We can expect there to be 684 trout in the lake.
In the given statement is:
To determine the number of trout in a lake, a conservationist catches 171 trout, tags them and throws them back into the lake. Later 52 trout are caught; 13 of them are tagged.
Proportion:
A ratio gives us the measure of one quantity as compared to another quantity, and it is represented either as a fraction, decimal or a notation like a : b. When the same ratio is applicable to other quantities.
Now, According to the question:
Number of trout / number of trout = number of trout caught / caught that were tagged
Number of trout / 171 = 52/13
Number of trout = (171 x 52) / 13
Number of trout = 8,892 / 13 = 684
Hence, We can expect there to be 684 trout in the lake.
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Simplify each expression.
(9/-3) - 2
(9/-3) - 2
= (-3)(-2)
= -6
What is algebraic equation?
An algebraic equation or polynomial equation is an equation of the frame P=0 where P could be a polynomial with coefficients in a few fields, regularly the field of the rational numbers.
algebraic equation, a statement of the equality of two expressions defined by applying to a set of factors the algebraic operations, namely, expansion, subtraction, increase, division, raising to a control, and extraction of a root.
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in the figure below, B is between A and C and C is between B and D. if BC=4, BD=12, and AD=15 and AC
For the given values, the value of line AC has a value of 7 units.
What kinds of lines are there?There are two subsets of lines: line segments with two end points and rays with one beginning point and an infinite length on the other side, each symbolized by an arrow.
A line with several segments is provided in accordance with the supplied figure.
Segment BC equals 4, Segment BD equals 12, Segment AD equals 15, and Segment AC must be located.
Since, AC = AB + BC.
(AD - BD) Plus BC Equals AC.
AC = ( 15 - 12 ) + 4.
AC = 3 + 4
AC = 7.
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Complete Question -
in the figure below, B is between A and C and C is between B and D. if BC=4, BD=12, and AD=15 and AC
Draw ΔX Y Z and find the slope of each side of the triangle. Determine whether the triangle is a right triangle. Explain. X(0,0), Y(1, h), Z(2 h, 0)
A right-angled triangle is a triangle whose two adjacent sides form a right-angle triangle between them. The given triangle is a right-angled triangle.
What is a right-angle triangle?A right-angled triangle is a triangle whose two adjacent sides form a right-angle triangle between them.
The slope of the sides of the triangle can be written as,
The slope of XY = (2h - 0)/(2h - 0) = 1The slope of YZ = (0-2h)/(4h - 2h) = -2h/2h = -1The slope of XZ = (0 - 0)/(4h - 0) = undefined, therefore, the line will be horizontalThe given triangle is a right-angle triangle because the slope of the two lines is 1 and -1, whose product is -1. Therefore, the two lines are perpendicular to each other.
Hence, the given triangle is a right-angled triangle.
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what value of X makes this equation true? -9x+15=3(2-x)
Answer:
3/2
Hope this helps <3
Answer:
Step-by-step explanation:
Equation
-9x+15=3(2-x) Remove the brackets.
Solution
-9x + 15 = 6 - 3x Add 9x to both sides
-9x+9x + 15 = 6 - 3x + 9x Combine
15 = 6 + 6x Subtract 6 from both sides
15 - 5 = 6 -6 + 6x Combine
10 = 6x Divide by 6
10/6 = 6x/6
Answer
x = 1 2/3 or 1.66666 ...
Tisha's class is having a gift exchange. Tisha will draw first and her friend Brandi second. If there are 18 students participating, what is the probability that Brandi and Tisha draw each other's names?
According to the question, in the gift exchange event. Tisha draws first gift and her friend Brandi second gift.
The total number of participating students is [tex]18[/tex].
To calculate the probability that Brandi and Tisha draw each other’s name is as follows:
Using conditional probability, the solution is as follows:
[tex]P(E) = \frac{1}{18}\frac{1}{17} = \frac{1}{306} = 0.3%[/tex]
The calculated percentage is [tex]0.3[/tex].
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
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Explain what it means for a sequence to be an arithmetic sequence.
Any sequence is termed as the arithmetic sequence when the common difference between two consecutive values are same.
What is the sequence of AP arithmetic progression?In Arithmetic Progression, the difference between the two numerical orders is a fixed value (AP). Arithmetic Sequence is another name for it.
We'd come across a few particular words in AP that had been labeled as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)As shown below, the AP can also be defined in concepts of common differences.
The following is the procedure for evaluating an AP's n-th term: an = a + (n − 1) × dThe arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, for the given question;
Let the initial term be 'a₁'.
Let the second term be 'a₂'.
Let the third term be 'a₃'.
And, consider the fourth term as 'a₄'.
The AP must have the equal common difference. So,
d = a₃ - a₂ or d = a₄ - a₃
When the value of the common difference 'd' is found same in any of the cases, it said to form an AP.
Therefore, for the sequence to be an arithmetic sequence in common difference must be equal.
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Which inequality is equivalent to I x-4 I <9
(B) –9 < x – 4 < 9 inequality is equivalent to Ix-4I <9.
What is inequality?Inequality is a statement of an order relationship between two numbers or algebraic expressions (greater than, greater than, or equal to, less than, or less than or equal to). Inequality is defined as a difference in size, amount, quality, social position, or another factor. Inequality occurs when you have ten of something and someone else has none. (mathematics) A statement stating that one quantity is less than (greater than) another.So, Ix-4I <9:
|x-4|<9 ⇒ -9 < x-4 < 9-5 < x < 13Therefore, (B) –9 < x – 4 < 9 inequality is equivalent.
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The complete question is given below:
Which inequality is equivalent to I x-4 I <9?
A –9 > x – 4 < 9
B –9 < x – 4 < 9
C x – 4 < –9 or x – 4 < 9
D x – 4 > –9 or x – 4 < 9
Samra's guardians invested money for her into a 529 College Savings Plan, which compounds annually. The growth of the savings plan per year, x, can be represented by the exponential function f(x) = 500(1.03)x. What is the meaning of the y-intercept in the context of the problem?
A. The percent rate of change is 500%.
B. The initial value of the investment is $500.
C. The principal amount put into the savings plan is $1.03.
D. The average rate of change that is occurring is 1.03.
In the context of this problem, the meaning of the y-intercept is: D. The average rate of change that is occurring is 1.03.
What is the average rate of change?The average rate of change can be defined as a type of function that describes the average rate at which a quantity decreases or increases with respect to another quantity.
In Mathematics, the y-intercept of any graph occurs at the point where the value of "x" is equal to zero (0). Similarly, the x-intercept refers to the point at which the graph of a function crosses the x-axis and the value of "y" is equal to zero (0).
In the context of this problem, we can reasonably infer and logically deduce that the meaning of the y-intercept is the average rate of change that is occurring is 1.03 while 500 represents the initial investment.
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Find the sum of each finite series. Σ⁵ n=1(2 n-1)
The sum of the given finite series is 25
The summation notation means that we have to add the terms of the given series with n moves from the lower limit to the upper limit.
The given series is:
[tex]\sum\limits^5_{n=1} {(2n-1)}[/tex]
In this series, the lower limit is n = 1 while the upper limit is n=5.
n = 1 ⇒ 2n - 1 = 2(1) -1 = 1
n = 2 ⇒ 2n - 1 = 2(2) -1 = 3
n = 3 ⇒ 2n - 1 = 2(3) -1 = 5
n = 4 ⇒ 2n - 1 = 2(4) -1 = 7
n = 5 ⇒ 2n - 1 = 2(5) -1 = 9
Hence,
[tex]\sum\limits^5_{n=1} {(2n-1)}=1+3+5+7+9[/tex]
We can evaluate the sum of the series directly, or by using the sum formula as follow:
S(n) = n/2 [a(1) + a(n)]
Substitute n = 5, a(1) =1, and a(n) = 9:
S(5) = 5/2 (1 + 9) = 25
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Determine whether each list is a sequence or a series and finite or infinite. 4/3, 7/3, 10/3, 13/3,16/3, . . . . . .
From the list of numbers presented:
4/37/310/313/316/3we can determine that this is a infinite serie.
What are sequences?A sequence is an order of elements that are governed by a pattern, that is, it has variations between each element that remain constant and allow us to determine values before or after the known elements.
A sequence maintains an order, and this numerical order can be finite or infinite, in the given case we have the following list:
4/3, 7/3, 10/3, 13/3, 16/3
(4 + 3(x - 1))/3 = (4 + 3x - 3)/3 = (1 + 3x)/3(1 + 3*1)/3 = 4/3(1 + 3*2)/3 = 7/3(1 + 3*3)/3 = 10/3(1 + 3*4)/3 = 13/3(1 + 3*5)/3 = 16/3(1 + 3x)/3
In this series we have the initial value of the same, but we do not know the final value, although we know its behavior, we can say that this series has no end, it is an infinite serie.
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A dishwasher is priced at $475 there are two options offered to reduce the price either a 15% discount off the price or a rebate of $75 which is the better choice and what is the extra amount saved
Answer:
The better choice is a rebate of $75. You would save $3.75 more.
Find the slope of the line that passes through the two points. (1,3) and (4,9)
The slope passing through the two given two points (1,3) and (4,9) is 2.
What is meant by the slope of the line?The slope of a line is a measurement of its steepness and direction.
A line's slope is defined like a change in y coordinate with respect to a change in x coordinate.
The net y coordinate change is Δy, whereas the net x coordinate change is Δx. As a result, the change in y coordinate in relation to the change in x coordinate could be written as,m = Δy/Δx
where,m is the slope
Where, tan θ = Δy/Δx
This tanθ is also known as the line's slope.
A line's slope can be determined by calculating using two points just on straight line. We can use the slope of line formula with the coordinates of a two points.
Consider the coordinates of those 2 points,
P1 = (x₁, y₁)
P2 = (x₂, y₂)
Then slope will become;
Slope = m = tan θ = (y₂ - y₁)/(x₂ - x₁)
Now, as per the given question;
(x₁, y₁) = (1,3) and,
(x₂, y₂) = (4,9)
Substitute the values in the formula of the slope;
m = (9 - 3)/(4 - 1)
m = 6/3
m = 2.
Therefore, the slope of the line passing through the stated points is found to be 2.
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What is the length of one leg of the triangle?
11 units
O 11√2 units
0 22 units
O 22√2 units
ww
Answer:
22
Step-by-step explanation:
45°
leg a = 1k
leg b = 1k
and leg c = hypotenuse = k * square root 2
k [tex]\sqrt{2}[/tex] = 22[tex]\sqrt{2}[/tex]
k = 22
-----------------------
leg a or b = k = 22
By rounding to 1 significant figure, estimate
174.2 x 23.46
162.9 x 10.73
By rounding to 1 significant figure is 2.
What is significant figures ?Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value The first non-zero digit is where we start counting significant figures. The first non-zero digit of a number is considered the first significant figure when counting significant figures. The second digit is considered the second significant figure, and so on. The decimal point may be followed by a significant figure to the left or right of it.
Given: ([tex]\frac{(174.2 × 23.46)}{162.9 × 10.73}[/tex])
174.2 × 23.46 = 4086.732
162.9 × 10.73 = 1747.917
[tex]\frac{4086.732}{1747.917}[/tex] = 2.338 (approx)
= 2 ( rounding to 1 significant figure )
Hence the rounding to 1 significant figure is 2.
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Type the correct answer in the box. Use numerals instead of words.The graphs of functions fand g are shown.Function g is defined as g(x)
= k f(x). What is the value of K?
Answer:
k = 1
This is because when g(x) = 8, f(x) = 8
and when g(x) = 2, f(x) = 2
and this continues throughout the graph
In one hour a machine can make
300 paper clips
or
360 springs.
At 1 pm the machine starts working.
It makes 450 paper clips and then changes to making springs.
How many springs will the machine make by 6 pm?
The amount of springs the machine will make by 6 pm is; 96 strings
How to solve Algebra Word problems?We are given that;
Amount of paper clips machine can make in an hour = 300 paper clips
Amount of strings the machine can make in an hour = 360 strings
Now, the machine starts working at 1pm and makes 450 paper clips.
Thus, time taken = 450/360 = 1.25 hours
This is at 2:15 pm
By 6pm, time taken would be 6:00 - 2:15 = 3:45 or 3.75 hours
Thus, number of springs made = 360/3.75 = 96 springs
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Answer:
1260 springs
SBS answer:
(pc = paper clips)
(s = springs)
300 pc = 1 hour
therfore
450 pc = 1.5 hours
1 pm + 1.5 hours will take us to 2:30 pm
2:30pm to 6:00pm will take 3.5 hours
360 c = 1 hour
so
1080 c = 3 hours
so
1260 = 3.5 hours
taking us to 6pm
what does ^3^ mean
please i dont know
Step-by-step explanation:
it looks like a smiley face
if 0 < x < 90 degrees and sin sin x = 5/13, what is tan x?
Step-by-step explanation:
If cos x = 5/13 and x is between 0 and 90 degrees, since we know that tan2x = sin2x/cos2x = (2 sinxcosx)/(cos^2x - sin^2x) and we are dealing with a 5-12-13 right triangle,
tan (2x) = 2(12/13)(5/13)/((5/13)^2 - (12/13)^2) = (2*12*5/13^2) / (25/13^2) - (144/13^2)= 120/(-119)= -1.008403
Kevin is 6 years older than Timothy. 4 years ago, Kevin was twice as old as Timothy. Find their present ages.
Answer:
k=12
t=8
Step-by-step explanation:
two equations from the question
1 k=t+6
2 (k-4)=(t-4)×2
develop these
3. k-4=2t-8
4. 2 times first equation
2k=2t+12
subtract 4 from 3
-k-4=-20
k=16
sub back in
t=10
4 1/5 divided 2 3/5
7 1/2 divded 6 2/3
6 1/2 divded by 1/2
1 1/5 divded 1 2/5
1 2/3 divded 5
6 divded by 1 1/5
5 2/5 divded 1 1/5
HELP ME PLEASE THNX THNXIREFJJFOEEO
A fraction represents a part by whole.4 1/5 divided 2 3/5 is 21/13,7 1/2 divded 6 2/3 is 9/8,6 1/2 divded 1/2 is 13, 1 1/5 divded 1 2/5 is 6/7,1 2/3 divded 5 is 1/3,6 divded by 1 1/5 is 5,5 2/5 divded 1 1/5 is 27/6.
What is fraction?
A fraction represents a part by whole.
4 1/5 divided 2 3/5
=(21/5)/(13/5)=21/13
7 1/2 divded 6 2/3
=(15/2)/(20/3)=15/2*3/20=9/8
6 1/2 divded 1/2
=(13/2)/(1/2)=13
1 1/5 divded 1 2/5
=(6/5)/(7/5)
=6/7
1 2/3 divded 5
(5/3)/5/1
=5/3*1/5=5/15=1/3
6 divided by 1 1/5
6/(6/5)=6/1*5/6
=5
5 2/5 divded 1 1/5
=27/5/6/5
=27/6
Therefore 4 1/5 divided 2 3/5 is 21/13,7 1/2 divded 6 2/3 is 9/8,6 1/2 divded 1/2 is 13, 1 1/5 divded 1 2/5 is 6/7,1 2/3 divded 5 is 1/3,6 divded by 1 1/5 is 5,5 2/5 divded 1 1/5 is 27/6.
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On the Math SAT, men have a distinct edge. In 2005, for instance, the men averaged about 538, and the women averaged about 504. You may assume (i) the histograms followed the normal curve, and (ii) both SDs were about 120. Estimate the percentage of men getting over 700 on this test in 2005.
The percentage of men getting over 700 on this test in 2005 is 8.85%.
How to calculate the value?It should be noted that based on the information illustrated, the percentage will be calculated thus:
= P(X - 538/120) > (700 - 538/120)
= P(Z > 1.35)
= 1 - P(Z <= 1.35)
Using normal table
= 1 - 0.9115
= 0.0885
Therefore, the percentage of men getting over 700 on this test in 2005 is 8.85%.
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Solve y3 = −8.
please helpp
Answer:
-2
Step-by-step explanation:
Cube root of eight is 2
y= -2
what statement best defines an angle
Chemistry The time required for a certain chemical reaction is related to the amount of catalyst present during the reaction. The domain of the relation is the number of grains of catalyst, and the range is the number of seconds required for a fixed amount of the chemical to react. The table shows the data from several reactions.
a. Is the relation a function?
If the x values do repeat, quickly determine whether the y values match (y values are the second ones in the parenthesis). if, given the identical x values, the y values diverge.
What is a domain in math?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.The most crucial aspect of a function to keep in mind is that there is ONLY ONE Y value for EVERY X value.
The x values shouldn't repeat if you look at your set of points, according to this (x is the first value in the parenthesis).
If the x values do repeat, quickly determine whether the y values match (y values are the second ones in the parenthesis).
if, given the identical x values, the y values diverge.
Example: Because the second and third points both have the same x value (in this case 3, in this case), but different y values, (2,8)(3,5)(3,7)(5,8) is not a function (in this case 5 and 7).
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Brian has $24 worth of pizza delivered to his house. He pays the bill plus a 15% tip and 7% sales tax. He also pays a 3$ delivery fee that is charged after the tax and tip how much change does he receive, if he pays with two $20 bills?
Pizza costing $24 is being delivered to Brian's home. The change $7.72 he get if he uses two $20 bills as payment.
Given that,
Pizza costing $24 is being delivered to Brian's home.
He pays the amount in addition to the 7% sales tax and 15% tip.
In addition, he pays the delivery price of $3, which is added on after tax and tip.
We have to find how much change does he get if he uses two $20 bills as payment.
To figure out the sales tax
$24×0.07=$1.68
To figure out the tip
$24×0.15=$3.6
The Total cost=$24+$1.68+$3.6+$3=$32.28
Now, To find change we have to add the Total cost and the bill
Change=2($20)-$32.28
Change=40-32.28
Change=$7.72
Therefore, The change $7.72 he get if he uses two $20 bills as payment.
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Triangles ABC and DEF are mathematically similar.
A
9 cm
6/44
B
The area of triangle ABC is 34 cm².
Calculate the area of triangle DEF.
A
F
13.5 cm
E
Triangles ABC and DEF are mathematically similar. The area of triangles ABC is 34cm^2. Calculate the area of triangle DEF from the picture.
The required Area of Triangle DEF is 51cm square.
Given that,
The triangles ABC=DEF
Then, height of ABC= height of DEF
By the given picture we have
CB = 9cm
FE =13.5cm
Area of ABC= 34cm square
According to the question,
The area of a triangle= [tex]\frac{1}{2}[/tex] × base × height,
Again, Area of ABC = [tex]\frac{1}{2}[/tex] × base × height= 34cm square
= [tex]\frac{1}{2}[/tex] × 9cm × height= 34cm square
= [tex]\frac{9}{2}[/tex] cm × height= 34cm square
= Height= [tex]\frac{34cmsquare}{\frac{9}{2} }[/tex]
= Height = [tex]\frac{68}{9}[/tex]cm.
The height of the triangle ABC is [tex]\frac{68}{9}[/tex]cm.
Therefore,
Area of DEF = [tex]\frac{1}{2}[/tex] × base × height
= [tex]\frac{1}{2}[/tex] × 13.5cm × ([tex]\frac{68}{9}[/tex])cm
= 51cm square
Therefore, the Area of Triangle DEF is 51cm square.
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There are 130 people in a sport centre. 73 people use the gym. 62 people use the swimming pool. 58 people use the track. 22 people use the gym and the pool. 29 people use the pool and the track. 25 people use the gym and the track. 11 people use all three facilities. how many people use at least two facilities? check skip do not use a calculator get help report a mistake to hegartymaths on-screen keypad on off 789qwertyui
Using Venn diagram, out of the 130 people in the sport center, 54 people use at least two facilities.
Venn diagram is a diagram used to present the relationship between sets in a logical form. (See attached image)
Let n = number of people who use at least two facilities
A = people who use the gym = 73
B = people who use the swimming pool = 62
C = people who use the track = 58
A ∩ B = 22
B ∩ C = 29
A ∩ C = 25
A ∩ B ∩ C = 11
n = (A ∩ B - A ∩ B ∩ C) + (B ∩ C - A ∩ B ∩ C) + (A ∩ C - A ∩ B ∩ C) + A ∩ B ∩ C
n = (22 - 11) + (29 - 11) + (25 - 11) + 11
n = 11 + 18 + 14 + 11
number of people who use at least two facilities = 54
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The students in the astronomy club are selling snacks to raise money for a planetarium field trip. If they sell x muffins at $0.35 apiece and y bags of carrot sticks at $0.15 apiece, the total number of dollars raised will be T = 0.35x + 0.15y. How many dollars will they raise if they sell 210 muffins and 120 bags of carrot sticks?
Answer:
$91.5
Step-by-step explanation:
muffins: 210 carrot sticks:120
T= 0.35x + 0.15y (replace x as no. of muffins & y as no. of carrot sticks)
T= (0.35×210) + (0.15×120)
T= 73.5 + 18
T= 91.5
Evaluate each expression 10+8^3 divid 16
Answer:
42
Step-by-step explanation:
= 10+8^3/16
= 10+512/16
= 10+32
= 42
Find the sum of pair of vectors. < 13,-4 > + <-11,9>
The given statement states that the sum of two vectors is = (2 , 5).
What specifically is vector addition?Vector addition is the process of joining two or maybe more vectors to get a vector sum. The parallelogram law specifies the rules for adding and multiplying two or more vectors. When eigenvectors are aligned head to tail, this same vector total is calculated by drawing the same vector from the free tail to the free head.
According to the given data:Given two vectors are:
a =(13,-4 )
b = (-11,9)
The vector sum is,
M = [a1 + b1, a2 + b2]
= (Mx, My).
Substitution of the value we get:
M = (13 + (-11), (-4) + (9))
= (2 , 5)
The given statement states that the sum of two vectors is = (2 , 5).
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