The number of the different outfits do David have to choose is 768.
Here we will use the concept of Combinations,
Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.
Different outfits do Damian have to choose, will be;
⇒ 8C₁×4C₁×8C₁×3C₁
⇒ 8×4×8×3
⇒ 768
Hence, the number of the different outfits do David have to select is 768.
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a certain forest covers an area of 1700km^(2). Suppose that each year this area descreases by 7.5%. What will the area be after 11 years?
round your answer to the nearest square kilometer.
The area of the forest after 11 years will be 298 km².
To calculate the area of the forest after 11 years, we need to decrease the initial area of 1700 km² by 7.5% each year for 11 years.
First, let's calculate the decrease in area for one year:
Decrease in area for one year = 7.5% of 1700 km²
7.5% of 1700 km² = (7.5/100) × 1700 km²
= 127.5 km²
Now, we can calculate the total decrease in area over 11 years:
Total decrease in area over 11 years = 11 × 127.5 km² = 1402.5 km²
Finally, we can subtract the total decrease in area from the initial area to get the area of the forest after 11 years;
Area of the forest after 11 years = Initial area - Total decrease in area
= 1700 km² - 1402.5 km²
= 297.5 km²
Therefore, Rounding to the nearest square kilometer, the area of the forest after 11 years will be approximately 298 km².
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What is the meaning of "there is some [tex]k \in I[/tex] such that [tex]D_{i}\subseteq D_{k}[/tex] and [tex]D_{j}\subseteq D_{k}[/tex]?
The given statement "there is some k∈I such that [tex]D_{i}[/tex]⊆[tex]D_{k}[/tex] and [tex]D_{j}[/tex]⊆[tex]D_{k}[/tex]means that there is a set [tex]D_{k}[/tex] in a collection of sets I that contains all the elements of both sets [tex]D_{i}[/tex] and [tex]D_{j}[/tex].
For example, let's say we have a collection of sets I that includes sets A, B, C, D, E, and F. If we have two sets [tex]D_{i}[/tex] and [tex]D_{j}[/tex], where [tex]D_{i}[/tex] is the set of all even numbers, and [tex]D_{j}[/tex] is the set of all positive integers less than or equal to 10, then we can say that there exists a set [tex]D_{k}[/tex] in I that contains both [tex]D_{i}[/tex]and [tex]D_{j}[/tex] as subsets.
In this case, the set [tex]D_{k}[/tex] could be the set of all even positive integers less than or equal to 10. This set contains all the elements of [tex]D_{i}[/tex] and [tex]D_{j}[/tex], making them both subsets of [tex]D_{k}[/tex]. The statement "there is some k belongs I such that [tex]D_{i}[/tex] is a subset of [tex]D_{k}[/tex] and [tex]D_{j}[/tex] is a subset of [tex]D_{k}[/tex]" is a way to express this relationship between the sets.
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Plot the coordinates on the number line provided and then find the coordinate of the indicated point
on a number line that partitions the segment into the given ratio.
A is at 1, and B is at 10. Find the point, T, so that T is two-thirds of the distance from A to B.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3
4 5 6 7 89
+
10
Answer:
t = 6.8
Explanation:
We know that A is at 1, B is at 10, so that is where we place those two.
First, we need to know what 2/3 of 10 is because the distance between A and B is 10.
Solving 2/3 of 10:
_____________________
- Divide 10 by the denominator, 3
10 ÷ 3 = 3.3333......
- Multiply 3.3333..... by 2
3.3333..... x 2 = 6.6666666666667
or about 6.8 if we round up, which is prefered in these scenarios
Now that we know what 2/3 of 10 is, we can use that number as where to put it on the number line.
So t = 6.8
Hope this helps :)
F(x) = 2^x
Elija todas las siguientes afirmaciones que describen el gráfico.
A. Cuando x tiende a infinito negativo, f(x) tiende a 0.
B. Cuando x tiende a infinito negativo, f(x) tiende a infinito.
OC. Cuando x tiende a infinito, f(x) tiende a 0.
OD. Cuando x tiende a infinito, f(x) tiende a infinito.
By analyzing the end behavior of the function we can see that the correct options are A and D.
Which statements are true for the given function?Here we have the exponential function:
[tex]F(x) = 2^x[/tex]
This is an exponential growth, this means that as x increases also does the function, then the end behavior of the function is:
as x → ∞, f(x) → ∞
And when x is a really large negative number, the function tends to zero, then we have:
as x →-∞, f(x) → 0
Then the correct options are A and D.
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Please please help me with my work thank you
The match to A line that has a slope of 5/3 and a y-intercept of 4 is 2y - x = -4.
We are given that;
The four equations to match from
Now,
Using the slope-intercept form, we can plug in m = 3/2 and b = -8:
y = (3/2)x - 8
This equation matches with y = 3/2x - 5 if we multiply both sides by 2:
2y = 3x - 16
Therefore, the correct equation is 2y - x = -16.
A line that contains the points (0,-2) and (4,0)
m = (0 - (-2)) / (4 - 0) m = 2 / 4 m = 1/2
Then we can plug in m = 1/2 and any of the given points to find b. For example, using (0, -2), we have:
-2 = (1/2)(0) + b -2 = b
Therefore, the equation is:
y = (1/2)x - 2
This equation matches with -5x - 3y = -12 if we multiply both sides by -6:
6y = -3x + 12
Therefore, the correct equation is -5x - 3y = -12.
A line that contains the y-intercept (0-2) and the slope of -3/4
Using the slope-intercept form, we can plug in m = -3/4 and b = -2:
y = (-3/4)x - 2
This equation matches with y = -3/4x - 2.
A line that has a slope of 5/3 and a y-intercept of 4
Using the slope-intercept form, we can plug in m = 5/3 and b = 4:
y = (5/3)x + 4
This equation matches with 2y - x = -4 if we multiply both sides by 3:
3y = (5/3)x + 12
Therefore, the correct equation is 2y - x = -4.
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math hw for tonight
help solve this problem! Thank you!
ap cal bc
Answer:
3t^2i + 2tj is the correct answer.
Find the total cost for the month in dollars. The federal tax is 3%. Use the figure below.
Monthly phone service plan is $52.00. Four lines and 3,487 minutes are used.
Answer:
The total cost per month is $190.76 to the nearest cent.
Step-by-step explanation:
From the given table, the monthly service plan costing $52.00 is:
Monthly Service Plan = $52.00Number of included minutes per month = 2,000 minutesCost per additional line per month = $21.99Overage per minute rate = $0.06The base calling plan includes two lines.
Therefore, for 4 lines, we will need to pay for 2 additional lines per month:
⇒ $21.99 × 2 = $43.98 per month
If 3,487 minutes are used per month, then the overage of minutes is:
⇒ 3487 - 2000 = 1487 minutes per month
As the overage rate is $0.06 per minute, then the cost of the additional minutes is:
⇒ 1487 × $0.06 = $89.22 per month
Therefore, the total cost per month before tax is:
⇒ $52.00 + $43.98 + $89.22 = $185.20
To apply the federal tax of 3%, multiply the total cost by 1.03:
⇒ $185.20 × 1.03 = $190.756 = $190.76 (nearest cent)
Therefore, the total cost per month is $190.76 to the nearest cent.
Circle the students error in the problem below and rewrite what correct step should be
The students error is in step 3 and the correct solution is g(x) = 2x² + 4x - 4
Circling the students errorFrom the question, we have the following parameters that can be used in our computation:
The steps to solve the expression
From step 2 to step 3, we have
g(x) = 2(x + 1)(x + 1) - 6
g(x) = 2(x² + 1x + 1) - 6
The step 3 is incorrect
Because when the expression is expanded, we have
g(x) = 2(x² + 2x + 1) - 6
This gives a solution of
g(x) = 2x² + 4x - 4
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quadratic equations. A positive real number is 4 less than another. When 8 times the larger is added to the square of the smaller, the result is 48.
2. Solve 4.3(n + 6) > 47.3. Then graph the solution.
Answer: n>5
Step-by-step explanation:
PLEASE HELP ME !!! I NEED THIS TO GRADUATE
Find the interquartile range using the following.
Minimum: 1
Q1: 3
Median: 5
Q3: 7
Maximum: 9
A. 8
B. 4
C. 5
D. 10
Answer: B. 4
Step-by-step explanation: The interquartile range is just the distance in between the upper and lower quartiles. Therefore, to find the interquartile range, the equation in this case is 7 - 3, which equals 4.
use your knowledge of transformations to find matching graph f (x) = ½ √x - 1
Answer:
Step-by-step explanation:
down 1
compress 1/2
how much cardboard is needed to make the single slice pizza box shown
that would be 5 pieces of cardboard needed
If the price of a particular chocolate bar is increased by 20%, and it used to be $2, what is the new price after the increase?
What is the initial value of Y=2x+3
Answer:3
Step-by-step explanation: Initial value = y-intercept
please help me i relly need help
Answer:
h(x) = 3·2^x
Step-by-step explanation:
You want the equation of the exponential curve h(x) = a·b^x when it goes through the points (0, 3) and (1, 6).
PointsWhen x=0, the equation is ...
h(0) = a·b^0 = a
We know that h(0) = 3, so a = 3.
When x=1, the equation is ...
h(1) = 3·b^1 = 3b
We know that h(1) = 6, so 3b = 6, or b = 2.
The equation is h(x) = 3·2^x.
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What is the slope of the line that passes through
the points (2,-4) and (2, 4)?
A. -3 B.0. C.8. D. Undefined
The line is a vertical line, then the correct option is D, the slope is undefined.
How to find the slope of the line?A general linear equation can be written as:
y = a*x + b
Where a is the slope, b is the y-intercept, and x is the variable.
If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope of that line is given by the formula:
a = (y₂ - y₁)/(x₂ - x₁)
Here we know that the two points are (2, -4) and (2, 4)
Replacing that we would have a problem, that is because we have the same x-value in both points.
Then we have a vertical line at x = 2.
That line has no defined slope, thus, the correct option is D.
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Which choices are equivalent to the expression below? Check all that apply.
4√3
A. 48
B. 12.4
C. √24√2
D. 3 16
E. 4.3
F. 48
The choices that are equivalent to the expression 4√3 will be ✓48 and ✓24.✓2.
How to explain the expressionIt is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.
In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
4✓3 will be:
= ✓4² × ✓3
= ✓48
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∠A and ∠ � ∠B are vertical angles. If m ∠ � = ( 2 � − 2 ) ∘ ∠A=(2x−2) ∘ and m ∠ � = ( 3 � − 15 ) ∘ ∠B=(3x−15) ∘ , then find the value of x.
The calculated value of x if ∠A and ∠B are vertical angles is 13 degrees
How to find the value of x.From the question, we have the following parameters that can be used in our computation:
∠A = (2x − 2)
∠B = (3x − 15)
Since the ∠A and ∠B are vertical angles, then they are congruent angles
So, we have
3x - 15 = 2x - 2
Evaluate the like terms
So, we have
x = 13
Hence, the solution is x = 13
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Molly has four t-shirts in her closet that she plans to wear over the next four days without wearing the same one twice. She has a blue, green, yellow, and black shirt. What are the chances that she will wear the black shirt the first day?
Write your answer as an exact fraction which is reduced as much as possible.
Answer:
Molly has four choices for which shirt to wear on the first day, and one of those choices is the black shirt. So the probability that she will wear the black shirt on the first day is 1/4. Therefore, the answer is 1/4.
Step-by-step explanation:
107/103 X 101/100 =
What is 107 over 103 times 101 over 100
107 over 103 times 101 over 100 would result in 10807/10300.
Mathematical operationsIn order to multiply the fractions 107/103 and 101/100, we can simply multiply their numerators together and their denominators together:
(107/103) x (101/100) = (107 x 101) / (103 x 100)
Now we can simplify this fraction by finding the greatest common factor of the numerator and denominator and dividing both by it:
(107 x 101) / (103 x 100) = 10807 / 10300
Therefore, 107/103 times 101/100 simplifies to 10807/10300.
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y is less than or equal to two-thirds times x plus 1 y is greater than negative one-fourth times x plus 2 Which ordered pair is included in the solution to this system? (6, −2) (6, 0.5) (6, 5) (6, 8)
Answer:(6, −2), (6, 0.5) I’m pretty sure
answer quick i need done
The new vertices of the triangle after moving the triangle 5 units down, are A(1,-7), B(9,-7), and C(5,-3). So, correct option is B.
To determine the coordinates of the triangle after it is translated 5 units down, we need to subtract 5 from the y-coordinates of each vertex.
Let's start with vertex A(1,-2). If we subtract 5 from -2, we get -7. Therefore, the new coordinates of vertex A are (1,-7).
Next, let's look at vertex B(9,-2). Again, if we subtract 5 from -2, we get -7. So the new coordinates of vertex B are (9,-7).
Finally, let's consider vertex C(5,2). If we subtract 5 from 2, we get -3. So the new coordinates of vertex C are (5,-3).
In this case, we are moving the triangle 5 units down, which means that we are subtracting 5 from the y-coordinates of each vertex. This is a common transformation in geometry, and it's important to be familiar with it when working with shapes and figures in the Cartesian plane.
So, correct option is B.
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An online television company is sending out surveys to rank 10 TV-show genres watched. What is the probability that you guess the top 3 genres correctly and in the correct order?
Write your answer as an exact fraction which is reduced as much as possible.
Answer:
The probability of guessing the first genre correctly is 1/10. After guessing the first genre, the probability of guessing the second genre correctly is 1/9. Similarly, the probability of guessing the third genre correctly is 1/8. Therefore, the probability of guessing the top 3 genres correctly and in the correct order is:
1/10 * 1/9 * 1/8 = 1/720
So the exact probability is 1/720, which is already reduced to its simplest form.
A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),}. Find the probability of getting two numbers whose sum is greater than 9. Group of answer choices
The probability of getting two numbers whose sum is greater than 9 = 5/36
We know that the probability is nothing but the number of favourable outcomes divided by the total number of outcomes.
Here, a single die is rolled twice.
and we get the set of 36 equally likely outcomes.
so, the total number of outcomes n(S) = 36
Let us assume that event A: getting two numbers whose sum is greater than 9
A = {(4, 6), (5,5), (5, 6), (6, 4), (6, 5)}
n(A) = 5
Using above formula of probability,
P(A) = n(A)/n(S)
P(A) = 5/36
Thus the required probability = 5/36
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Please help me PLEASE ANYEONE?!!!?!!
Step-by-step explanation:
1/3 ÷ 3
= 1/3 ÷ 3/1
= 1/3 X 1/3 = 1/9
Similarly
1/4 ÷ 5 = 1/4 X 1/5 = 1/20
The change in water level of a pond is shown in the table.
Week
1
2
3
4
5
Water level (inches)
-1 1/4
1 3/8
2 1/2
-1 5/8
-1 3/4
Between which two weeks did the water level change the most? Calculate the change.
Between Weeks 3 and 4, the water level varied the greatest.
To determine which two weeks had the greatest change in water level, we need to find the difference between each pair of consecutive weeks and identify the largest difference.
Here are the differences between consecutive weeks:
Week 1 to Week 2: (1 3/8) - (-1 1/4) = 2 5/8
Week 2 to Week 3: 2 1/2 - 1 3/8 = 1 1/8
Week 3 to Week 4: (-1 5/8) - 2 1/2 = -4 1/8
Week 4 to Week 5: (-1 3/4) - (-1 5/8) = -1/8
The largest difference is between Week 3 and Week 4, with a difference of 4 1/8 inches.
Therefore, the water level changed the most between Week 3 and Week 4.
Note that the differences are calculated by subtracting the water level of the earlier week from the water level of the later week.
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A painter needs 3/8 gallon of green paint to finish a job. He has 5/8 gallon of red paint. He has 1/2 gallon more red paint than green paint. Can he finish the job?
Answer: 17/24 for both jobs
Step-by-step explanation:
geometry pls helpppppp
A graph of triangle TOW is shown below.
A graph of triangle T'O'W, the image of ΔTOW after a reflection in the y-axis is shown below.
The coordinates of ΔT'O'W are: T' (5, 6), O' (-1, 8), and W' (4, -2).
What is a reflection over the y-axis?In Mathematics and Geometry, a reflection over or across the y-axis is represented by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over or across the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.
Next, we would apply a reflection over or across the x-axis;
(x, y) → (-x, y)
T (-5, 6) → (-(-5), 6) = T' (5, 6)
O (1, 8) → (-(-1), 8) = O' (-1, 8)
W (-4, -2) → (-(-4), -2) = W' (4, -2)
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