The total cost of the fence is given by:
Cost = 3Cw + C(2l + w) = 2C(l + w) + Cw
To minimize the cost, we take the derivative of the cost function with respect to w and set it equal to zero:
dCost/dw = 2C - C[tex]w^{(-2)}[/tex]l = 0
Solving for l, we get:
l = 2w
Substituting this value of l in the area equation, we get:
w(2w) = 1000000
2w² = 1000000
w² = 500000
w = √(500000) m = 707.1 m
So, the width of the rectangular region is 707.1 m and the length is 2w = 2 x 707.1 m = 1414.2 m.
Therefore, the dimensions that minimize the cost of the fence are 707.1 m x 1414.2 m and the minimum cost of the fence is:
Cost = 2C(l + w) + Cw = 2C(1414.2 + 707.1) + C(707.1) = 3555C.
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the integers from 1 to 15, inclusive, are partitioned at random into two sets, one with 7elements and the other with 8. what is the probability that 1 and 2 are in the same set?
The chance/
probability
is
16/33
, or roughly 0.485 that 1 and 2 are in the
same set.
Let's say we divide the range of numbers from
1 to 15
into two sets, each containing seven and eight numbers, respectively. Finding the likelihood that the numbers 1 and 2 are included in the same
set
is our goal.
We can determine the
total number
of ways to divide the numbers into the two sets of
7
and
8
in order to begin solving this issue. Calculating this yields the result 6435 using a formula.
The number of ways in which the pairs 1 and 2 can be found in the same set must then be determined. Considering that there are
seven numbers
in the set, we must select six more from the remaining thirteen to complete the set, presuming that one is among the seven .There are
1716
ways to do this. The number of methods remains the same, 1716, even if we suppose that 2 is among the set of 7 numbers.
Hence, there are
3432
different ways to combine the numbers 1 and 2 into one set. The chance is 16/33, or roughly 0.485, when we divide this number by the total number of possible
divisions
of the numbers.
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You need to lower your debt to credit limit ratio by $1000. Your current limit is $1400. $1000 is what percent of your credit limit
$1000 is 71.43 percent of the credit limit.
To lower the debt to credit limit ratio by $1000, you have a few options. The first option is to increase your credit limit by requesting a higher limit from your credit card issuer. Alternatively, you can pay off some of your outstanding balance to reduce your debt. Either way, it's important to make sure you're not maxing out your credit limit, as this can negatively impact your credit score.
It's also a good idea to review your spending habits and create a budget to ensure you're not overspending and accumulating debt. By making responsible financial decisions and managing your credit wisely, you can improve your credit score and achieve your financial goals.
To calculate the percentage of $1000 in terms of the credit limit of $1400, we need to divide $1000 by $1400 and multiply the result by 100. This gives us,
($1000 / $1400) x 100 = 71.43%
Therefore, $1000 is approximately 71.43% of the credit limit of $1400.
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an appropriations bill passes the u.s. house of representatives with 47 more members voting in favor than against. if all 435 members of the house voted either for or against the bill, how many voted in favor and how many voted against? in favor members against mem
194 member voted against the bill whereas 241 members voted in favour of the bill.
What is bill refers to?A bill usually refers to a piece of paper money, such as a dollar bill or a euro bill.
To solve this problem, we can use algebra. Let's call the number of members who voted against the bill "x". Then, the number of members who voted in favor of the bill would be "x + 47" (since there were 47 more members voting in favor than against).
We know that the total number of members who voted (either for or against) was 435. So, we can write an equation:
x + (x + 47) = 435
Simplifying this equation, we get:
2x + 47 = 435
Subtracting 47 from both sides:
2x = 388
Dividing both sides by 2:
x = 194
So, 194 members voted against the bill, and the number of members who voted in favor would be:
x + 47 = 194 + 47 = 241
Therefore, 241 members voted in favor of the bill.
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State the amplitude, period, phase shift, and vertical shift of the function kt=cos2pit/3
Answer:
The given function is k(t) = cos(2πt/3).
The general form of a cosine function is A*cos(Bx - C) + D, where:
A is the amplitudeB is the frequency (which is related to the period)C is the phase shiftD is the vertical shiftComparing this form to the given function, we can see that:
The amplitude of k(t) is A = 1, since the maximum value of the cosine function is 1 and the minimum value is -1.The frequency of k(t) is B = 2π/3, since the argument of the cosine function is 2πt/3. The frequency is related to the period T by the formula T = 2π/B. Therefore, the period of k(t) is T = 3.The phase shift of k(t) is C = 0, since there is no horizontal shift in the argument of the cosine function.The vertical shift of k(t) is D = 0, since the average value of the cosine function over one period is zero.Therefore, the amplitude of k(t) is 1, the period of k(t) is 3, the phase shift of k(t) is 0, and the vertical shift of k(t) is 0.
Lin notices that the number of cups of red paint is always 2/5 of the total number of cups. She writes the equation r = 2/5 to describe the relationship.
In the given equation r = 2/5 t "r" is the dependent variable.
Dependent variables:In mathematics, a variable is a symbol that represents a quantity that can take on different values. In many cases, variables can be divided into two types: dependent variables and independent variables.
An independent variable is a variable that can be changed freely, and its value is not dependent on any other variable in the equation.
A dependent variable is a variable whose value depends on the value of one or more other variables in the equation
Here we have
Lin notices that the number of cups of red paint is always 2/5 of the total number of cups.
She writes the equation r = 2/5 t to describe the relationship.
In the equation, r = 2/5 t, "t" represents the total number of cups, while "r" represents the number of cups of red paint.
Here "t" is the independent variable because it represents the total number of cups, which can be changed arbitrarily.
The value of "r" depends on the value of "t" because the number of cups of red paint is always 2/5 of the total number of cups.
Therefore,
In the given equation r = 2/5 t "r" is the dependent variable.
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Complete Question:
Lin notices that the number of cups of red paint is always 2/5 of the total number of cups. She writes the equation r = 2/5 t to describe the relationship. Which is the independent variable? Which is the dependent variable? Explain how you know.
The function:
V(x) = x(10-2x)(16-2x), 0
a) Find the extreme values of V.
b) Interpret any valuse found in part (a) in terms of volumeof the box.
The minimum value of V occurs at x ≈ 0.93, which means that the volume of the box is smallest when the height is about 0.93 units.
To find the extreme values of V, we need to take the derivative of V and set it equal to zero. So, let's begin:
[tex]V(x) = x(10-2x)(16-2x)[/tex]
Taking the derivative with respect to x:
[tex]V'(x) = 10x - 4x^2 - 32x + 12x^2 + 320 - 48x[/tex]
Setting V'(x) = 0 and solving for x:
[tex]10x - 4x^2 - 32x + 12x^2 + 320 - 48x = 0\\8x^2 - 30x + 320 = 0[/tex]
Solving for x using the quadratic formula:
[tex]x = (30 ± \sqrt{(30^2 - 4(8)(320))) / (2(8))\\x = (30 ± \sqrt{(1680)) / 16\\x = 0.93 or x =5.07[/tex]
So, the extreme values of V occur at x ≈ 0.93 and x ≈ 5.07. To determine whether these are maximum or minimum values, we need to examine the second derivative of V. If the second derivative is positive, then the function has a minimum at that point. If the second derivative is negative, then the function has a maximum at that point. If the second derivative is zero, then we need to use a different method to determine whether it's a maximum or minimum.
Taking the second derivative of V:
V''(x) = 10 - 8x - 24x + 24x + 96
V''(x) = -8x + 106
Plugging in x = 0.93 and x = 5.07:
V''(0.93) ≈ 98.36 > 0, so V has a minimum at x ≈ 0.93.
V''(5.07) ≈ -56.56 < 0, so V has a maximum at x ≈ 5.07.
Now, to interpret these values in terms of the volume of the box, we need to remember that V(x) represents the volume of a box with length 2x, width 2x, and height x. So, the maximum value of V occurs at x ≈ 5.07, which means that the volume of the box is greatest when the height is about 5.07 units. The minimum value of V occurs at x ≈ 0.93, which means that the volume of the box is smallest when the height is about 0.93 units.
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a) The extreme values of V are:
Minimum value: V(0) = 0
Relative maximum value: V(3) = 216
Absolute maximum value: V(4) = 128
b) The absolute maximum value of V at x = 4 represents the case where the box has a square base of side length 4 units, height 2 units, and width 8 units, which has a volume of 128 cubic units.
a) To find the extreme values of V, we first need to find the critical points of the function. This means we need to find where the derivative of the function equals zero or is undefined.
Taking the derivative of V(x), we get:
[tex]V'(x) = 48x - 36x^2 - 4x^3[/tex]
Setting this equal to zero and solving for x, we get:
[tex]48x - 36x^2 - 4x^3 = 0[/tex]
4x(4-x)(3-x) = 0
So the critical points are x = 0, x = 4, and x = 3.
We now need to test these critical points to see which ones correspond to maximum or minimum values of V.
We can use the second derivative test to do this. Taking the derivative of V'(x), we get:
[tex]V''(x) = 48 - 72x - 12x^2[/tex]
Plugging in the critical points, we get:
V''(0) = 48 > 0 (so x = 0 corresponds to a minimum value of V)
V''(4) = -48 < 0 (so x = 4 corresponds to a maximum value of V)
V''(3) = 0 (so we need to do further testing to see what this critical point corresponds to)
To test the critical point x = 3, we can simply plug it into V(x) and compare it to the values at x = 0 and x = 4:
V(0) = 0
V(3) = 216
V(4) = 128
So x = 3 corresponds to a relative maximum value of V.
b) In terms of the volume of the box, the function V(x) represents the volume of a rectangular box with a square base of side length x and height (10-2x) and width (16-2x).
The minimum value of V at x = 0 represents the case where the box has no dimensions (i.e. it's a point), so the volume is zero.
The relative maximum value of V at x = 3 represents the case where the box is a cube with side length 3 units, which has a volume of 216 cubic units.
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if p is a prime number and a is a positive inte- ger, how many distinct positive divisors does pa have?
If p is a prime number and a is a positive integer, then pa has (a+1) distinct positive divisors.
A prime number is a positive integer greater than 1, which is divisible only by 1 and itself. Divisors are the numbers that evenly divide a given number.
For a prime number p raised to the power of a (p^a), the number of distinct positive divisors can be found using the following formula:
Number of divisors = (a + 1)
This is because each power of p from 0 to a can divide p^a without any remainder, giving us a total of a + 1 distinct divisors. These divisors are:
1, p, p^2, p^3, ..., p^(a-1), p^a
For example, if p = 2 (a prime number) and a = 3 (a positive integer), then the number of distinct positive divisors for 2^3 (which is 8) would be:
Number of divisors = (3 + 1) = 4
The divisors for 2^3 (8) are 1, 2, 4, and 8.
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You are helping with some repairs at home. You drop a hammer and it hits the floor at a speed of 4 feet per second. If the acceleration due to gravity (g) is 32 feet/second 2, how far above the ground (h) was the hammer when you dropped it? Use the formula:
Step-by-step explanation:
vf = vo + at vo = 0 in this case ( you dropped it from 'at rest')
4 f/s = 32 t
t = 1/8 s
df = do + vot + 1/2 at^2 df = final position = 0 ft (on the ground)
0 = do + 0 + 1/2 (-32)(1/8)^2
solve for do = 1/4 foot
Write a sine function that has an amplitude of 3, a midline of y =2 and a period of 1
the sine function that meets the given conditions is:
[tex]y(t) = 3 \times sin ((2\pi / 1200) \times t) + 2[/tex]
Function with the given characteristics.
The terms and their definitions we need to consider:
Amplitude:
The maximum displacement from the midline (in this case, 3)
Midline:
The horizontal line that passes through the center of the wave (y = 2)
Period:
The length of one complete cycle of the wave (1200)
Now, let's write the sine function:
[tex]y(t) = A \times sin (B \times t) + C[/tex]
Where:
y(t) is the sine function with respect to time (t)
A is the amplitude (3)
B is the frequency (to be determined)
C is the midline (2)
First, we need to find the frequency (B).
The period and frequency are related by the following formula:
[tex]Period = 2\pi / B[/tex]
In this case, the period is 1200:
[tex]1200 = 2\pi / B[/tex]
Now, solve for B:
[tex]B = 2\pi / 1200[/tex]
Now, we can plug in the amplitude (A), frequency (B), and midline (C) into our sine function:
[tex]y(t) = 3 \times sin((2\pi / 1200) \times t) + 2[/tex]
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What is the range of this data set?
Length in Roses length in cm 22cm 23cm 24cm 25cm 26cm Number of roses 2 4 5 3 1
Find the volume of a pyramid with a square base, where the area of the base is 19. 6 ft 2 19. 6 ft 2 and the height of the pyramid is 11. 6 ft 11. 6 ft. Round your answer to the nearest tenth of a cubic foot
If the area of the base is 19. 6 ft^2 and the height of the pyramid is 11. 6 ft, the volume of the pyramid is approximately 79.1 cubic feet.
The formula for the volume of a pyramid is given by:
V = (1/3) × base area × height
In this case, we are given that the pyramid has a square base, so the base area is simply the area of a square with side length s:
base area = s^2 = 19.6 ft^2
We are also given the height of the pyramid:
height = 11.6 ft
Substituting these values into the formula for the volume of a pyramid, we get:
V = (1/3) × base area × height
= (1/3) × 19.6 ft^2 × 11.6 ft
≈ 79.1 ft^3 (rounded to the nearest tenth)
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Lucia has three separate pieces of ribbon. Each piece is 5 yards long. She needs to cut pieces that are 27 inches long to decorate folklorico dance dresses. What is the greatest number of 27-inch pieces that she can cut from three pieces of ribbon?
A 20
B 18
C 7
D 6
The greatest number of 27-inch pieces that she can cut from three pieces of ribbon is found to be 19. So, option B is the correct answer choice.
Each yard is equal to 36 inches, so 5 yards are equal to 180 inches. Therefore, each piece of ribbon is 180 inches long.
To find out how many 27-inch pieces Lucia can cut from each piece of ribbon, we divide 180 by 27.
180/27 = 6.67
Since Lucia can only cut whole pieces, she can cut 6 pieces of ribbon from each piece of ribbon.
Therefore, she can cut a total of 6 x 3 = 18 pieces of ribbon from the three separate pieces of ribbon.
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6 greater than a number is 24.
Answer:
Step-by-step explanation:
6 greater than a number is 24.
This means adding 6 to a number, x, will equal 24.
6 + x = 24
subtract 6 from both sides of the equation, and you are left with x=18
18 is your answer!!
the weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3245 grams and a standard deviation of 625 grams. if a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be greater than 2620 grams. round your answer to four decimal places.
The probability that the weight of a randomly selected newborn baby boy born at the local hospital will be greater than 2620 grams is 0.9099 (rounded to four decimal places).
The probability can be calculated using the standard normal distribution as follows:
P(Z > (2620 - 3245) / 625) = P(Z > -1.335)
Using a standard normal distribution table, we find that the probability of Z being greater than -1.335 is 0.9099.
We use the standard normal distribution because we know the mean and standard deviation of the population of newborn baby boys' weights. We convert the raw score of 2620 grams to a z-score, which tells us how many standard deviations the raw score is away from the mean.
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at the summer olympics, ten women qualify for the 100 meters race. considering that there can be no ties and that only three people can win medals, how many different ways could the gold, silver and bronze medals be awarded for that event?
There are 120 different ways to award the gold, silver, and bronze medals to the 10 women in the 100 meters race.
The number of ways that the gold, silver, and bronze medals can be awarded to 10 women is a combination problem.
We can use the formula for combinations to determine the number of ways to choose 3 women out of 10 for the medals:
[tex]nCr = n! / (r! * (n - r)!)[/tex]
Where n is the total number of women (10) and r is the number of medals (3).
So, the number of ways to award the gold, silver, and bronze medals to the 10 women is:
[tex]10C3 = 10! / (3! * (10 - 3)!) = 120[/tex]
Therefore, there are 120 different ways to award the gold, silver, and bronze medals to the 10 women in the 100 meters race.
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If you spin the spinner 36 times, what is the best prediction possible for the number of times
it will land on green or blue?
The best prediction possible for the number of times the spinner will land on green or blue is given as follows:
30 spins.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
Out of six regions, three are green and two are blue, hence the probability of one spin resulting in green or blue is given as follows:
p = (3 + 2)/6
p = 5/6.
Thus the expected number out of 36 trials of spins resulting in green or blue is given as follows:
E(X) = 5/6 x 36
E(X) = 30 spins.
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Which property was used to simplify the expression? 3c+ 9 + 4c = 3c + 4c + 9
The property used to simplify the expression is the Commutative Property of Addition, which states that changing the order of addends does not change the sum.
What is Commutative Property?The Commutative Property is a property of operations that states that the order in which two numbers are added or multiplied does not affect the result. In other words, the property says that changing the order of the terms being added or multiplied will not change the final answer.
According to given information:The property that was used to simplify the expression is the Commutative Property of Addition. This property states that the order in which we add two numbers does not affect the result. In other words, if we have two numbers a and b, then a + b is equal to b + a.
In the given expression, we have two terms, 3c and 4c, that are being added together. By applying the Commutative Property of Addition, we can rearrange the terms to get 4c + 3c. This gives us the simplified expression 7c + 9.
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An angle measures 37.6° more than the measure of its complementary angle. What is the measure of each angle?
The pair of required complementary angles are 26.2° and 63.8° respectively.
What are complementary angles?Two angles are said to be supplementary angles because they combine to generate a linear angle when their sum is 180 degrees.
When two angles add up to 90 degrees, however, they are said to be complimentary angles and together they make a right angle.
If the total of two angles is 90o (ninety degrees), then the angles are complementary.
A 30-angle and a 60-angle, for instance, are two complementary angles.
So, to find the 2 angles which are complementary:
x + x + 37.6 = 90
Now, solve it as follows:
x + x + 37.6 = 90
2x = 90 - 37.6
2x = 52.4
x = 52.4/2
x = 26.2
Now, x = 26.2 and the second angle x + 37.6 is = 26.2 + 37.6 = 63.8°.
Therefore, the pair of required complementary angles are 26.2° and 63.8° respectively.
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consider straight wires of equal lengths with their ends soldered together to form the edges of a cube. either silver or copper wire can be used for each edge. how many different ways can the cube be constructed?
The number of valid ways to construct the cube is [tex]4096 - 48 = 4048[/tex]
Each corner of the cube is formed by three wires coming together. Since the wires are soldered together at the ends, each corner must have either 3 silver wires or 3 copper wires coming together.
There are two choices for each wire: it can be silver or copper. Since there are 12 edges in a cube, there are 2 choices for each edge, giving a total of [tex]2^12 = 4096[/tex] possible arrangements of the edges.
However, not all of these arrangements are valid. We must eliminate the arrangements where at least one corner has two silver wires and one copper wire
There are 8 corners in a cube, and for each corner, there are 3 ways to choose which wire is different from the other two. Once we choose which wire is different, there are 2 choices for its color (silver or copper). Thus, there are [tex]8 x 3 x 2 = 48[/tex] invalid arrangements.
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in a study of the treatment of congestive heart failure (chf), a new surgical procedure was compared to the standard surgical procedure. the study enrolled 550 people with chf and randomly assigned half to receive the new procedure and half to receive the standard procedure. among those that received the new procedure, 98 died within 5 years. among those that received the standard procedure, 190 died within 5 years. what is the result for the appropriate measure to describe the strength of the association between surgical procedure and death?
The result for the appropriate measure, relative risk, is approximately 0.515.
This indicates that the risk of death within 5 years is about 51.5% lower in the new procedure group compared to the standard procedure group.
This suggests a strong association between the surgical procedure and the reduction in the risk of death.
To determine the strength of the association between the surgical procedures and death, we can calculate the relative risk.
Identify the numbers given in the question.
- Total participants: 550
- New procedure group: 275 (half of 550)
- Deaths in new procedure group: 98
- Standard procedure group: 275 (half of 550)
- Deaths in standard procedure group: 190
Calculate the death rate (proportion of deaths) in each group.
- Death rate in new procedure group = (Number of deaths in new procedure group) / (Total in new procedure group) = 98/275 ≈ 0.356
- Death rate in standard procedure group = (Number of deaths in standard procedure group) / (Total in standard procedure group) = 190/275 ≈ 0.691
Calculate the relative risk.
- Relative risk = (Death rate in new procedure group) / (Death rate in standard procedure group) = 0.356/0.691 ≈ 0.515.
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