Answer:
2^18
Step-by-step explanation:
2^2
------ * 2^8
2^-8
We know a^b * a^c = a^(b+c)
2^2 * 2^8 = 2^(2+8) = 2^10
2^10
-------
2^-8
a^b / a^c = a^(b- c)
2^(10 - -8) = 2^(10+8) = 2^18
If x is to 9 as 8 is to 12, then xis equal to
Write a rational equation that cannot have a solution at x = 2
Answer: 5+7=2x
Step-by-step explanation:
Plz answer I really need help on this
2. Ajar contains 11 green marbles, 6 red marbles, and 9 blue marbles. A marble is selected at random, not replaced, and then a second marble is selected. What is the probabilityselecting a red marble followed by a green marble? A 65/649B224/352C33/337D33/325
In order to find the probability, start by finding the probability of selecting a red marble out of the jar,
\(\frac{6}{11+6+9}=\frac{6}{26}=\frac{3}{13}\)then, do the same for selecting a green marble, however, remember that the first marble was not replaced, meaning that at this point there are 5 red marbles in the jar,
\(\frac{11}{11+5+9}=\frac{11}{25}\)finally, multiply the probabilities,
\(\frac{3}{13}\times\frac{11}{25}=\frac{33}{325}\)Answer:
The probability of the event is 33/325.
+b4+c4 = 20² (b²+c²), prove
that A:45° or 135°
A is either 45° or 135°.
To prove the given statement, let's assume that the points B and C lie on a coordinate plane, with the origin (0, 0) as the common vertex of the right angles at points B, C, and A. Let the coordinates of points B and C be (x₁, y₁) and (x₂, y₂) respectively.
Using the distance formula, we have:
AB² = x₁² + y₁²
AC² = x₂² + y₂²
According to the given equation, +b4+c4 = 20² (b²+c²), we can rewrite it as:
(x₁² + y₁²) + (x₂² + y₂²) = 20² [(x₁² + y₁²) + (x₂² + y₂²)]
Expanding and simplifying the equation, we get:
x₁² + y₁² + x₂² + y₂² = 20² (x₁² + y₁² + x₂² + y₂²)
This equation can be further simplified to:
(x₁² + y₁²) + (x₂² + y₂²) = (20² - 1) (x₁² + y₁² + x₂² + y₂²)
Since the left side represents the sum of the squares of the distances from the origin to points B and C, and the right side is a constant multiplied by the same sum, we can conclude that the points B and C must lie on a circle centered at the origin.
In a circle, the sum of angles subtended by two perpendicular chords at the center is either 180° or 360°. Since the given problem involves right angles, we consider the sum of angles to be 180°.
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4.
Write an equation and solve it. Anything goes as long as you address the following points:
a. The equation must start with an 'x' variable in an exponent.
b. The equation must require logarithms to solve.
c. In the solution you must use the power rule, the product rule and the quotient rule at least once each.
d. Explain each step as you solve; which rules are you using and why?
e. What challenges did you face as you were writing your problem? Did you run into any dead ends?
My problem lies in finding an exponential equation \(N^x=N^x\) (N being any positive number) that needs all 3 rules to solve. I can come up with an equation that uses 2 of the rules but I'm stuck on adding the third. Any suggestions would be nice. Thanks
Step-by-step explanation:
hope you understand. :)
for each parallel lines. you are given the measure of one angle
Answer:
The question is not complete
You could take a 15-week, three credit college course, which requires 10 hours per week of your time for $740 per credit hour in tuition. Or during those hours you could have a job paying $10 per hour. What is the net cost of the class compared to working? Based on your answer and the fact that the average college graduate earns nearly $28,000 per year more than a high school graduate, write a few sentences giving your opinion as to whether the college course is a worthwhile experience.
The cost of the class would be $740 x 3 = $2220. If you were to work instead, at $10 per hour for 10 hours per week for 15 weeks, you would earn $1500. So, the net cost of the class would be $2220 - $1500 = $720.
In general, a college degree can lead to higher earning potential and greater career opportunities, so in most cases, it can be considered a worthwhile investment. However, the decision to take a particular class should be based on individual circumstances and goals. If the class is relevant to your future career aspirations and you can afford the cost, it may be a good investment. However, if the class is not directly related to your career goals, or you are not able to afford the cost, it may not be worth it.
I need to know the surface area for all of them.
1) In this triangular pyramid, we can see that there are some measurements. Let's enlist them:
Slant height: 14.866 yd
Height=14
height of the base: 8.66
length of the base side: 10 yd
2) So, let's find the area of that pyramid:
\(\begin{gathered} Base\:Area=\frac{a^2\sqrt{3}}{4}=\frac{10^2\sqrt{3}}{4}=25\sqrt{3} \\ Lateral\:Area=3\times(\frac{10\times14}{2})\Rightarrow210 \\ TSA=210+25\sqrt{3}\approx253.30\:yd² \end{gathered}\)Note that we have used the base times height time 1/2 for the3 lateral triangle area the base triangle is an equilateral one.
Kevin and Randy Muise have a jar containing 100 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $15.00. How many of each type of coin do they have?
Answer:
what do we know?
we know that a quarter is $0.25 and a nickel is $0.05
4x$.25 = $1
20x$0.05 = $1
and we have 84 coin
n = the number of nickels
q = the number of quarters
(1) n + q = 84 and
(2) 5*n + 25*q = 100*11.80 (always work in cents)
(3) 5*n + 25*q = 1180
Now substitute n from equation (1) into equation (3) and get
5*(84 - q) + 25*q = 1180
420 - 5*q + 25*q = 1180
20*q = 1180 - 420
20*q = 760
q = 38
Then using equation (1), plug in q
n + 38 = 84
n = 46
now check these values.
Is (.05*38 + .25*46 = 11.80)?
Is (2.30 + 9.50 = 11.80)?
Is (11.80 = 11.80)? Yes
Step-by-step explanation:
Plz Mark me as brainliest
Answer: 7 quarters and 19 nickels
Step-by-step explanation:
the rule for converting yards to feet
Answer:
1 yard=3 feet
Step-by-step explanation:
If it needs more, then 3 feet=36in.
ASAP Evaluate the expression: 20.16(0.375)
Answer:
7.56
Step-by-step explanation:
Just multiply
20.16 times 0.375
7.56
Answer:
Hii
The answer is 7.56.
Step-by-step explanation:
you multiply the value outside of the bracket with the value inside of the bracket.
what is the slope of the line shown below
Answer:
The slope is 3/4
Step-by-step explanation:
To get the slope of a line you need to do rise over run. This means how many units you go up (rise), and how many you go to the side (run). In this problem you go 3 units up and 4 units right. so, the slope would be 3/4.
ABCDEF form a regular hexagon with centre O.−−→OA=10a−−→OB=10bX is the midpoint of BC. Y is the point on AB extended such that AB : BY = 3 : 2. Express: (i) the vector −−→EX in terms of a and/or b. (ii) the vector −−→XY in terms of a and/or b.
Results:
(i) The vector −→EX in terms of a and/or b, →X = 1/2 (10b →OB + 10a →OA)
(ii) The vector −−→XY in terms of a and/or b→XY = →Y - 1/2 (10b →OB + 10a →OA)
How to express the vector?(i) We can use the midpoint formula, which states that the midpoint of a line segment is the average of the coordinates of its endpoints to express the vector −→EX in terms of a and/or b.
Since X is the midpoint of BC, we can express X as the average of the coordinates of B and C:
→X = 1/2 (→B + →C)
Since B is located at 10b units in the direction of vector →OB from O, and C is located at 10a units in the direction of vector →OA from O, we can express →B and →C in terms of a and b:
→B = 10b →OB
→C = 10a →OA
Substituting these values into the expression for →X, we get:
→X = 1/2 (10b →OB + 10a →OA)
(ii) To express the vector −→XY in terms of a and/or b, we can use the given ratio AB: BY = 3: 2.
Since AB is a vector from A to B, we can express it as →AB = →B - →A.
Substituting the expressions for →B and →A, we get:
→AB = 10b →OB - →OA
Since AB: BY = 3: 2, we can express BY as 2/3 of AB:
→BY = 2/3 (→AB)
Substituting the expression for →AB, we get:
→BY = 2/3 (10b →OB - →OA)
Finally, we can express →XY as the vector from Y to X, which is the opposite of →X to →Y:
→XY = →Y - →X
Substituting the expressions for →X and →Y, we get:
→XY = →Y - 1/2 (10b →OB + 10a →OA)
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Simplify (x-6)(-x-6)
Answer:
36 - x²
Step-by-step explanation:
(x-6)(-x-6) = (-1)(x-6)(x+6) = (-1)(x² - 36) = 36 - x²
this is based on the "well known" (a+b)(a-b) = a²-b²
Plz help I will mark branliest
The last one.
........
The length of a rectangle is nine more than triple the width. If the perimeter is 98 inches, find the dimensions. The width is ___inches. The length is ___ inches.
Given a rectangle of which its length is nine more than triple the width. The width is _10_inches. The length is 39 inches.
Let:
l = length of the rectangle
w = width of the rectangle
"The length of a rectangle is nine more than triple the width" can be translated as:
l = 9 + 3w
perimeter = 2 l + 2w
Substitute perimeter = 98 and l = 9 + 3w into the perimeter equation:
98 = 2 x (9 + 3w) + 2w
98 = 18 + 8w
8w = 98 - 18
8w = 80
w = 80/8 = 10 inch.
Substitute w = 10 into the length equation:
l = 9 + 3w
l = 9 + 3 x 10
l = 9 + 30 = 39
Therefore the correct answer is:
The width is _10_inches. The length is 39 inches.
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How long can someone shower to use only 10 gallons of water?
What is the Factors of 6
Answer:
1, 2, 3, 6
Step-by-step explanation:
Factors are numbers that divide evenly into another number.
Which answer choice best represents 3/15?
Select the Hint button to view a hint. You will get 14 points.
A: 5/6 5
B: 5/1 5
C: 6/1 5
D: 6/6 5
The equivalent fraction for the given fraction is 1/5.
What is an equivalent fraction?Equivalent fractions are two or more fractions that are all equal even though they different numerators and denominators.
The given fraction is 3/15.
The equivalent fraction is 3/15 =1/5
Therefore, the equivalent fraction for the given fraction is 1/5.
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PLEASE HELPE ME FAST
Answer:
S would now only be 3 units from R instead of 6 units from R. Move S three units to the left.
Step-by-step explanation:
Help please
Condense to a single logarithm is possible
In(6x^9)-In(x^2)
The logarithm expression can be simplified to:
In(6x^9)-In(x^2) =7·ln(6x)
How to write this as a single logarithm?There are some logarithm properties we can use here.
log(a) - log(b) = log(a/b)
log(a^n) = n*log(a)
(these obviously also apply to the natural logarithm)
Now let's look at our expression, it says that:
In(6x^9)-In(x^2)
Using the first rule, we can rewrite this as.
In(6x^9)-In(x^2) = ln(6x^9/x^2)
Now solving the quotient in the argument:
ln(6x^9/x^2) = ln(6x^7) = 7·ln(6x)
That is the expresison simplified.
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VI. In a class of 40 students, the marks obtained in Mathematics (out of 50) are as under: 44,50,44,49,42,47,45,42,44,48,49,48,47 49,47,41,45,48,41,48,41,42,47,49,49,48, 50.47.49.48.46.44.45.45.46.44.42.47.48.45 ow answer the following questions: a) b) c) d) e) Find the number of students getting more than 45 marks. Find the number of students getting less than 45 marks. Find the maximum number of students getting the same marks. Find the average marks obtained by the students in the class. Find the number of students getting more than average marks.
a) To find the number of students getting more than 45 marks, we count the students whose marks are greater than 45 in the given list.
In the given list, the students with marks greater than 45 are: 50, 49, 47, 48, 49, 48, 47, 49, 48, 50, 47, 49, 48, 46, 47, 48, 47.
Counting these numbers, we find that there are 17 students who obtained more than 45 marks.
b) To find the number of students getting less than 45 marks, we count the students whose marks are less than 45 in the given list.
In the given list, the students with marks less than 45 are: 44, 44, 42, 41, 41, 42, 41, 44, 44, 42, 45, 45, 45, 44, 45.
Counting these numbers, we find that there are 15 students who obtained less than 45 marks.
c) To find the maximum number of students getting the same marks, we look for the mark that appears most frequently in the given list.
In the given list, the marks obtained by the students are: 44, 50, 44, 49, 42, 47, 45, 42, 44, 48, 49, 48, 47, 49, 47, 41, 45, 48, 41, 48, 41, 42, 47, 49, 49, 48, 50, 47, 49, 48, 46, 44, 45, 45, 46, 44, 42, 47, 48, 45.
Counting the frequency of each mark, we find that the marks 47 and 48 appear most frequently, with a count of 6 each. Therefore, the maximum number of students getting the same marks is 6.
d) To find the average marks obtained by the students in the class, we sum up all the marks and divide by the total number of students.
Total marks = 44 + 50 + 44 + 49 + 42 + 47 + 45 + 42 + 44 + 48 + 49 + 48 + 47 + 49 + 47 + 41 + 45 + 48 + 41 + 48 + 41 + 42 + 47 + 49 + 49 + 48 + 50 + 47 + 49 + 48 + 46 + 44 + 45 + 45 + 46 + 44 + 42 + 47 + 48 + 45
= 1912
Total number of students = 40
Average marks = Total marks / Total number of students
= 1912 / 40
= 47.8
Therefore, the average marks obtained by the students in the class is 47.8.
e) To find the number of students getting more than the average marks, we count the students whose marks are greater than 47.8.
In the given list, the students with marks greater than 47.8 are: 50, 50, 49, 48, 49, 48, 49, 48, 50, 49, 49, 48, 48, 50, 49, 49, 48, 48, 47, 49, 49, 48, 50, 47,
49, 49, 48, 50, 47, 49, 49, 48, 48, 49, 48, 47, 48, 49, 49, 48, 50, 49.
Counting these numbers, we find that there are 40 students who obtained more than the average marks.
There are thirty-one rose bushes and nineteen walnut trees currently in the park. Park workers will plant more rose bushes today. When the workers are finished there will be eighty rose bushes in the park. How many rose bushes did the workers plant today?
After using the subtraction method 49 rose bushes the workers plant today.
What do mean by the subtraction method?
A method of estimating how long a psychological process will take by measuring how long it takes to react to an activity that involves the process in question and how long it takes to react to a task that doesn't, then subtracting the second from the first.
total rose bushes are 31
total bushes to be finished in the park, 80
rose bushes planted today =(80-31)
=49
Hence, the rose bushes in the worker's plant today are 49
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Solve the equation for y. Then find the value of y for each value of x.
3x-7y=13;x= -3, 0, 3
When x is -3
\(3\left(-3\right)-7y=13\quad :\quad y=-\frac{22}{7}\quad \left(\mathrm{Decimal}:\quad y=-3.14285\dots \right)\)
When x is 0
\(3\cdot \:0-7y=13\quad :\quad y=-\frac{13}{7}\quad \left(\mathrm{Decimal}:\quad y=-1.85714\dots \right)\)
When x is 3
\(3\cdot \:3-7y=13\quad :\quad y=-\frac{4}{7}\quad \left(\mathrm{Decimal}:\quad y=-0.57142\dots \right)\)
30 POINTS!! NEED HELP ASAP
The solution to 2x-5 = 27 is also a solution of which of the following equations?
3x2 - 31
3+5 x=58
27- 2 x=5
2x+3 = 35
Answer: It’s B
Step-by-step explanation:
STREAM EXPENSIVE BY NICKI MINAJ !
The graph below shows the relationship between the number of months different students practiced boxing and the number of matches they won:
The title of the graph is Boxing Matches. On x axis, the label is Number of Months of Practice. On y axis, the label is Number of Matches Won. The scale on the y axis is from 0 to 21 at increments of 3, and the scale on the x axis is from 0 to 12 at increments of 2. The points plotted on the graph are the ordered pairs 0, 3 and 1, 6 and 2, 7 and 3, 9 and 4, 11 and 5, 13 and 6, 14 and 7, 16 and 8, 17 and 9, 18 and 10,20. A straight line is drawn joining the ordered pairs 0, 4 and 2, 7.1 and 4, 11 and 6, 13.5 and 8, 17 and 10, 20.5.
Part A: What is the approximate y-intercept of the line of best fit and what does it represent? (5 points)
Part B: Write the equation for the line of best fit in the slope-intercept form and use it to predict the number of matches that could be won after 13 months of practice. Show your work and include the points used to calculate the slope. (5 points)
Answer:
(a) y intercept is approximately 4.3
(b) \(y = 1.5x+4.5\)
Step-by-step explanation:
Given
See attachment for graph
Solving (a) The y intercept
This is the point where \(x =0\)
From the attached graph; By observation
\(y \approx 4.3\) when \(x =0\)
So, the y intercept is approximately 4.3
Solving (b): The equation of best fit.
First, calculate the slope of the line using:
\(m = \frac{y_2 - y_1}{x_2 - x_1}\)
Where
\((x_1,y_1) = (9,18)\)
\((x_2,y_2) = (8,16.5)\)
So:
\(m = \frac{16.5- 18}{8 - 9}\)
\(m = \frac{-1.5}{- 1}\)
\(m = 1.5\)
The equation is then calculated using:
\(y =m(x - x_1) + y_1\)
Where: \(m = 1.5\) and \((x_1,y_1) = (9,18)\)
\(y = 1.5(x - 9) + 18\)
\(y = 1.5x - 9*1.5 + 18\)
\(y = 1.5x - 13.5 + 18\)
\(y = 1.5x+4.5\)
Find the difference between the actual quotient and the estimated quotient of 54,114÷29 . (Dividend is rounded off to nearest thousand and divisor to nearest ten)
The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.
To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.
Actual quotient:
Dividing 54,114 by 29, we get:
54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)
Estimated quotient:
Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:
54,000 ÷ 30 = 1,800
Difference between actual and estimated quotient:
Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379
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I NEED HELP WITH STATISTICS
A. The null hypothesis H₀ and the alternative hypothesis H₁ are:
H₀: μ = 35 minutes H₁: μ > 35 minutes
B. If the consultant decides not to reject the null hypothesis, she might be making a Type II error.
C. A Type II error would be failing to reject the hypothesis that μ is = to 35 minutes when, in fact, μ is 43 minutes.
What is a Type II error?A Type II error occurs when the null hypothesis is false, but the test does not reject it.
In this case, the consultant would be concluding that the mean shopping time is 35 minutes, when in fact it is greater than 35 minutes.
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What is the slope of a line perpendicular to a line with slope -8
Answer:
1/8
Step-by-step explanation:
You would need to get the reciprocal of negative eight and then change the sign so you would get 1/8