The time it will take for Helen and Reid to meet is given as follows:
3/7 of an hour = 26 minutes.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:
v = d/t.
The parameters for this problem are given as follows:
Distance of 3 miles.Relative velocity of 7 miles, as they are moving in opposite directions, and 4 + 3 = 7.Hence the time is obtained as follows:
7 = 3/t
7t = 3
t = 3/7 of an hour = 26 minutes.
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The bar graph shows the number of games a soccer team played each month. Use the data to find each listed value.
Median =
Lower quartile =
Upper quartile =
Interquartile range =
By using the data from the bar graph, each of the statistical value are as follows;
Median = 6.
Lower quartile = 4.
Upper quartile = 7.5.
Interquartile range = 3.5
How to calculate the median number of game?From the information provided in the bar graph above, we can logically deduce the following data set:
Data set = {3, 5, 6, 7, 8}
Median = 6.
For Q₁ of the lower half of the data set, we have:
Lower quartile, Q₁ = {3, 5}
Lower quartile, Q₁ = (3 + 5)/2
Lower quartile, Q₁ = 8/4 = 4.
For Q₃ of the upper half of the data set, we have:
Upper quartile, Q₃ = {7, 8}
Upper quartile, Q₃ = (7 + 8)/2
Upper quartile, Q₃ = 15/2 = 7.5.
Mathematically, interquartile range (IQR) is the difference between lower quartile (Q₁) and upper quartile (Q₃):
IQR = Q₃ - Q₁
IQR = 7.5 - 4
IQR = 3.5
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\text{Determine the values of all positive} \ k \ \text{ for which the series}Determine the values of all positive k for which the series \text{will converge. } \ \ \text{ Express your answer in interval notation. }will converge. Express your answer in interval notation. LaTeX: \displaystyle \underset{n
The best way is to use the Ratio Test to see that the series = ∑∞ₙ₋₁ n/5ⁿ converges.
In mathematics, convergence definition is the property (some described by myriad series and functions) that it approaches its limit more and more distinctly as the arguments (variables) of the function increase or decrease, or as the number of terms in the series increases.
For example, the function y = 1/x converges to zero as x increases. Even in this case, the final value of x doesn't affect the value of y to actually be zero, and the marginal value of y is zero, since y can be made arbitrarily small by choosing a large enough "x". The line y = 0 (x-axis) is known as the asymptote of the function.
According to the Question:
Let aₙ= n/5ⁿ. If lim(n→∞)
|an+1|/ |an| <1, the Ratio Test will imply that
∑∞ₙ₋₁ aₙ = ∑∞ₙ₋₁ n/5ⁿ converges.
Now,
aₙ₊₁ = n + 1/ 5ⁿ⁺¹
= n + 1 /5.5ⁿ.
Therefore,
since these terms are positive,
|aₙ₊₁|/|aₙ| = n + 1 /5⋅5ⁿ
⇒ n +1/ 5ⁿ → 1/5 as n→∞
Hence,
∑∞ₙ aₙ = ∑∞ₙ₋₁ n/5ⁿ converges.
Full Question:
How do you test the series (n/5ⁿ ) from n = 1 to infinity for convergence? Determine the values of all positive, for which the series. Determine the values of all positive k for which the series. Express your answer in interval notation will converge. Express your answer in interval notation.
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suppose sean makes 10 tables a month, each of which he can sell for $200. given that the average cost of making each table is $150, should sean make more or fewer tables each month?
It's impossible to say Sean should base his decision on the marginal cost and marginal benefit of creating another table. The marginal cost of making a table is not the same as the average cost of making a table. As a result, there is insufficient information to determine what Sean should do.
The opportunity cost of an activity is the value of what must be sacrificed in order to engage in the activity (plus the cost). A cost that cannot be recovered at the time a decision must be made.
The science of decision-making is often used as a crude definition of economics. This stems from the fact that economics is frequently concerned with making the best decision in the most efficient manner. One way to quantify this is to consider total costs and total benefits.
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a. what's the probability that she chooses to teach both classes? b. what are the odds in favor of her choosing to teach both classes?
The odds of an event are calculated by taking the number of positive outcomes and dividing it by the number of negative outcomes.the odds in favor of her teaching both classes are 15:85 or 1:5.5.
a. The probability that she chooses to teach both classes is 15%.
b. The odds in favor of her choosing to teach both classes are 1:5.5.
a. The probability of an event is calculated by taking the number of positive outcomes and dividing it by the total number of outcomes. In this case, the professor has a 50% chance of teaching the first class and a 30% chance of teaching the second class. Therefore, the probability of her teaching both classes is 0.5 x 0.3 = 0.15 or 15%.
b. The odds of an event are calculated by taking the number of positive outcomes and dividing it by the number of negative outcomes. In this case, there is a 15% chance of her teaching both classes and an 85% chance of her not teaching both classes. Therefore, the odds in favor of her teaching both classes are 15:85 or 1:5.5.
The complete question is :
A professor is deciding whether to teach two classes. There is a 50% chance that she will teach the first class and a 30% chance that she will teach the second class.
a. What's the probability that she chooses to teach both classes?
b. What are the odds in favor of her choosing to teach both classes?
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if she drove back home using the same path she took out to the university and arrives 7.1 h after she first left home, what was her average speed for the entire trip, in kilometers per hour?
Her average speed for the entire trip, in kilometers per hour, is equal to 2d / (7.1 * 3600) * 3600 km/h
Let's assume that the total distance of the round trip is d kilometers and that she drove at a constant speed of v km/h for the entire trip. The time it takes for her to travel the entire distance at speed v is given by t = d/v.
Since she drove back home using the same path she took out to the university, her average speed for the entire trip must be equal to her speed on the way out and back. Therefore, the total time it took for her to complete the round trip is 2t = 2d/v.
Since the total time it took for her to complete the round trip is 7.1 hours, we can set up an equation:
2d/v = 7.1 hours
Converting hours to seconds and solving for v, we have:
v = 2d / (7.1 * 3600) km/s
Finally, converting to km/h, we get:
v = 2d / (7.1 * 3600) * 3600 km/h
Therefore, her average speed for the entire trip, in kilometers per hour, is equal to 2d / (7.1 * 3600) * 3600 km/h
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Cost and revenue functions. The operating cost of
a company can be approximately modelled as
C(x) = 17- 8x - 2x², where x is the time in years.
Given that its revenue function is R(x) = 5 - 3x,
find the number of months during which the
company is not making a profit.
The number of months for which the company made no profit is 18 months.
What is profit?Generally speaking, a product's profit is defined as the sum received from sales, which should exceed the product's cost price. It is the gain from any type of commercial activity. In other words, if a product's selling price (SP) is higher than its cost price (CP), there has been a gain or profit. It explains the monetary gain realised if the revenue from the company activity is greater than the costs, such as taxes and expenses, involved in maintaining the business activity.
The cost function is given as: C(x) = 17- 8x - 2x²
The revenue function is given as: R(x) = 5 - 3x
Profit = Revenue - Cost
For no profit the equation becomes:
5 - 3x - 17 + 8x + 2x² = 0
2x² + 5x - 12 = 0
2x² + 8x - 3x - 12 = 0
2x(x + 4) - 3(x + 4) = 0
2x - 3 = 0 and x + 4 = 0
x = 3/2 and x = -4
Since, month cannot be a negative quantity we have x = 3/2.
That is 3/2 (12) = 18 months.
The number of months for which the company made no profit is 18 months.
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Find the length of YZ
The length of YZ in the triangle is 12.5 units
How to determine the length of YZFrom the question, we have the following parameters that can be used in our computation:
The triangle
On the triangle, we have the following equivalent ratio
YZ : 5 = 10 : 4
Express as fraction
So, we have
YZ/5 = 10/4
This gives
YZ = 5 * 10/4
Evaluate
YZ = 12.5
Hence, the length is 12.5 units
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what 2848x4848x495948+3858 / 384
if your still awake doing school stuff, take a break if you want you can talk with me in ch.at
The result of the expression 2848 × 4848 × 495948 + 3858 / 384 is equal to 684,114,389,002.05 approximately to 2 decimal place using PEDMAS
What is PEDMASP – Parentheses First: B – Brackets First
E – Exponents
D – Division
M – Multiplication
A – Addition
S – Subtraction
The expression 2848 × 4848 × 495948 + 3858 / 384 can be simplified as follows:
2848 × 4848 × 495948 + 3858 / 384
(2848 × 4848) × 495948 + (3858 / 384)
13807104 × 495948 + 10.0469
6811753718272 + 10.0469
684,114,388,992 + 10.0469
684,114,389,002.05
Therefore, the result from applying the right order of mathematics operations for the expression 2848 × 4848 × 495948 + 3858 / 384 is equal to 684,114,389,002.05 approximately to 2 decimal place using PEDMAS.
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What is −203 − (−136)?
I need help! :((
Answer:
-67
Step-by-step explanation:
- 203 - (-136)
The 2 minuses cancel out each other, turning it into a plus sign.
-203 + 136 = -67
Basic addition
Step-by-step explanation:
Because there is a double negative in between 203 and 136 that would turn into a positive
So
-203+136
Now because 203 is negative you would take 203 and subtract 136 to get 67
Because 136 is less then 203 it would still be negative
So
The answer is -67
A rectangle has a length of 12 inches and a width of 5 inches whose sides are
changing. The length is increasing by 9 in/sec and the width is growing at 2 in/sec.
What is the rate of change of the area?
The rate of change of the area of the rectangle as required in the task content is; 87 in²/sec.
By what rate if the area of the Rectangle changing?It follows from the task content; The length is increasing by 9 in/sec which represents 75% of the initial length and the width is growing at 2 in/sec which represents 40% of the initial width.
Since the area of a rectangle is; A = l × w
A (initial) = 60in².
Therefore, the new area of the rectangle after every second is;
Area (new) = 1.75l × 1.4w
Area (new) = 2.45 lw
This therefore translates to the fact that the area of the rectangle is increasing by a factor of 1.45 which is equivalent to 145% of initial Area.
Therefore, the area is increasing by 1.45 × 60 = 87in²/sec.
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At what point does the line given by the following equation cross the y-axis?
y = -2x + 3
The given line y = -2x + 3 will cross the y-axis at (0, 3).
Coordinate plane:A coordinate plane is a two-dimensional plane that consists x-axis and a y-axis. These are perpendicular to each other and will be intersected at the point called the origin.
The coordinates of the point that lies on the y-axis are (0, y), Similarly, the coordinates of the point that lies on the x-axis are (0, x).
Here we have
The equation of the line is y = -2x + 3
To find the required point take x = 0
=> y = -2(0) + 3
=> y = 0 + 3
=> y = 3
Therefore,
The given line y = -2x + 3 will cross the y-axis at (0, 3).
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Determine the nature of the roots of ax² + bx + c = 0 if a > 0, b < 0 and c < 0
Answer: Roots are real and distinct
Step-by-step explanation:
a = +ve b = -ve c = -ve
determinant = +ve
if determinant is positive then roots are real and distinct
Iara makes salad dressing by mixing 8 88 spoonfuls of oil and some vinegar. The tape diagram shows the ratio of oil to vinegar. A tape diagram with 2 tapes of unequal lengths. The first tape has 2 equal parts. A curved bracket above the first tape is labeled Oil. The second tape has 1 part of the same size as in the first tape. A curved bracket below the second tape is labeled Vinegar. A tape diagram with 2 tapes of unequal lengths. The first tape has 2 equal parts. A curved bracket above the first tape is labeled Oil. The second tape has 1 part of the same size as in the first tape. A curved bracket below the second tape is labeled Vinegar. Complete the table. Original ratio Amount (spoonfuls) Oil 8 88 Vinegar 1 11 Total dressing 3 33
Answer:
Step-by-step explanation:
Based on the information in the tape diagram and table, we can see that the ratio of oil to vinegar in Iara's salad dressing is 8 to 1. This means that for every 8 spoonfuls of oil, she uses 1 spoonful of vinegar.
To calculate the amount of oil and vinegar in the dressing, we can use the following formula:
amount = original ratio * total amount of dressing ÷ (original ratio + 1)
For the oil, the formula would be:
oil amount = 8 * 33 ÷ (8 + 1) = 8 * 33 ÷ 9 = 88 spoonfuls
And for the vinegar, the formula would be:
vinegar amount = 1 * 33 ÷ (8 + 1) = 1 * 33 ÷ 9 = 11 spoonfuls
So the final answer is:
Oil: 88 spoonfuls
Vinegar: 11 spoonfuls
2x+y=18 and y=4x+6 using substitioiuntion
so your problem is 2x+y=18 and y=4x+6
solution
solve for the first variable in one of the equations then substitute the result into the other equation
point form:
(2,14)
equation form
x=2, y=14
5. Are the triangles similar?
If yes, which angles are congruent?
The triangles ΔABC and ΔDEF are congruent with each other by the SAS postulate. And ∠ABC = ∠DEF, ∠BCA = ∠EFD, ∠CAB = ∠FDE, and AB / DE = BC / EF = CA / FD.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
In triangles ΔABC and ΔDEF, then we have
AB = DE
BC = EF
∠ABC = ∠DEF = 92°
Then the triangles ΔABC and ΔDEF are congruent with each other. Then we have
∠ABC = ∠DEF
∠BCA = ∠EFD
∠CAB = ∠FDE
And the corresponding ratios are given as,
AB / DE = BC / EF = CA / FD
The triangles ΔABC and ΔDEF are congruent with each other by the SAS postulate.
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A teacher plans to use a 40-inch long roll of string to form a border around a rectangular space on her bulletin board reserved for student use. What is the maximum amount of space, in square inches, that she can reserve on her bulletin board using this roll of string?
The maximum amount of space that the teacher can reserve on her bulletin board using the 40-inch long roll of string is 400 square inches.
A rectangle is a two-dimensional shape with four sides and four right angles. It is characterized by having two equal sides that are parallel to each other and two equal sides that are perpendicular to the first two sides.
First, let's consider the perimeter of the rectangle. The perimeter is the total length of the four sides of the rectangle.
So, if we use the entire 40-inch long roll of string to form the border, it will equal the perimeter of the rectangle. We can represent the length and width of the rectangle using variables "l" and "w", respectively.
The perimeter of the rectangle can be calculated using the formula: P = 2l + 2w.
Now, we can set the perimeter equal to 40 inches and solve for l and w.
P = 40
2l + 2w = 40
l + w = 20
Next, we want to find the maximum area of the rectangle. The area of a rectangle can be calculated using the formula: A = l * w.
So, to find the maximum area, we need to maximize the product of l and w. This can be done by setting l and w equal to half of the perimeter, or 20 inches each.
l = w = 20
A = l * w
A = 20 * 20
A = 400 square inches
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The area of a rhombus is 360 sq cm if one of its diagonal is 40 cm , find the other diagonal
According to the area of rhombus and length of one diagonal, the length of other diagonal is 10.5 cm.
The formula for the length of the diagonal is as follows -
Area = product of diagonal 1 and diagonal 2/2
Keep the values in formula to find the length of diagonal
360 = 40 × diagonal 2/2
Rewriting the equation with diagonal 2 on Left Hand Side of the equation
Diagonal 2 = (360 × 2)/40
Performing multiplication on Right Hand Side of the equation
Diagonal 2 = 420/40
Performing division on Right Hand Side of the equation
Diagonal 2 = 10.5 cm
Thus, the diagonal 2 is 10.5 cm.
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Given that 6048 = 2^5 • 3^3 • 7,
find the smallest possible integer value of n for 6048y to be a perfect cube number, giving your answer as the product of its prime factors.
Answer:
6048 should be multiplied by 98.
Step-by-step explanation:
6048 = 2⁵ * 3³ * 7
To make 6048 a perfect cube, 6048 should be multiplied by 2 * 7 * 7.
2* 7 *7 = 98
Check: 6048 * 98 = 592704
592704 = 2⁶ * 3³ * 7³
[tex]\sqrt[3]{592704}= 2 * 2 * 3 * 7[/tex]
= 84
Write an equation of the parabola in vertex form. Round any decimal to the nearest thousandth.
The required form of a parabola in vertex form is y = a(x - h)² + k.
What is a parabola?A parabola is a cross-section cut out of the cone and represented by an equation.
Here,
The standard form of a parabola in vertex form is:
y = a(x - h)² + k
where (h, k) is the vertex of the parabola and a determines the direction of opening (a > 0 for an upward-facing parabola and a < 0 for a downward-facing parabola). The coefficient also determines the shape and steepness of the parabola.
Thus, the required form of a parabola in vertex form is y = a(x - h)² + k.
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Unit 8 Right triangles and trigonometry Homework 3
The value of x for each triangle are:
x = 6√7x = 11.6x = 21.3x = 3√29; y = 6.46; z = 2.4Please note that I only answer the circled number and please refer to the attached picture for any additional annotations.
Note that each triangles are a right angled triangle. We use phytagoras theorem to find any unknown side of a triangle.
Triangle 1x² = 14² + y²
a² = y² + 4²
x² + a² = 18²
x² + a² = 18²
(14² + y²) + (y² + 4²) = 18²
14² + 2y² + 4² = 18²
196 + 2y² + 16 = 324
2y² = 112
y² = 56
x² = 14² + y²
x² = 196 + 26
x² = 252
x = 6√7
Triangle 2(x + 28)² = a² + b²
a² = 28² + 18²
b² = x² + 18²
(x + 28)² = a² + b²
(x + 28)² = (28² + 18²) + (x² + 18²)
x² + 56x + 784 = 1432 + x²
56x = 648
x = 11.6
Triangle 3a² = b² + (x - 12)²
b² = 16² - 12²
x² = 16² + a²
x² = 16² + a²
x² = 16² + (b² + (x - 12)²)
x² = 16² + [(16² - 12²) + (x - 12)²]
x² = 256 + 112 + (x - 12)²
x² = 368 + x² - 24x + 144
24x = 512
x = 21.3
Triangle 4x² = 15² + 6²
x² = 261
x = 3√29
(15 + z)² = x² + y²
y² = z² + 6²
(15 + z)² = x² + y²
(15 + z)² = 261 + (z² + 6²)
225 + 30z + z² = 261 + z² + 36
225 + 30z + z² = 297 + z²
30z = 72
z = 2.4
y² = z² + 6²
y² = 36 + 5.76
y² = 41.76
y = 6.46
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from 6 positive and 8 negative numbers, 4 numbers are chosen at random (without replacement) and multiplied together. what is the probability that the product is a positive number?
Let's say event A is the selection of four positive numbers, event B the selection of four negative numbers, and event C the selection of two positive and two negative numbers.
Since four numbers are chosen without replacement, n(A) = 6 × 5 × 4 × 3 = 360 n(B) = 8 × 7 × 6 × 5 = 1680. In event C, four numbers are to be chosen without replacement such that two numbers are positive and two numbers are negative.
This can be done in following ways: + + – – OR + – + – OR + – – + OR – + – + OR – – + + OR – + + – ∴ n(C) = 6 × 5 × 8 × 7 + 6 × 8 × 5 × 7 + 6 × 8 × 7 × 5 + 8 × 6 × 7 × 5 + 6 × 5 × 8 × 7 + 8 × 6 × 5 × 7 = 6 × (8 × 7 × 6 × 5) =10080 Here, total number of numbers = 14 ∴ n(S) = 14 × 13 × 12 × 11 = 24024
Since A, B, C are mutually exclusive events,
Required probability = P(A) + P(B) + P(C)
= n(A)/n(S) + n(B)/n(S)+ n(C)/n(S)
= 360+1680+10080/24024
= 505/1001
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I need to find x and y, help pls
How to do Surface Area and Volume.?
Answer:
Surface Area : find the area of each face and add them together.
Volume : multiplying height, width, and depth.
Write an equation that you can use to find the value of x.
Perimeter of triangle: 16 in.
An equation that you can use is 16=
.
Answer:
16 = 3x
Step-by-step explanation:
We are here given a equilateral triangle in which each side length measure is " x " .
By perimeter we mean the sum of all the side lengths of the figure.
By question , we have each side length as x ,
So its perimeter would be ,
x + x + x = 3x
But it is given that the perimeter is 16in . So they must be equal .
Hence our required equation is ,
16 = 3x
and if we want to solve out for x , divide both the sides by 3 ,
x = 16/3
and we are done!
5-6. For the next school year, the soccer team will need to come up with $600.
b. Jeff is a member of a new sports team. His dad owns a bakery. to help raise money for the team, jeff's dad agrees to provide the team with cookies to sell at the concession stand usually sells about 60 to 8- baked goods per games. Using your answer from part (a), determine a percent markup for the cookies the team plans to sell at next year's opening game. Justify your answer.
The markup is of amount $97.5
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
P = $500
i = 0.5%
n= 1
Using the formula
F = P + P x i x n
F= 500 + 500 x 0.005 x 1
F= 500+ 2.5
F= $502.5
So, the team need to raise
= 600- 502.5
= $97.4
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Heather's school is selling tickets to the annual talent show. One the first day of ticket sales the school sold 3 senior citizen tickets and 4 child tickets for
a total of $46. The school took in $48 on the second day by selling 4 senior citizen tickets and 2 child tickets. What is the price of each ticket type?
The price of a child ticket is $4 and the price of a senior citizen ticket is $10
Let's call the price of a senior citizen ticket "x" and the price of a child ticket "y".
On the first day, the school sold 3 senior citizen tickets and 4 child tickets for a total of $46, so we can write the equation:
3x + 4y =46
On the second day, the school took in $48 by selling 4 senior citizen tickets and 2 child tickets, so we can write another equation:
4x + 2y = 48
Now that we have two equations, we can use substitution or elimination to find the value of x and y.
For substitution, we can solve one equation for one variable and then substitute that expression into the other equation. For example, let's solve the first equation for x:
x = (46 - 4y)/3
Then, we can substitute this expression for x into the second equation:
4((46 - 4y)/3) + 2y = 48
Expanding the left side of the equation:
(184 - 16y)/3 + 2y = 48
Multiplying both sides by 3:
184 - 16y + 6y = 144
Combining like terms on the left side:
184 - 10y = 144
Subtracting 184 from both sides:
-10y = -40
Dividing both sides by -10:
y = 4
So the price of a child ticket is $4. To find the price of a senior citizen ticket, we can substitute this value back into the equation we solved for x:
x = (46 - 4y)/3 = (46 - 4 * 4)/3 = (46 - 16)/3 = 30/3 = $10
So the price of a senior citizen ticket is $10.
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Scientist tag and release a group of salmon after they hatch. Later, they catch a sample of salmon that Return To The River and check them for tags. One sample 20 out of 400 returning salmon have tags what is the best prediction of the total number of tagged salmon in a sample of 2000?
The best prediction of the number of tagged salmon in a sample of 2000 is 100.
The best prediction of the number of tagged salmon in a sample of 2000 returning salmon can be estimated using the proportion of tagged salmon in the sample of 400.
The proportion of tagged salmon in the sample of 400 is [tex](\frac{20}{400} )=(\frac{1}{20} )[/tex].
According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other. Proportions are denoted using the symbol '::' or '='.We can use this proportion:
To estimate the number of tagged salmon in a sample of 2000:
Tagged salmon in a sample of 2000 = [tex](\frac{1}{20}) * 2000[/tex] = 100
Therefore, the best prediction of the number of tagged salmon in a sample of 2000 is 100.
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need help asap cause its my next class in 10 minutes
Answer: 6) 33° , 7) x=3°
Step-by-step explanation:
The sum of the three angles of any triangle is equal to 180 degrees.
6) ∡SUT= 180-102 = 78 Linear Pair
∴ ∡UTS=180-(69+78)
=180-147
= 33°
7) ∡DBC=180-123=57 Linear Pair
57+25x+2+15x+1=180
60+40x=180
40x=180-60
=120
x=120/40=3°
∴ ∡D=77
∡C=46
the size of an equilateral triangle are 6 cm long calculate the vertical height of the triangle
Answer:
6
Step-by-step explanation:
Let x be the vertical height
area of triangle=1/2×6×6=18
1/2×3×x=18/2
1.5x=9
x=6
Given the equation −15a = 75, solve for a. −60 −5 5 90
Answer:
-5
Step-by-step explanation:
−15a = 75
a = 75/-15
a = -5