The amount that the jeweler would charge Mrs. Luisa, given the prices of the successive jewelry would be $ 19, 680
How to find the total cost ?The charge for repairing the jewelry pieces is calculated in a geometric progression:
= 6, 63, 63 ², 63 ³, ..., 63 ⁷
The sum of the first n terms in such a progression is:
S = a x (r ⁿ - 1) / ( r - 1 )
Seeing as there are 8 pieces of jewelry, the total cost to Mrs. Luisa would be:
S = 6 x ( 3 ⁸ - 1) / ( 3 - 1 )
S = 6 x ( 6561 - 1 ) / 2
S = 6 x 6560 / 2
S = 3 x 6560
S = $ 19, 680
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Find the value of x. Round to the nearest tenth, if necessary. NEED ANSWERS FAST WILL MARK BRAINLIEST
Answer:
Step-by-step explanation:
[tex]28^{2} = 11^2 + x^2\\ 784 = 121 + x^2\\x^2 = 663\\x = 25.74\\x[/tex]≅ [tex]26[/tex]
Find the median the data. 55,44,40,55,48,44,58,67
Answer:
51.5
Step-by-step explanation:
Answer:
51.5---------------------------
To find the median of the given data set, we need to first arrange the data in numerical order:
40, 44, 44, 48, 55, 55, 58, 67There are a total of 8 numbers in this set, which is an even number, so to find the median we need to take the average of the two middle numbers:
Median = (55 + 48)/2 = 51.5Therefore, the median of the data set is 51.5.
Which of the following is the result of expanding
8.5
15.5
32
60
Based on the information, the required result of the expansion for the expression is 8.
How to calculate the value of the expressionIn mathematics, an expression is a combination of numbers, variables, operators, and/or functions that can be evaluated to obtain a numerical or symbolic result. Expressions can take many forms, but typically involve some combination of mathematical symbols such as +, -, ×, ÷, =, and parentheses.
The given expression is 2x-3 .
when x =1, we will get 2(1)-3 = 2-3 =-1
When x=2, we will get, 2(2) -3 = 4-3 =1
When x=3, we will get 2(3)-3 = 6-3=3
When x=4, we will get 2(4)-3 = 8-3=5
The required result of the expansion is -1+1+3+5=8
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The parabola y = x, squared is shifted down by 3 units and to the left by 2 units.
It's important to note that shifting a function involves changing the corresponding variables (x or y) in the equation to achieve the desired translation.
The parabola y = x^2 represents a standard upward-opening parabola with its vertex at the origin (0, 0). To shift this parabola down by 3 units, we subtract 3 from the y-coordinate of each point on the original parabola. Thus, the equation of the shifted parabola becomes y = x^2 - 3.
Similarly, to shift the parabola to the left by 2 units, we subtract 2 from the x-coordinate of each point on the original parabola. The equation of the parabola shifted down by 3 units and to the left by 2 units is y = (x + 2)^2 - 3.
In the shifted parabola, the vertex will be at the point (-2, -3). The parabola retains its general shape, but its position in the coordinate plane has changed. It is now translated 2 units to the left and 3 units down compared to the original parabola y = x^2.
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Help please I will give brainlist!!
The angles in the circle are as follows:
mBC = 107°m∠BAC = 53.5° mBC = 92°How to find arc angles?The central angle of an arc is the central angle subtended by the arc.
The measure of an arc is the measure of its central angle.Therefore,mBC = 107 degrees
The angle subtended by an arc at the center is twice the angle subtended at the circumference.
Therefore, m∠BAC = 107 / 2 = 53.5 degrees
The inscribed angle is half the intercepted arc angle.
Therefore, to find mBC, we solve:
46 = 1 / 2
Next, we cross multiply mBC = 46 × 2
Therefore, mBC = 92 degrees
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how do you solve 3/(n-1) = 2n/(n=4)
Given f of x is equal to the quantity x plus 3 end quantity over the quantity x squared plus 2 times x minus 3 end quantity and g(x) = x + 2, evaluate (g – f )(2).
The composite function (g - f)(2) when evaluated is 3
Evaluating the composite functionsFrom the question, we have the following parameters that can be used in our computation:
f(x) = (x + 3)/(x² + 2x - 3)
Also, we have
g(x) = x + 2
The composite function (g - f)(2) is calculated as
(g - f)(2) = g(2) - f(2)
Where, we have
g(2) = 2 + 2 = 4
Also, we have
f(2) = (2 + 3)/(2² + 2(2) - 3) = 1
So, we have
(g - f)(2) = 4 - 1
Evaluate
(g - f)(2) = 3
hence, the composite function (g - f)(2) when evaluated is 3
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QUESTION 1
Use the sine rule to find x. Rationalise and leave your answer in surd form; a+b√c
Use special angles where Sine 30 = and sine 45 = 2x-1 45 2x + 2 30
It can be seen that x = (3 ± √(9 + 32√3)) / 8, which can be expressed in surd form as (3 + √(9 + 32√3)) / 8 or (3 - √(9 + 32√3)) / 8.
How to solveTo find x using the sine rule, we need to solve the equation:
sine(45) / x = sine(30) / (2x + 2√3)
Simplifying this equation, we have:
(2x - 1) / x = 1 / (2x + 2√3)
Cross-multiplying and simplifying further, we get:
(2x - 1)(2x + 2√3) = x
Expanding the brackets, we have:
[tex]4x^2 + 4\sqrt3x - 2x - 2\sqrt3 = x[/tex]
Rearranging the terms and simplifying, we get:
[tex]4x^2 - 3x - 2\sqrt3 = 0[/tex]
Using the quadratic formula, we can solve for x:
x = (-(-3) ± √((-3)^2 - 4(4)(-2√3))) / (2(4))
x = (3 ± √(9 + 32√3)) / 8
Therefore, x = (3 ± √(9 + 32√3)) / 8, which can be expressed in surd form as (3 + √(9 + 32√3)) / 8 or (3 - √(9 + 32√3)) / 8.
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The answer choices are:
A. 4
B. 2 radical 5
C. 4 radical 2
D. 2 radical 10
The calculated length of the segment WK is (b) 2√5
Calculating the length of the segment WKFrom the question, we have the following parameters that can be used in our computation:
The right triangle
Where we have
W = (-6, -2)
K = (-2, 0)
The length of the segment WK is calculated as
WK = √[(x2 - x1)² + (y2 - y1)²]
Substitute the known values in the above equation, so, we have the following representation
WK = √[(-6 + 2)² + (-2 - 0)²]
Evaluate
WK = √20
This gives
WK = 2√5
Hence, the length of the segment WK is (b) 2√5
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Given: ABCD is a trapezoid.
CD
BA
Prove: BD
B
A
CA
D
C
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Angles Segments Triangles Statements Reasons
ZBAD
201
Statements
ZCDA
Reasons
Note that
1.BA~CD Given
2.ABCDis a trapezoid Given
3.ABCD is and isosceles trapezoid - Definition of of isosceles trapezoid
4. AD~AD - reflective property
5.6. Triangle BAD ~ triangle CDA - SAS Axiom
7.BD~ CA - CPCTC
What is an Isosceles Trapezoid?
The top and bottom sides of an isosceles trapezoid are parallel, but the other two non-parallel sides are the same length. A trapezoid is a quadrilateral having two parallel sides and two non-parallel sides, as we know.
The bases (top and bottom) are perpendicular to one other. The bases (top and bottom) are perpendicular to one other. Congruent angles can be found on either side of the base. Congruent angles can be found on either side of the base.
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Given f(x) = x2 – 7x + 10 and g(x) = x – 5, find (f + g)(x).
Answer:
b,x²-6x+5
Step-by-step explanation:
(f+g)(x)=f(x)+g(x)
=x²-7x+10+(x-5)
=x²-7x+10+x-5
=x²-7x+x+10-5
=x²-6x+5
Given △RST≅△LMN, m∠R=65°, and m∠M=70°, what is the measure of ∠T?
Enter your answer in the box.
m∠T=
Answer: ∠T=45°
Step-by-step explanation:
If triangle RST is congruent to triangle LMN, then the angles R=L, S=M, and T=N. Knowing that the sum of angles in a triangle= 180 degrees, then:
∠R+∠S+∠T=180°
∠R=65°
∠M=∠S=70°
180°-∠R-∠S=∠T
180°-65°-70°=
∠T=45°
Create a table of values to show that the exponential expression 2^x eventually overtakes the quadratic expression 8x^2
The exponential function, 2ˣ, eventually overtakes the quadratic function 8·x², when 2ˣ = 8·x², such that at x = 10, 2ˣ > 8·x². Please see the required table in the following section
The shape of a quadratic function is a parabola
An exponential function is a function in which the input variable is an exponent.
The table of values, obtained by creating equations using MS Excel spreadsheet can be presented as follows;
x [tex]{}[/tex] 2ˣ 8·x²
0 [tex]{}[/tex] 1 0
1 [tex]{}[/tex] 2 8
2[tex]{}[/tex] 4 32
3[tex]{}[/tex] 8 72
4[tex]{}[/tex] 16 128
5[tex]{}[/tex] 32 200
6[tex]{}[/tex] 64 288
7 [tex]{}[/tex] 128 392
8[tex]{}[/tex] 256 512
9[tex]{}[/tex] 512 648
10[tex]{}[/tex] 1024 800
11[tex]{}[/tex] 2048 968
The shape of a quadratic function is called a parabola
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A comparison of two unrelated samples (n = 8 and n = 10) yield an estimated standard error of 2 points and a t statistic of t = 1.500. What is the difference between the sample means?
The difference between the sample means is A = ( 4√10/3 )
Given data ,
Difference between sample means A = (t-statistic) * (estimated standard error) / √(1/n1 + 1/n2)
On simplifying , we get
To find the difference between the sample means, we need to multiply the estimated standard error by the t-statistic and then divide by the square root of the sum of the reciprocals of the sample sizes.
Given that the estimated standard error is 2 points, the t-statistic is 1.500, and the sample sizes are n1 = 8 and n2 = 10, we can substitute these values into the formula:
Difference between sample means = (1.500) x (2) / √(1/8 + 1/10)
Calculating the sum of the reciprocals of the sample sizes:
1/8 + 1/10 = 5/40 + 4/40 = 9/40
Difference between sample means = (1.500) x (2) / √(9/40)
A √(9/40) = √(9) / √(40) = 3 / (2 x √(10))
Difference between sample means = 1.500 x 2 x (2 x √(10) / 3)
Difference between sample means ≈ 4√(10) / 3
Therefore, the difference between the sample means is ( 4√10/3 )
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Feature Question What is the area of a parallelogram whose vertices are A(−12, 2), B(6, 2), C(−2, −3), and D(−20, −3)? Enter your answer in the box. units²
The area of the parallelogram with vertices A(-12, 2), B(6, 2), C(-2, -3), and D(-20, -3) is 90 units².
To find the area of a parallelogram, we need to know the length of one of its bases and its corresponding height. We can find the length of the base by computing the distance between two parallel sides of the parallelogram.
In this case, we can see that sides AB and CD are parallel, and they both have a length of 18 units (6 - (-12) = 18).
To find the height, we need to compute the distance between the parallel sides. We can do this by computing the vertical distance between either AB and CD or AD and BC.
Let's use AD and BC. The vertical distance between A and D is 5 units (2 - (-3) = 5), and the vertical distance between B and C is also 5 units (2 - (-3) = 5). Therefore, the height of the parallelogram is 5 units.
Now we can use the formula for the area of a parallelogram:
Area = base x height
Area = 18 x 5
Area = 90 units²
Therefore, the area of the parallelogram with vertices A(-12, 2), B(6, 2), C(-2, -3), and D(-20, -3) is 90 units².
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Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Determine each segment length in right triangle ABC
The length of segment BD of the right triangle is 7 units.
The length of segment BC of the right triangle is 7√2.
What is the length of segment of the triangle?
The length of each segment of the triangle is calculated applying trig ratio as follows;
The length of segment BD is calculated as follows;
tan 45 = opposite side / adjacent side
The adjacent side of the right triangle is given as 7 units, the opposite side which is the height (BD) is calculated as follows;
tan 45 = BD/7
BD = 7 x tan 45
BD = 7 x 1
BD = 7
The segment BC is calculated as follows;
cos 45 = CD / BC
cos 45 = 7 / BC
BC = 7/ cos 45
BC = 7√2
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plot -8/5 and 1.8 on number line
The points are shown on the number line as below.
The given numbers are,
-8/5 and 1.8
Now convert -8/5 into decimal form
therefore,
Divide 8 by 5 we get,
-8/5 = -1.6
Since we know that,
On a number line, arithmetic procedures can be better described. To begin, one needs understand how to locate numbers on a number line. A number line's midway point is zero.
Positive numbers occupy the right side of the zero on the number line, whereas negative numbers occupy the left side of the zero. The value of a number diminishes as we travel to the left side. 1 is greater than -2, for example.
Integers, fractions, and decimals may all be simply expressed on a number line.
The points are plotted on number line shown below.
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The table shows the relationship between the participants walking and running for the week's cross-country practices.
Walk (laps) 3 B 15
Run (laps) 5 10 D
Total (laps) A C 40
At this rate, how many laps will the participants walk and run if the total distance is 24 laps?
They will walk 7 laps and run 17 laps.
They will walk 15 laps and run 9 laps.
They will walk 9 laps and run 15 laps.
They will walk 6 laps and run 18 laps.
The table to set up a System of equations to solve for the number of laps walked and run if the total distance is 24 laps.the correct answer is not listed among the options given.
The table to set up a system of equations to solve for the number of laps walked and run if the total distance is 24 laps:
3 + 5 = A (the total number of laps walked and run is equal to A)
B + 10 = C (the total number of laps walked and run is equal to C)
15 + D = 40 (the total number of laps walked and run for the week is 40)
Simplifying each equation, we get:
A = 8
B = 5
C = 15
D = 25
To find how many laps will the participants walk and run if the total distance is 24 laps, we can set up the following proportion:
3x/8 + 5x/15 = 24
Multiplying both sides by 120 (the least common multiple of 8 and 15), we get:
45x + 40x = 2880
Simplifying, we get:
85x = 2880
Dividing both sides by 85, we get:
x ≈ 33.88
Therefore, the participants will walk approximately:
3x/8 ≈ 12.66 laps
And run approximately:
5x/15 ≈ 21.22 laps
Rounding to the nearest whole number, we get:
They will walk 13 laps and run 21 laps.
Therefore, the correct answer is not listed among the options given.
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what is greater 54300ml or 54L?
Answer:
54300 ml is greater than 54 L. This is because 54300 ml is equivalent to 54.3 L, which is larger than 54 L.
A rectangular container is 25cm by 37cm by 21cm
The volume of this of rectangular container is equal to 19,425 cubic centimeter.
How to calculate the volume of a rectangular prism?In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:
Volume of a rectangular prism = L × W × H
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;
Volume of rectangular container = 25 × 37 × 21
Volume of rectangular container = 19,425 cubic centimeter.
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Complete Question:
A rectangular container is 25cm by 37cm by 21cm. What is the volume of this rectangular container?
Solve these using quadratic formula
Write out your work!
I need the vertex
Axis of symmetry
Intercepts -also include the function to find the intercepts-
The vertex is at (1, 4).
The vertex is at (-1, -4).
The axis of symmetry is x = 1.
The axis of symmetry is x = -1.
The x-intercepts are (3, 0) and (-1, 0).
The x-intercepts are approximately (-2.3, 0) and (0.3, 0).
The y-intercept is (0, 3).
The y-intercept is (0, -6).
We have,
To solve the equations using the quadratic formula, we need to rewrite them in the standard form ax² + bx + c = 0.
-x² + 2x + 3 = 0 can be rewritten as -1x² + 2x + 3 = 0
Here, a = -1, b = 2, and c = 3
Using the quadratic formula, we have:
x = (-b ± √(b² - 4ac)) / 2a
x = (-2 ± √(2² - 4(-1)(3))) / 2(-1)
x = (-2 ± √(16)) / -2
x = 1 ± 2
So, x = 3 or x = -1
2x² + 4x - 6 = 0 is already in the standard form with a = 2, b = 4, and c = -6
Using the quadratic formula, we have:
x = (-4 ± √(4² - 4(2)(-6))) / 2(2)
x = (-4 ± √(52)) / 4
x = (-2 ± √(13)) / 2
To find the vertex of each parabola, we can use the formula x = -b / 2a and then substitute the value of x into the equation to find y.
For -x² + 2x + 3 = 0
We have a = -1 and b = 2, so the vertex is at
x = -b / 2a = -2 / (2(-1)) = 1.
Substitute x = 1 into the equation to find y:
y = -1(1)² + 2(1) + 3 = 4.
So the vertex is at (1, 4).
For 2x² + 4x - 6 = 0,
We have a = 2 and b = 4, so the vertex is at x = -b / 2a = -4 / (2(2)) = -1. Substitute x = -1 into the equation to find y: y = 2(-1)² + 4(-1) - 6 = -4.
So the vertex is at (-1, -4).
The axis of symmetry is a vertical line that passes through the vertex.
For -x² + 2x + 3 = 0, the axis of symmetry is x = 1.
For 2x² + 4x - 6 = 0, the axis of symmetry is x = -1.
To find the x-intercepts, we can set y = 0 in each equation and solve for x using the quadratic formula.
For -x² + 2x + 3 = 0, we have:
x = (-2 ± √(2² - 4(-1)(3))) / 2(-1)
x = (-2 ± √(16)) / -2
x = 1 ± 2
So the x-intercepts are (3, 0) and (-1, 0).
For 2x² + 4x - 6 = 0, we have:
x = (-4 ± √(4² - 4(2)(-6))) / 2(2)
x = (-4 ± √(52)) / 4
x = (-2 ± √(13)) / 2
So the x-intercepts are approximately (-2.3, 0) and (0.3, 0).
To find the y-intercept, we need to set x = 0 and solve for y.
Setting x = 0 in -x² + 2x + 3 = 0.
-0 + 0 + 3 = 3
Therefore, the y-intercept is (0, 3).
Setting x=0 in 2x² + 4x - 6.
2(0)² + 4(0) - 6 = -6
Therefore, the y-intercept is (0, -6).
Thus,
The vertex is at (1, 4).
The vertex is at (-1, -4).
The axis of symmetry is x = 1.
The axis of symmetry is x = -1.
The x-intercepts are (3, 0) and (-1, 0).
The x-intercepts are approximately (-2.3, 0) and (0.3, 0).
The y-intercept is (0, 3).
The y-intercept is (0, -6).
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find the area of each triangle using the formula of A=L×W/2
The areas of the triangles are 5 square units and 35 square units
Calculating the areas of the trianglesFrom the question, we have the following parameters that can be used in our computation:
Area = Length * Width/2
Where
Length = L
Width = W
Triangle (a)
L = 2 and W = 5
When the given values are substituted, we have the following equation
Area = 2 * 5/2
Area = 5
Triangle (b)
L = 10 and W = 7
When the given values are substituted, we have the following equation
Area = 10 * 7/2
Area = 35
Hence, the areas of the triangles are 5 square units and 35 square units
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Complete question
Find the area of each triangle using the formula of A=L×W/2
(a) L = 2 and W = 5
(b) L = 10 and W = 7
If f(x) = (3+x)/(x-3) , what is f(a+2)
Answer:
Step-by-step explanation:
f(x) = [tex]\frac{3+x}{x-3}[/tex]
f(a+2) = [tex]\frac{3+a+2}{a+2-3}[/tex]
f(a+2) = [tex]\frac{5+a}{a-1}[/tex]
Paige Inc. has a division that makes paint and another division that constructs houses. The paint division incurs the following costs for one litre of paint: Direct materials R1.10 Direct labour R1.45 Variable overhead R0.90 Fixed overhead R1.15 Total R4.60 The Paint Division can make 1 000 000 litres per year, and is operating at capacity. The Construction Division currently buys paint from an outside supplier for R5.20 per litre (the same price that the Paint Division receives). What is the minimum transfer price?
The solution is, $85,500 are the total cost savings for Leather Stuff.
Explanation:
In this case, we need to calculate the saving per zipper which is external price minus agreed transfer price.
Then, we will multiply the saving per zipper by the quantity of zipper required by Leather Stuff, which is 90,000 zippers.
Cost saving per zipper
= External price - Agreed transfer price
= $3.50 - $3.25
= $0.25
Total cost saving
= $0.95 x 90,000 zippers
= $85,500
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complete question:
Quinn Inc. has a number of divisions. One division, Style, makes zippers that are used in the manufacture of boots. Another division, LeatherStuff, makes boots that use the zippers and needs 90,000 zippers per year. Style incurs the following costs for one zipper: Direct materials $0.23 Direct labor 0.20 Variable overhead 0.95 Fixed overhead 1.32 Total $2.70 Quinn has capacity to make 950,000 zippers per year, but due to a soft market, only plans to produce and sell 620,000 zippers next year. LeatherStuff currently buys zippers from an outside supplier for $3.50 each (the same price that Style receives). Assume that Style and LeatherStuff have agreed on a transfer price of $3.25. What are the total cost savings for LeatherStuff?
Calculate the depreciation expense per mile under units of activity method.
The depreciation expense per mile for the truck is $0.29 per mile.
What is the depreciation expense per mile?A depreciation expense refers to the amount that a company's assets are depreciated for a single period.
Given that:
Delivery truck cost = $33,000
Expected salvage value = $1,680
Estimated total miles = 108,000.
Depreciation rate per mile = (Cost - Salvage value) / Estimated total miles
Depreciation rate per mile = ($33,000 - $1,680) / 108,000 miles
Depreciation rate per mile = $31,320 / 108,000 miles
Depreciation rate per mile = $0.29 per mile
Full question:
Calculate depreciation expense per mile under units-of-activity method Sarasota Company purchased a delivery truck for $33,000 on January 1, 2020. The truck has an expected salvage value of $1,680, and is expected to be driven 108,000 miles over its estimated useful life of 10 years. Actual miles driven were 16,000 in 2020 and 11,300 in 2021.
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Triangle angle sun
Can someone explain how they solved this so I know for future reference :)
Answer: n = 70
Step-by-step explanation:
The sum of all angles in a triangle is 180 degrees. We know this because the formula for degree measure in a polygon is (180) * (n-2) where n is the number of sides. (ie a square with 4 sides would have 360 total degrees because (180) * (4-2) = 360)
Given the angle of 40 degrees we know that the remaining angles need to add up to 140 degrees. because n = n we can say that 2n = 140 divide by 2 and get n=70
11 rain jackets were collected. At the end of the the drive, 10 times that number of rain jackets were collected. How many rain jackets were sold
On an overnight camping trip, the Adventure Scouts could choose to sleep in a cabin, in a tent, or outside under the stars. A total of 115 scouts went on the trip. Twice as many scouts slept in a cabin as slept in a tent. The same number of scouts slept outside as slept in a cabin.
How many Adventure Scouts slept outside?
There are 58 Adventure Scouts slept outside on the camping trip.
Let's denote the number of scouts who slept in a cabin, tent, and outside as c, t, and o, respectively. We know that the total number of scouts is 115, so:
c + t + o = 115
We also know that twice as many scouts slept in a cabin as slept in a tent, so:
c = 2t
And we know that the same number of scouts slept outside as slept in a cabin, so:
o = c
We can use these equations to solve for the number of scouts who slept outside:
c + t + o = 115
2t + t + t = 115 (substituting c = 2t and o = c)
4t = 115
t ≈ 28.75
Since we can't have a fractional number of scouts, we need to round this up or down. However, we also know that the number of scouts who slept outside is the same as the number who slept in a cabin, which means that either c or o must be even (since c is twice t). Therefore, we'll round t up to 29 and use that to solve for c and o:
c = 2t ≈ 58
o = c ≈ 58
So, we can conclude that 58 Adventure Scouts slept outside on the camping trip.
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Answer:
46
Step-by-step explanation:
You need to find how many Adventure Scouts slept outside. Start with the information in the problem.
A total of 115 scouts went camping.
Twice as many slept in a cabin as slept in a tent.
The same number slept outside as slept in a cabin.
You can use a diagram to model the problem. Fewer scouts slept in a tent than the other choices. So, start with the scouts who slept in a tent.
Twice as many scouts slept in a cabin as slept in a tent. So, draw 1 box to represent the number who slept in a tent and 2 boxes to represent the number who slept in a cabin.
tent
cabin
outside
The same number of scouts slept outside as slept in a cabin. There are 2 boxes for scouts who slept in a cabin. So, draw 2 boxes to represent the number who slept outside.
tent
cabin
outside
There are 5 boxes in the diagram in all. There were 115 scouts on the trip altogether. So, each box represents 115÷5 scouts. Divide.
2 3
5
1 1 5
– 1 0
1 5
– 1 5
0
Each box represents 23 scouts. There are 2 boxes for the scouts who slept outside. Multiply to find the number of scouts who slept outside.
2 3
× 2
4 6
46 Adventure Scouts slept outside.
Help Quickly! The table shows bear population data gathered by researchers in the Wild Horse Forest. If the total bear population was 2,008 bears in May 2002, estimate the number of total bears counted in 2002 to complete the chart. (Click the picture to zoom in more)
A. 1,060 bears
B. 2,008 bears
C. 1,101 bears
D. 1,823 bears
The number of total bears counted in 2002 will be: A. 1060 bears.
How to determine the total bear estimateTo determine the total bear estimate, we will use the mark-recapture formula. In this formula, we equate the number of the population to MC/R where:
M = Number marked initially
C = Number captured in the second sample
R = The recaptured number
Also, R/C = M/N
For the given problem,
M = 2008
C = 38
R = 72
So, N = 2008 * 38/72
= 1059 approximately 1060 bears.
So, the bear population will amount to 1060.
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Solve the system of equations.
3
�
−
11
�
=
−
1
2
�
−
5
�
=
−
3
3x−11y=−1
2x−5y=−3
�
=
x=x, equals
�
=
y=y, equals
The solution to the system is x = -4, y = -1.
How to solveOne can employ the techniques of substitution or elimination to obtain solutions for the given set of equations.
Let's apply the elimination approach in this scenario.
To ensure that the coefficients of x are equal, multiply the first equation by 2 and the second by 3.
6x - 22y = -2,
6x - 15y = -9.
Subtract the second equation from the first:
0x - 7y = 7.
So, y = -1.
Substitute y = -1 into the second equation:
2x - 5(-1) = -3,
2x + 5 = -3,
2x = -8.
So, x = -4.
The solution to the system is x = -4, y = -1.
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The Complete Question:
Solve the system of equations.
3x – 11y = -1
2x – 5y = -3
