Divide and give the answer in scientific notation.
8.4 x 10^7
----------------
3 x 10^3
A store had 888 sodas, both diet and regular. The ratio of diet sodas to regular sodas was 8:4. How many diet sodas were there?
Answer:no. I don’t understand. Where did the 12 come from
Step-by-step explanation:
Check the answer that best describes the relationship between f(x) and x. (for example if f(x) is θ(x)θ(x) check that as your answer and not o(x)o(x) or ω(x)ω(x) even though these are true also in this case.)
2+1.25f=10−2.75f solve for f
The value of f is 0.02.
What is an expression ?Expression is a formation of numbers and variables with mathematical operations.
According to the given question we have to solve for f or we can say we have to find the value of f for the given expression which is
2+1.25f=10−2.75f (lets multiply each term by 100 to remove
decimals )
∴ 200 + 125f = 1000 - 275f
125f + 275f = 1000 - 200
400f = 800
f = 800/400
f = 2.
As we have multiplied by 100 we have to divide by 100 we obtain the exact result.
So, 2/100 is = 0.02
f = 0.02.
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Write the rate as a unit rate
A Jockey had 1053 wins in 31 years of riding
The unit rate is win per year
What does it mean to say that lim n → ∞ an = ∞? the terms an become small as n becomes large. the terms an approach zero as n becomes large. the terms an become large as n becomes large. the terms an become small as n becomes small. the terms an become large as n becomes small?
The limit [tex]\lim_{n \to \infty} a_n = \infty[/tex] means that the term [tex]a_n[/tex] becomes large as n becomes large
The limit of a function describes the behavior of such function as the independent variable approaches a certain value
Infinity [tex]\infty[/tex] represents a very large number
In the limit, both n and [tex]a_n[/tex] tend to infinity
The given limit is:
[tex]\lim_{n \to \infty} a_n = \infty[/tex]
The limit above describes the behavior of [tex]a_n[/tex] as n approaches infinity
As n approaches infinity [tex]a_n[/tex] also approaches infinity
Therefore, the description of the limit [tex]\lim_{n \to \infty} a_n = \infty[/tex] is that the term [tex]a_n[/tex] becomes large as n becomes large
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The statement 'lim n → ∞ an = ∞' means that the terms an become large as n becomes large.
Explanation:The statement lim n → ∞ an = ∞ means that the terms an become large as n becomes large.
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A scientist placed 22.854 grams of sodium chloride in a beaker. He then added five times as much calcium chloride as sodium chloride. Finally, he divided the mixture evenly into four dishes.
How much of the mixture did each dish contain?
A .28.5675 g
B. 34.2810 g
C. 137.1240 g
D. 548.4960 g
What is the distance between 0.5 to -1.5
How do I figure this out?
By decreasing each dimension by 1 unit, the area of a rectangle decreased from 40 square feet (on the left) to 28 square feet (on the right). Find the percent decrease in area.
The percent decrease in the area of a rectangle from 40 square feet to 28 square feet is calculated by dividing the difference in areas (12 sq ft) by the original area (40 sq ft) and multiplying by 100%. The result is a 30% decrease in area.
Explanation:The percent decrease in the area of a rectangle can be found by first calculating the difference in the areas and then dividing that difference by the original area. In this case, the original area of the rectangle was 40 square feet and it decreased to 28 square feet, a difference of 12 square feet.
We use the formula for percentage change which is:
(change in value) / (original value) × 100%
Here, the change in value is the difference in areas (12 square feet) and the original value is the original area of the rectangle (40 square feet). Thus we calculate:
(12 sq ft/ 40 sq ft) * 100% = 30%
So, the percent decrease in the area of the rectangle is 30%.
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on Monday 2/3 of the team practiced Tuesday 7/8 Wednesday 1/2 and Thursday 3/4 on which date were the most team members present at practice
rewrite y^2(9y^2+4y-9) in standard form
Makayla's local movie theater has a moviegoer club that charges an annual registration fee of 25 dollars.However, movie tickets are discounted for members at 6 dollars per ticket, instead of 9 dollars per ticket.Let m equal the number of movie tickets Makayla purchases in a year. Write a function to model the amount of money Makayla spent going too the movies during the year she joined the club. C(m)=6x+25 The domain is best represented by: A)integers B)whole numbers C)rational numbers D)real numbers Algebra chestercat
The perimeter of a college athletic field is 104 meters and the length is 16m more than the width find the length and width
The length and width of the rectangle will be 19 meters.
What is the perimeter of the rectangle?The sum of all the sides of the rectangle will be known as the perimeter of the rectangle. Let L be the length and W be the width of the rectangle.
Then the perimeter of the rectangle will be
Perimeter of the rectangle = 2(L + W) units
The perimeter of a college athletic field is 104 meters and the length is 16 meters more than the width.
L = 14 + W
Then the length and width of the rectangle will be
P = 2(L + W)
104 = 2(14 + W + W)
52 = 14 + 2W
2W = 38
W = 19 meters
The length and width of the rectangle will be 19 meters.
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A family paid 23,100 as a down payment for a home if this represents 14% of the price of the home find the price of the home
Let f(x) = 3x+2 and g(x) = 7x+6. find f×x
Prove or disprove that the product of two irrational numbers is irrational
The product of two irrational numbers can be either rational or irrational.
The product of two irrational numbers is not always irrational. To understand this, let's consider an example and a counterexample.
Example of an Irrational Product
Take the square root of 2 (\/(2)) and the square root of 3 (\/(3)). Both of these numbers are irrational. Their product is:
\/2 × \/3 = \/6
Since \/6 cannot be expressed as a fraction of two integers (making it irrational), this is an example where the product of two irrational numbers is irrational.
Counterexample of a Rational Product
Now, consider another example with \/(2) and \/(2). Since both are irrational, their product is:
\/2 × \/2 = 2
Here, 2 is a rational number because it can be written as a fraction (2/1). Therefore, this is a counterexample where the product of two irrational numbers is rational.
In summary, the product of two irrational numbers can be either rational or irrational depending on the specific numbers involved.
The Clemson Tiger Football team won the 2016 College Football National Championship. During the regular season, they won 11 games and lost 1. The data set below is the number of points by which they won (positive values) or lost (negative value) each game.
{6,6,59,19,6,46,7,3,54,−1,22,49} = {-1,3,6,6,6,7,19,22,46,49,54,59}
What is the median? ________
What is the mode? _________
What is the mean? _________
What is the 5% trimmed mean? (Round to the nearest whole number when determining the number of values to trim).
Are these averages parameters or statistics?
median is the middle value, since there is an even number, add the 2 middle numbers and divide by 2
median = 9 +17 = 26/2 = 13
mode is the number that is repeated most often
mode = 6
mean is the average of all the numbers, when added they equal 276
276/12 = 23
mean = 23
5% trimmed mean = 218 /10 = 21.8
the averages are statistics since the points of a football game can vary
What is the probability that x is between $34 and $38?
The probability that ( x) is between $34 and $38 is 0.6826 or 68.26%.
To find the probability that a random variable ( x) is between $34 and $38, we need to use the probability density function (PDF) if ( x) follows a continuous distribution. Let's assume ( x ) follows a normal distribution with a mean [tex](\( \mu \))[/tex] of $36 and a standard deviation [tex](\( \sigma \))[/tex] of $2.
Calculate the z-scores for $34 and $38:
[tex]\[ z_1 = \frac{34 - 36}{2} = -1 \][/tex]
[tex]\[ z_2 = \frac{38 - 36}{2} = 1 \][/tex]
Look up the z-scores in the standard normal distribution table:
[tex]\[ P(z_1 < Z < z_2) = P(-1 < Z < 1) \][/tex]
Find the probabilities corresponding to these z-scores:
[tex]\[ P(Z < 1) = 0.8413 \][/tex]
[tex]\[ P(Z < -1) = 0.1587 \][/tex]
Subtract the two probabilities:
[tex]\[ P(-1 < Z < 1) = P(Z < 1) - P(Z < -1) = 0.8413 - 0.1587 = 0.6826 \][/tex]
So, the probability that ( x) is between $34 and $38 is 0.6826 or 68.26%.
if f'(2) = 3.1 and g'(2)=7.3 then the graph of f(x)+g(x) has slope 10.4 at x=2.True or false
Final answer:
The statement is true, as the slope of the graph of f(x)+g(x) at x=2 is the sum of the slopes of f and g at that point, which equals 10.4.
Explanation:
The statement is true.
In calculus, the derivative of a function at a particular point measures the rate at which the function is changing at that point. It is analogous to the slope of the tangent line to the graph of the function at that point.
When we are given that f'(2) = 3.1 and g'(2) = 7.3, these values represent the slopes of the functions f and g at x = 2, respectively.
To find the slope of f(x) + g(x) at x = 2, we simply add the slopes of f and g at that point. This is based on the rule that the derivative of the sum of two functions is the sum of their derivatives, or symbolically, (f+g)' = f' + g'.
Therefore, the slope of the graph of f(x)+g(x) at x=2 is indeed 10.4 (3.1 + 7.3).
Jane saved $ 800. Her sister has 10 times as much money. How much money does Jane's sister have? Use number or words to explain your answer.
Let a and b be events in a sample space s such that p(a) = 0.41, p(b) = 0.46 and p(a ∩
b.= 0.14. find p(a | b).
The conditional probability that event a will occur given that event b has occurred, denoted as p(a | b), is approximately 0.3 or 30%.
Explanation:The question is asking for the conditional probability of the event a given that event b has occurred, written as p(a | b). In probability theory, the formula for conditional probability is p(a | b) = p(a ∩ b) / p(b). Here, we already know that p(a ∩ b) = 0.14 and p(b) = 0.46. Substituting these values into the formula gives us:
p(a | b) = 0.14 / 0.46 = 0.304347826.
So, the probability of event a occurring given that event b has occurred is approximately 0.3 or 30%.
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Sarah polled 40 randomly selected students at her high school and found that 20% ( = 0.2) are happy with the quality of the cafeteria food. With a desired confidence level of 99%, which has a corresponding z*-score of 2.58, what is the approximate margin of error of Sarah’s poll? Remember, the margin of error, E, can be determined using the formula E = z*
If rectangle ABCD is resized with a central point (−1, 1) and scale factor 3, what are the coordinates of D'?
A)(−3, 3)B)(−10, −5)C)(−5, −10)D)(−15, −15)
A video editor takes 15 hours to add a
Determine whether or not f is a conservative vector field. if it is, find a function f such that f = ∇f. if it is not, enter none. f(x, y) = (yex + sin y) i + (ex + x cos y) j
The vector field f(x, y) = (yex + sin y) i + (ex + x cos y) j is conservative because its curl vanishes everywhere. The function F such that ∇F = f is yex + cos y + C.
Explanation:To determine if the given function f(x, y) = (yex + sin y) i + (ex + x cos y) j is a conservative vector field, we need to see if the curl of the vector field vanishes everywhere. The curl of a vector field in two dimensions is the partial derivative of the j component with respect to x minus the partial derivative of the i component with respect to y.
For f(x, y), the partial derivative of the j component (ex + x cos y) with respect to x is ex + cos y, and the partial derivative of the i component (yex + sin y) with respect to y is ex + cos y. Both derivatives are equal, implying the curl is zero. Hence, f(x, y) is a conservative vector field.
Next, to find a function F such that ∇F = f, we need to integrate. The potential function, F, can be obtained by integrating the i component of f with respect to x (since it does not involve y), and the j component of f with respect to y (since it does not involve x): ∫yex dx + ∫sin y dy = yex + cos y + C. This is the function F such that ∇F = f.
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I REALLY NEED HELP WITH MY CALC CORRECTIONS. THIS IS THE THIRD TIME IVE POSTED THIS. I NEED HELP ASAP PLS!! I HATE CALC 1
a consumer purchased a computer after a 15% price reduction. if x represents the computer's original price, the reduced price can be represented by
2/3 x 5/8 in simplest form
The weight of 1000 identical samples of a substance is 10 pounds. What is the weight of 10 samples?