Final answer:
The weight of the red marble is 16 grams, and the weight of the blue marble is 18 grams, based on the solution of the system of linear equations derived from the given total weights of the marbles.
Explanation:
To solve the problem of determining the weight of each marble, we can set up a system of linear equations based on the given information:
Let r be the weight of a red marble in grams.
Let b be the weight of a blue marble in grams.
The total weight of 3 red marbles and 2 blue marbles is 84g.
The total weight of 12 red marbles and 5 blue marbles is 282g.
Based on these statements, we can write two equations:
3r + 2b = 84 (1)
12r + 5b = 282 (2)
We can solve this system of equations by multiplying equation (1) by 4 to eliminate variable b.
(4)(3r + 2b) = (4)(84)
12r + 8b = 336 (3)
Subtract equation (2) from equation (3) to solve for r:
(12r + 8b) - (12r + 5b) = 336 - 282
3b = 54
b = 18 (weight of blue marble)
Substitute value of b in equation (1) to solve for r:
3r + 2(18) = 84
3r + 36 = 84
3r = 48
r = 16 (weight of red marble)
Therefore, the weight of the red marble is 16 grams and the weight of the blue marble is 18 grams.
Tony makes an hourly salary of 15.40 for 40 Regular hours of work. For any time work beyond 40 hours, he is paid at a rate of time and a half per hour. Last week, Tony worked 46 hours. Find each of the following for this period.
Tony's total earnings for the week are $754.60, which includes his regular pay for 40 hours at an hourly rate of $15.40 and overtime pay for 6 extra hours at a rate of time and a half.
Explanation:The subject of this question is Mathematics, specifically, it involves calculations relating to wage and overtime pay.
Calculating Regular and Overtime Pay
Tony earns an hourly wage of $15.40 for regular hours and is paid at a time and a half rate for any hours worked beyond 40 hours. Since he worked 46 hours last week, we can calculate his earnings as follows:
Calculate regular pay for 40 hours: 40 hours × $15.40 = $616.00.
Calculate the overtime pay rate: $15.40 × 1.5 = $23.10 per hour.
Calculate overtime pay for 6 hours: 6 hours × $23.10 = $138.60.
Add regular pay and overtime pay to get total earnings: $616.00 + $138.60 = $754.60.
Therefore, Tony's total earnings for the week, including overtime, are $754.60.
Anyone know the answer?
2. Find the area of the regular polygon. Give the answer to the nearest tenth. Hexagon with a radius of 5 in.
A. 65.0 in.^2
B. 129.9 in.^2
C. 259.8^2
D. 53.0^2
3. Divers looking for a sunken ship have defined the search area as a triangle with adjacent sides of length 2.75 miles and 1.32 miles. The angle between the sides of the triangle is 35°. To the nearest hundredth, find the search area.
A. 2.08 mi.^2
B. 2.97 mi.^2
C. 1.49 mi.^2
D. 1.04 mi.^2
Answer: The correct options are (2). A, (3). A.
Step-by-step explanation: The calculations are as follows:
(1) We are to given the area of a regular hexagon with radius 5 in.
The AREA of a regular hexagon with side 'a' units is given by
[tex]A=\dfrac{3\sqrt3}{2}a^2.[/tex]
We know that the radius of a regular hexagon is equal to the length of each side, so we have
a = 5 in.
Therefore, the area of the hexagon will be
[tex]A=\dfrac{3\sqrt3}{2}\times 5^2=1.5\times 1.732\times 25=64.95\sim 65~\textup{in}^2.[/tex]
Thus, (A) is the correct option.
(2) Given that two adjacent sides of the triangle measure 1.32 miles and 2.75 miles.
The angle lying between the two sides measure 35°.
we are to find the area of the triangle.
We know that the area of a triangle with two adjacent sides of measure 'a' and 'b' units and 'β' be the measure of the angle lying between them is given by
[tex]A=\dfrac{1}{2}ab\sin \beta.[/tex]
Here, a = 2.75 miles, b = 1.32 miles and β = 35°.
Therefore, the total search area, in the form of triangle is given by
[tex]A=\dfrac{1}{2}\times 2.75\times 1.32\times \sin 35^\circ=1.815\times 0.5735=2.08~\textup{mi}^2.[/tex]
Thus, the correct option is (A) 2.08 mi².
Hence, the correct options are (2). A, (3). A.
Which expression is equivalent to x+2+ [4x - x2+6x+8\x+4]
A cross section of a right triangular prism is created by a plane cut through the points shown and is also perpendicular to the opposite base.
what is the most specific name of the shape representing the cross section?
A. triangle
B. Rectangle
C. Trapezoid
D. Paralellogram
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Answer:
B. Rectangle
Step-by-step explanation:
The cross section will be a rectangle, as illustrated in the attachment.
The correct answer is B. Rectangle.
To determine the shape of the cross section, we need to understand the properties of a right triangular prism and the nature of the plane cut. A right triangular prism has two congruent right triangles as its bases, and the lateral faces are rectangles.
When a plane cut is made through points that are vertices of the base right triangle and is perpendicular to the opposite base, the cross section will intersect all the lateral edges of the prism. Since the lateral edges are perpendicular to the base, the cross section will have four right angles, making it a quadrilateral.
Furthermore, because the cut is perpendicular to the opposite base, the cross section will have two pairs of parallel sides. One pair of parallel sides comes from the intersection with the two lateral faces that are parallel to each other, and the other pair comes from the intersection with the base and the top face of the prism, which are also parallel.
Given these properties, the most specific name for the shape of the cross section is a rectangle, as it is a quadrilateral with four right angles and opposite sides that are parallel and equal in length.
Therefore, the correct answer is B. Rectangle.
What is the equation of a parabola with a focus (-2,4) and directrix y = 0?
The equation of the parabola with focus (-2,4) and directrix y = 0 is (x + 2) = 8(y - 2). This is derived by finding the vertex and applying the general equation for a vertically oriented parabola.
To find the equation of a parabola with a given focus and directrix, we use the definition that a parabola is the set of all points that are equidistant from the focus and the directrix. In this case, the focus is at (-2,4) and the directrix is y = 0. The vertex of the parabola will thus be halfway between the focus and the directrix, which means it will lie on the line y = 2 (since the focus has a y-coordinate of 4 and the directrix is at y = 0).
The standard form equation of a vertically oriented parabola with its vertex at the origin is x = 4py, where p is the distance from the vertex to the focus (or to the directrix). For a parabola that is shifted to have a vertex not at the origin, the equation is (x-h)² = 4p(y-k) where (h,k) is the vertex.
In this scenario, because the vertex is not at the origin and the parabola opens upwards (since the directrix is below the focus), we'll adjust the standard form equation to take these factors into account. The vertex (h,k) is (-2,2), the focus is (-2,4), thus p = 2. Therefore, the equation is (x + 2)² = 4*2*(y - 2)
Use the distance formula to find the distance between (−8, 2.5) and (0, −4.5). 1. Substitute coordinates: 2. Simplify parentheses: 3. Evaluate powers: 4. Simplify. What is the distance between (–8, 2.5) and (0, –4.5)? Round to the nearest hundredth. d ≈
We have to use the distance formula to find the distance between (−8, 2.5) and (0, −4.5).
The distance formula states:
" For the given points [tex] A(x_{1},y_{1}) [/tex] and[tex] B(x_{2},y_{2}) [/tex], the distance between A and B is given as:
AB = [tex] \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}} [/tex]
We have to find distance between (−8, 2.5) and (0, −4.5). So, [tex] x_{1}= -8, y_{1}= 2.5 , x_{2}=0 , y_{2}=-4.5 [/tex]
AB = [tex] \sqrt{(0+8)^{2}+(-4.5-2.5)^{2}} [/tex]
AB = [tex] \sqrt{64+49} [/tex]
AB = [tex] \sqrt{113} [/tex]
AB = 10.630 units
By rounding to the nearest hundredth, we get
Distance between A and B = 10.63 units.
Anyone know this geometry question?
When it comes to reimbursement packages, company a offers $175 plus $0.55 per mile. company b offers $200 plus $0.45 per mile. what number of miles driven would make the two reimbursement packages equal?
Answer:250
Step-by-step explanation:
A surveying instrument aimed at a location can “shoot” the distance to the location, giving the surveyor a measurement. A surveyor used such an instrument to record the distance to a point on a tree 60 m from his position. After rotating his surveying instrument 57° to the left, he measured the distance from his same position to a fence post 35 m away.
a.) Draw the diagram and label the tree as point T, the surveyor as point S, and the fence post as point F.
b.) Determine the distance between the point on the tree and the fence post. (Show
the appropriate formula, substitutions, and work. Give the distance to the nearest tenth of
a meter.)
c.) Use the Law of Sines to find the measure of T. (Show the appropriate formula, substitutions, and work. Give the measure of T to the nearest degree.)
d.) Find mF
Please Help Me :(
What is the selling price of an item if the original cost is $784.50 and the mark up on the item is 6.5 percent?
from my calculations it should be $835.49
Answer:
30
Step-by-step explanation:
Each of the walls of a room with square dimensions has been built with two pieces of sheetrock, a smaller one and a larger one. the length of all the smaller ones is the same and is stored in the variable small. similarly, the length of all the larger ones is the same and is stored in the variable large. write a single expression whose value is the total area of this room. do not use the pow function. submit
Need help on this!!!
Marcia has $84 less than three times as much as sue. together they have $132. how much money does marcia have?
To find out how much money Marcia has, a system of linear equations is set up and solved. Sue has $54, which means Marcia has $78 since she has $84 less than three times Sue's amount. They together have $132.
Explanation:The question involves solving a system of linear equations to determine how much money Marcia has if she has $84 less than three times as much as Sue. Together they have $132. To solve this, let's name the amount Sue has as S, and consequently, Marcia has 3S - $84. Adding both amounts, we get the equation S + (3S - 84) = $132.
Combining like terms gives us 4S - 84 = $132. We solve for S by first adding 84 to both sides, which yields 4S = $216. Dividing both sides by 4 gives us S = $54. Knowing Sue's amount, we can compute Marcia’s by multiplying Sue’s amount by three and then subtracting 84, so 3 x $54 - $84 = $162 - $84 = $78. Therefore, Marcia has $78.
A ________________ event has a 100% chance of occurring. Example: Picking a red ball from a bag of only red balls.
We have been given that probability of the even is 100%. In other words we can say that the probability is 1. It means that the event will certainly occur.
Now, we know that the highest value of probability is 1 and lower value is 0.
Mathematically, we can represents it as
[tex]0\leq P(E)\leq 1[/tex]
If the probability is 0 then the event will never occur.
And if the probability is 1 then event will definitely occur.
Therefore, A certain event has a 100% chance of occurring.
you are purchasing a house 12 years from now the estimated purchase price is 171,600.00 you want to make a 20%down payment how much do you have to save per month to reach your goal
The product of two consecutive integers is 156. what are the integers?" what type of equation should she create to solve this problem?
Answer:
12 and 13 or
- 13 and - 12
A quadratic equation r² + r - 156 = 0
Step-by-step explanation:
Let the first number be r, it means that the second will be r + 1.Given that the product of two consecutive integers is 156. we may interpret that to mean that
r(r + 1) = 156
r² + r - 156 = 0
r² + 13r - 12r -156 = 0
(r + 13)(r - 12) = 0
r = -13 0r 12
if r = -13, r + 1 = -12
If r = 12, r + 1 = 13
You spin a spinner 48 times. Out of the 48 trials, the pointer lands 6 times on section two. What is the experimental probability of the pointer landing on section two?
1/3
1/27
1/8
1/7
Answer:
1/8
Step-by-step explanation:
what is 68 less than 5 times a number is equal to the number?
The number here is will be represented as under -
Let the number be x.
Thus, the 5 times the number will be = 5x.
Now, it says, the number is 68 less than 5 times a number.
The equation so formed will be -
5x - 68 = x
4x = 68
x = 68.
Thus, the number will be 17.
Let us re-check the number,
(5 × 17) - 68 = 17
85 - 68 = 17
17 = 17. Thus, the number will be 17.
True or False ? explain your answer
18.csc^{-1} (csc(-\frac{\pi}{4} )) = -\frac{\pi}{4}
19.sec(sec^{-1} (\sqrt{3} ))=\sqrt{3}
What is the domain of the function
Algebra question ( Matrices and Determinants ) 20 points
Answer:
.
Step-by-step explanation:
Which point is an x-intercept of the quadratic function f(x) = (x – 8)(x + 9)? (0,8) (0,–8) (9,0) (–9,0)
36 ants including the queen created a new colony. after 9 monthe there are now 766 ants. at 17 months how many ants will live in the conoly
Jake rented a kayak at $26 for 3 hours. If he rents the same kayak for 5 hours, he has to pay a tota rent of $42. Write an equation in the standard form to represent the total rent (y) that Jake has to pay for renting the kayak for X hours
A triangle has vertices A (1, 5) B(2, 8) and C(2,0). It moves 3 units right and 5 units down.
HELP QUICK PLEASE
Wich statement about the following equation is true ? 3x^2-8x+5=5x^2
Pamela drove her car 99 kilometers and used 9 liters of fuel. She wants to know how many kilometers shee can drive with 12 liters of fuel. How many kilometers can Pamela drive with 12 liters of fuel?
Answer:
132 km
Step-by-step explanation:
1. she can drive 99 km (kilometers) with 9 liters of fuel, 99/9 is 11
2. if she wants to find out how many kilometers she can drive with 12 liters of fuel, then just multiply 12x11 which is 132
Suppose you cut a small square from a square of fabric as shown in the diagram. Write an expression for the remaining shaded area. Factor the expression. Type your answer below.
Kendra has a painting canvas that is 20 inches wide by 37 inches high. She painted a red rose, which covered 50% of the canvas.
What was the area of the canvas which was covered by the red rose?
The area of the canvas covered by the red rose is 370 square inches, calculated by multiplying the width and height of the canvas to find the total area and then taking 50% of that area.
The task is to calculate the area of a canvas that was covered by a red rose painting, which took up 50% of the total canvas area. To find the area covered by the red rose, we first need to calculate the total area of the canvas. The total area (A) of a rectangle is calculated by multiplying its width (W) by its height (H), which gives us the formula:
A = W x H
In this case, Kendra's canvas is 20 inches wide and 37 inches high. Using the formula:
A = 20 inches x 37 inches = 740 square inches
Now, since the red rose covers 50% of the canvas, we simply take 50% of the total area to find the area covered by the red rose:
Area covered by the red rose = 50% of 740 square inches = 0.50 x 740 square inches = 370 square inches
Therefore, the area of the canvas covered by the red rose is 370 square inches.