Answer:
a) \(b^{3}\)
b) \(x^{3}\)
Step-by-step explanation:
a) Since it is division, you just subtract the powers from each other
\(b^{7} /b^{4} =b^{7-4} =b^{3}\)
b) First add the powers on the top, then divide
\(\frac{x^{1} *x^{5} }{x^{2} *x^{1} } =\frac{x^{1+5} }{x^{2+1} } =\frac{x^{6} }{x^{3} } =x^{6-3} =x^{3}\)
Just need some help
Step-by-step explanation:
D
a triangle is 180°
180-126= 54
Now you have:
56+54+X=180
110+X=180
-110 -110
X=70
Answer:
70 wanna know why add the sides then divide
Step-by-step explanation:
Plane H is shown. Plane H contains four points. Points A, C, and D form a diagonal line on the left. Point B is to the right of point C. Which points are coplanar and noncollinear? points A and D points C and D points A, C, and D points A, B, and D
Answer:
d
Step-by-step explanation:
edg 2021
Answer:
d
Step-by-step explanation:
Translate the following argument into symbolic form, and use Truth Tables to determine whether the argument is valid or invalid.
If the boss snaps at you and you make a mistake, then he’s irritable. He didn’t snap at you. So he’s not irritable.
The last column evaluates to "T" in all rows. Therefore, the argument is valid since the conclusion always follows from the premises.
Let's assign symbols to represent the statements in the argument:
P: The boss snaps at you.
Q: You make a mistake.
R: The boss is irritable.
The argument can be symbolically represented as follows:
[(P ∧ Q) → R] ∧ ¬P → ¬R
To determine the validity of the argument, we can construct a truth table:
P | Q | R | (P ∧ Q) → R | ¬P | ¬R | [(P ∧ Q) → R] ∧ ¬P → ¬R
---------------------------------------------------------
T | T | T | T | F | F | T |
T | T | F | F | F | T | T |
T | F | T | T | F | F | T |
T | F | F | F | F | T | T |
F | T | T | T | T | F | F |
F | T | F | T | T | T | T |
F | F | T | T | T | F | F |
F | F | F | T | T | T | T |
The last column represents the evaluation of the entire argument. If it is always true (T), the argument is valid; otherwise, it is invalid.
Looking at the truth table, we can see that the last column evaluates to "T" in all rows. Therefore, the argument is valid since the conclusion always follows from the premises.
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1, 1, 2, 3, 5, 8 are the first six numbers of the fibonacci sequence. what is the eighth number?
Answer:
21
Step-by-step explanation:
1, 1, 2, 3, 5, 8, 13, 21
The required eighth number in the Fibonacci sequence is 21.
Given that,
1, 1, 2, 3, 5, and 8 are the first six numbers of the Fibonacci sequence. what is the eighth number is to be determined
The sequence is defined as the specific pattern of numbers in which they are arranged.
Here,
given Fibonacci sequence is 1, 1, 2, 3, 5, 8
The Fibonacci numbers, sometimes known as Fn, are a set of numbers in mathematics where each number is the sum of the two numbers before it.
According to the above definition,
7 th number = 5th number + 6th number =
7 th number = 5 + 8 = 13
8th number = 8 + 13 = 21
Thus, the required eighth number in the Fibonacci sequence is 21.
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$34.98 with 8.2 tax
Answer:
$37.85
Step-by-step explanation:
Here the price is $34.98 and there's an 8.2% tax on that. To obtain the after-tax amount due, multiply $34.98 by (1 + 0.082), or 1.082, obtaining:
1.082($34.98) = $37.85 (rounded to the nearest cent)
John goes out to lunch. The bill, before tax and tip, was 19.20. A sales tax of 6% was added on. John tipped 12% on the amount after the sales tax was added. How much tip did he leave? Round to the nearest tenth
The restaurant in a large commercial building provides coffee for the occupants in the building. The restaurateur has determined that the mean number of cups of coffee consumed in a day by all the occupants is 2.0 with a standard deviation of .6. A new tenant of the building intends to have a total of 125 new mployees. What is the probability that the new employees will consume more than 240 cups per day?
To solve this problem, we can use the concept of the sampling distribution of the sample mean. The mean number of cups of coffee consumed in a day by all occupants is 2.0 with a standard deviation of 0.6. Since the sample size is large (125 employees) and the population standard deviation is known, we can approximate the sampling distribution of the sample mean as a normal distribution.
The mean of the sampling distribution is equal to the population mean, which is 2.0 cups per day Now, we need to calculate the z-score for the value of 240 cups per day using the formula:
z = (x - μ) / σ,
where x is the desired value (240 cups per day), μ is the mean of the sampling distribution (2.0 cups per day), and σ is the standard deviation of the sampling distribution (0.6 / sqrt(125)).
Plugging in the values, we have:
z = (240 - 2) / (0.6 / sqrt(125)) ≈ 58.01.
Finally, we can use a standard normal distribution table or a calculator to find the probability of obtaining a z-score greater than 58.01. However, since this z-score is extremely large, the probability will be very close to zero.
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How can I split 166 in half
You divide 166 by 2. The answer would be 83.
The value of splitting 166 in half gives two equal halves of 83 each.
When 'split' a number in half, dividing the number into two equal parts.
Here want to split the number 166 in half.
Perform a division operation by dividing 166 by 2.
Division is the opposite operation of multiplication.
When divide a number by 2, you are essentially finding the value of half of that number.
So, the calculation is as follows:
166 ÷ 2 = 83
This means that half of 166 is 83.
Divide the number 166 into two equal parts, each being 83.
If add both halves together, you get the original number back:
83 + 83 = 166
Therefore, dividing 166 by 2 allows to splitting it equally into two halves, each having a value of 83.
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Solve the following system: y = x 3 2x y = 9 (2, 5) (5, 2) (â’2, 5) (2, â’5).
The required solution of the equation is (2,5). The correct option is A. (2,5).
Given equations,\(y=x+3.....(1)\\2x+y=9......(2)\)
How to solve a system of equations?putting the value of y from eq. 1 in eq. 2 we get,
\(2x+x+3=9\\3x=9-3\\3x=6\\x=2\)
putting the value of x=2 in eq. 1 we get,
\(y=2+3\\y=5\)
Hence, the required solution of the equation is (2,5).
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3x +y = –15
-3x - 4y = 30
Which variable will eliminate in the system?
Answer:
x should be eliminated
hope it helps
If you wish to calculate the interest on an investment with a rate of 6. 17%, what number will you plug into your equation? a. 0. 00617 b. 0. 0617 c. 0. 617 d. 6. 17.
If you wish to calculate the interest on an investment with a rate of 6. 17%, you would plug the number 0.0617 into your equation. Therefore, the correct answer is option b) 0.0617.
Interest is the sum of money that a borrower pays to a lender in exchange for using the borrowed funds for a certain time. The amount of interest charged on the amount borrowed is known as the interest rate, which is stated as a percentage. Investments are made when products are purchased that will not be used immediately but instead will be used to generate wealth in the future. The phrase "investment" in finance refers to the acquisition of securities like stocks, bonds, and real estate.
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an unnormalized relation is a table that has more than one row.
An unnormalized relation refers to a table in a relational database that contains more than one row. This means that there are duplicate rows in the table, which violates the rules of normalization.
Normalization is a process in database design that aims to eliminate data redundancy and ensure data integrity. It involves breaking down a database into multiple tables and defining relationships between them. By doing so, we can efficiently store and retrieve data while minimizing inconsistencies.
In an unnormalized relation, duplicate rows can lead to various problems. For example, it can result in data inconsistencies, as updating one instance of a row may not reflect changes in other duplicate rows. Additionally, it can cause unnecessary storage and maintenance overhead.
To normalize an unnormalized relation, we need to identify the functional dependencies in the table and create separate tables for related data. This helps organize the data and reduces redundancy.
In summary, an unnormalized relation is a table in a relational database that has duplicate rows. It is important to normalize such relations to ensure data integrity and efficiency.
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What goes on the lines I don’t understand the problem
Answer:
Step-by-step explanation:
a). Let the number of spoons = x
And number of forks = y
Total number of spoons and forks bought by Perry = 10
x + y = 10 --------(1)
Cost of one spoon = $5
Cost of one fork = $3
Therefore, total cost of x spoons and y forks = $(5x + 3y)
5x + 3y = 42 -------(2)
b). Now we can convert these equations into the slope-intercept form.
x + y = 10 ⇒ y = -x + 10
Table for input output values,
x 2 4 6
y 8 6 4
5x + 3y = 42
3y = -5x + 42
y = \(-\frac{5}{3}x+14\)
x 0 3 6
y 14 9 4
Point of intersection of these lines will be (6, 4).
American black ducks migrate a great distance every year. a typical bird will travel 2,739 miles in 33 days. which of the following best represents this trip with a constant unit rate of travel?
Choice A - y = 83x
Choice B - The graph going up
Choice C - the T Table
Choice D - The graph with no arrow
Answer:
answer my most recent and ill answer this one.
Step-by-step explanation:
jill needs $50 000 for a round-the-world holiday in 3 years time. How much does Jill need to invest at 7% pa compounded yearly to achieve this goal?
Jill needs to invest approximately $40,816.33 at a 7% annual interest rate compounded yearly to achieve her goal of $50,000 for a round-the-world holiday in 3 years.
To solve this problemWe can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where
A is equal to the $50,000 future value that Jill hopes to acquire.P is the principle sum, which represents Jill's necessary initial investment.(7% or 0.07) is the annual interest rate.n is equal to how many times the interest is compounded annually (in this case, once).T equals the duration in years (3)We can rearrange the formula to solve for P:
P = A / (1 + r/n)^(nt)
Now we can substitute the given values into the formula and calculate:
P = 50000 / (1 + 0.07/1)^(1*3)
P = 50000 / (1 + 0.07)^3
P = 50000 / (1.07)^3
P = 50000 / 1.2250431
P ≈ $40,816.33
Therefore, Jill needs to invest approximately $40,816.33 at a 7% annual interest rate compounded yearly to achieve her goal of $50,000 for a round-the-world holiday in 3 years.
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Help me figure it out pls
Answer:
number 1 is 74
Step-by-step explanation:
number 4 is 100
number 2 is I think either 160 or 32
an I'm sorry I don't know what number 3 is but I hoped I helped
You report a confidence interval to your boss but she says that she wants a narrower range. SELECT ALL of the ways you can reduce the width of the confidence interval. o Increase the sample size o Decrease the sample size o Increase the confidence level o Decrease the confidence level I
o ncrease the mean o Decrease the mean
We can reduce the width of the confidence interval by increasing the sample size, reducing the confidence level and decreasing the mean (A, D, and F)
What is a confidence interval?A confidence interval is an estimate of the interval that has a specified probability of including an unknown population parameter.
The purpose of a confidence interval is to estimate the true value of the population parameter being measured, such as a mean, a standard deviation, or a proportion.
In general, a wider confidence interval indicates more uncertainty about the estimate, while a narrower confidence interval suggests more precision in the estimate.
We want narrower confidence intervals to demonstrate more precision, as this allows us to draw more reliable conclusions about population parameters.
We cannot reduce the width of the confidence interval by increasing the sample size, increasing the confidence level or increasing the mean.
Thus, the correct options are a, d, and f.
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20 points.
Find the equation of the line: which passes through (1,-7) and is perpendicular to (-4,6) and (5,-3)
Answer:
-9 6 that is because the line has to be perpenducular to the other line
Step-by-step explanation:
Slope of line between points (-4, 6) and (5, -3)
=> Rise / Run
=> [6 - (-3)] / [(-4) - 5]
= 9 / (-9)
= -1.
Thus slope of perpendicular line
= -1 / (-1) = 1.
We have y = x + c.
When x = 1, y = -7.
=> (-7) = (1) + c, c = -8.
Hence y = x - 8.
two tangents each intersect a circle at oppositea. endpoints of the same diameter. is it possible for the twob. tangents to intersect each other outside the c. circle? explain why or why not, using the information you d. learned in this lesson.
No, it is not possible for the two tangents to intersect each other outside the circle.
We have,
The concept used in this explanation is that a tangent to a circle is perpendicular to the radius at the point of tangency.
This is a fundamental property of circles and tangents, based on geometry and the definition of a tangent line.
No, it is not possible for the two tangents to intersect each other outside the circle.
This is because tangents to a circle are perpendicular to the radius at the point of tangency. If the tangents intersect with ed each other outside the circle, it would imply that they are not perpendicular to the radius, which contradicts the definition of a tangent.
Thus,
No, it is not possible for the two tangents to intersect each other outside the circle.
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Yes, it is possible for the two tangents to intersect each other outside the circle only when the tangents are perpendicular to the diameter. They will intersect at the point directly opposite to the center of the circle. This concept combines the properties of tangents and circles that are normally covered in high school geometry.
Explanation:In the context Mathematics and Geometry, the situation you have described where two tangents to a circle meet at opposite ends of a diameter is indeed possible, but only in one specific scenario: when the tangents are perpendicular to the diameter and they intersect each other at the point directly opposite to the center of the circle. This is because, by geometry, a tangent to a circle is perpendicular to the radius at the point of tangency. Thus, if the tangents are drawn at the endpoints of a diameter, they will be parallel and will not intersect each other outside the circle.
In contrast, if the tangents are drawn such that they are perpendicular to the diameter, they will intersect at a point that is a distance from the center of the circle equivalent to the length of the radius, and directly opposite the center of the circle. This point of intersection of the tangents is outside the circle.
The properties of tangents and circles, which we use in the explanation, are part of the standard curriculum in high school geometry.
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Write an expression for the sequence of operations described below.
Subtract three from the product of seven and eight
Type x if you want to use a multiplication sign. Type / if you want to use a division sign. Do not simplify any part of the expression.
An expression for the sequence of operations described "Subtract three from the product of seven and eight." is (7 × 8) - 3.
How to evaluate and solve the given expression?In order to evaluate and solve this expression, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right. Lastly, the mathematical operations of addition or subtraction would be performed from left to right.
Based on the information provided, we have the following mathematical expression:
Expression: (7 × 8) - 3
56 - 3
53
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Pumping stations deliver gasoline at the rate modeled by the function D, given by D(T) = 6t/1+2t with t measured in hours and and R(t) measured in gallons per hour. How much oil will the pumping stations deliver during the 3-hour period from t = 0 to t = 3? Give 3 decimal places.
To find how much oil the pumping stations will deliver during the 3-hour period from t=0 to t=3, we need to integrate the function D(T) from t=0 to t=3:
∫[0,3] (6t/1+2t) dt
Using substitution, let u = 1+2t, then du/dt = 2 and dt = du/2. The integral becomes:
∫[1,7] (3/u) du
= 3 ln|u| from 1 to 7
= 3 ln(7/1)
= 3 ln(7)
≈ 5.048
Therefore, the pumping stations will deliver approximately 5.048 gallons of oil during the 3-hour period from t=0 to t=3, to 3 decimal places.
Hi! I'd be happy to help you with your question. We need to find the total amount of gasoline delivered during the 3-hour period from t=0 to t=3 using the given function D(t) = 6t / (1 + 2t). We can do this by integrating the rate function with respect to time.
Step 1: Integrate the rate function, D(t), with respect to t:
∫(6t / (1 + 2t)) dt
Step 2: Evaluate the integral between t=0 and t=3:
|∫(6t / (1 + 2t)) dt| from 0 to 3
Step 3: Calculate the definite integral:
Since it's difficult to evaluate this integral directly, we can use a numerical integration method like the trapezoidal rule or Simpson's rule, or a calculator with an integration function. Using a calculator, we find that the integral value is approximately 1.802.
So, the pumping stations will deliver approximately 1.802 gallons of gasoline during the 3-hour period from t=0 to t=3.
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recall that an event is a collection of sample points, and the probability of an event is the sum of the probabilities of the sample points in the event. the sample points were given to be e1, e2, e3, e4, e5, e6, and e7. event a is made up of the sample points e1, e4, and e6. thus, how can the probability of event a be determined? p(e1) p(e4) p(e6) p(e2) p(e3) p(e5) p(e7) event b is made up of the sample points e2, e4, and e7. thus, how can the probability of event b be determined? p(e2) p(e4) p(e7) p(e1) p(e3) p(e5) p(e6) event c is made up of the sample points e2, e3, e5, and e7. thus, how can the probability of event c be determined? p(e2) p(e3) p(e5) p(e7) p(e1) p(e4) p(e6)
To determine the probability of event A, we need to add the probabilities of the sample points e1, e4, and e6:
P(A) = P(e1) + P(e4) + P(e6)
To determine the probability of event B, we need to add the probabilities of the sample points e2, e4, and e7:
P(B) = P(e2) + P(e4) + P(e7)
To determine the probability of event C, we need to add the probabilities of the sample points e2, e3, e5, and e7:
P(C) = P(e2) + P(e3) + P(e5) + P(e7)
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How many ways can Karen choose 5 pizza toppings from a menu of 12 toppings if each topping can only be chosen once?
Answer:
5 x 12 = 60
Step-by-step explanation:
35% of 15% of x is equivalent to which of the following?
A. 0.0525x
B. 0.125x
C. 0.25x
D. 0.525x
E. 5.25x
Answer:
a
Step-by-step explanation:
.35x.15=0.0525
If f(x) is not defined at c, then f(x) cannot be continuous on any interval. True False
Answer:
True
Step-by-step explanation:
The wording of the question is a little tricky, but here's what I think.
If a function f(x) is not defined at a point c, then the function has a discontinuity at that point. In order for a function to be continuous on an interval, it must be defined and have no abrupt changes or jumps within that interval. Since f(x) is not defined at c, it violates the condition of continuity, and therefore f(x) cannot be continuous on any interval that includes c.
The given statement "If f(x) is not defined at c, then f(x) cannot be continuous on any interval." is false because it does not automatically mean that f(x) cannot be continuous on any interval.
Continuity of a function depends on the behavior of the function around the point of interest, rather than just the absence of a definition at a single point. A function can still be continuous on an interval except at the specific point where it is not defined.
For example, consider the function f(x) = 1/x. This function is not defined at x = 0, but it is continuous on any interval that does not include x = 0. This is because f(x) approaches positive or negative infinity as x approaches 0 from the left or right side, respectively, indicating that there is no abrupt jump or discontinuity.
In general, the continuity of a function is determined by its behavior around a point, including its limit as x approaches that point. The absence of a definition at a single point does not automatically imply that the function cannot be continuous on any interval.
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PLEASEEEEEE HELPPPPPPPPP
\(5x + 3 = - 9 \\ = > 5x = - 9 - 3 \\ = > 5x = - 12 \\ = > x = \frac{ - 12}{5} \\ = > x = - 2 \frac{2}{5} \)
Answer:Option A .
\( - 2 \frac{2}{5} \)
the length of a rectangle is six inches more than eight times the width. the perimeter is 120 inches. find the length and width.
The length and width of a rectangle are 36cm and 4.5cm
Finding the Width:
The formula to find the perimeter of the rectangle is:
P=2(l+w),
where P is the perimeter, l be the length, and w be the width.
Now substitute the given values to solve for w, since we need to find the width.
The given information is:
the length of a rectangle is six inches more than eight times the width so the equation becomes:
L=8w+6
P=120
w=8w
now plug the values in the above formula:
P=2(l+w),
120=2(8w+6)+8w
120=16w+12+8w
120=24w+12
24w=108
w=4.5
To find the length just substitute in the L.
L=8(4.5)+6
L=30+6
L=36
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Eloy went shopping and bought 2 shirts for $12.95 each, a pair of pants for $35.89, and a hat for $11.47. Eloy paid with a $100 bill. How much change should he receive?
Answer:
26.74
Step-by-step explanation:
(12.95x2)+35.89+11.47=73.26
100-73.26=26.74
carmen is prepping for a party. she wants to serve 72 apple slices. if each apple can slice up to 6 slices per apple, what is the minimum number of apples she will have to buy?
Answer:
12
Step-by-step explanation:
72/6=12
define at least three (3) sources of experimental uncertainties for the experiments and explain specifically how each would have affected the accuracy of the data.
By identifying and minimizing these uncertainties, it is possible to improve the accuracy of the data and obtain more reliable results.
Experimental uncertainties refer to the errors or variations that may occur in the process of conducting an experiment. There are several sources of experimental uncertainties that can affect the accuracy of the data, specifically:
1. Instrument uncertainties: These uncertainties arise from the limitations of the instruments used in the experiment. For example, if a measuring device has a limited resolution or if it is not properly calibrated, it can lead to inaccuracies in the measurements.
2. Operator uncertainties: These uncertainties arise from the variations in the way different people conduct the experiment. For example, if different people are measuring the same quantity, they may have different techniques, which can lead to variations in the measurements.
3. Environmental uncertainties: These uncertainties arise from the variations in the environment in which the experiment is conducted. For example, if the temperature or pressure of the environment changes during the experiment, it can affect the measurements.
Each of these sources of experimental uncertainties can affect the accuracy of the data by introducing errors or variations in the measurements. By identifying and minimizing these uncertainties, it is possible to improve the accuracy of the data and obtain more reliable results.
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