Answer: The required value of y in the solution to the given system is 6.4.
Step-by-step explanation: We are given to find the value of y in the solution to the following system of linear equations :
[tex]x+y=1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2x-3y=-30~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
To find the value of y, we will try to eliminate x from both the equations.
Multiplying equation (i) by 2, we have
[tex]2(x+y)=1\times2\\\\\Rightarrow 2x+2y=2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Subtracting equation (ii) from equation (iii), we get
[tex](2x+2y)-(2x-3y)=2-(-30)\\\\\Rightarrow 2y+3y=2+30\\\\\Rightarrow 5y=32\\\\\Rightarrow y=\dfrac{32}{5}\\\\\Rightarrow y=6.4.[/tex]
Thus, the required value of y in the solution to the given system is 6.4.
A department store is holding a drawing to give away free shopping sprees. There are 10 customers who have entered the drawing: 2 live in the town of Gaston, 3 live in Pike, and 5 live in Wells. Two winners will be selected at random. What is the probability that the first winner lives in Pike and the second lives in Wells? Write your answer as a fraction in simplest form.
The probability that the first winner is from Pike and the second from Wells is 1/6, found by multiplying the individual probabilities of each event happening in sequence.
Explanation:The question asks for the probability that the first winner comes from Pike and the second from Wells in a random drawing. With 10 customers in total, 3 from Pike and 5 from Wells, the probability of drawing a Pike resident first is 3/10. If that happens, one less customer is available, leaving 9, with 5 still from Wells.
So, the probability for the second draw is 5/9. Multiplying these probabilities gives the combined probability for both events happening in sequence. Therefore, the required probability is (3/10) * (5/9), which simplifies to 1/6.
The probability that both customers selected are Pike residents is [tex]{\frac{28}{153}}[/tex]
To find the probability that both customers selected are Pike residents, follow these steps:
1. Calculate the probability that the first customer is a Pike resident:
- There are 18 customers in total.
- There are 8 Pike residents.
- So, the probability that the first customer is a Pike resident is:
[tex]\[ \frac{8}{18} = \frac{4}{9} \][/tex]
2. Calculate the probability that the second customer is also a Pike resident, given that the first one was a Pike resident:
- After selecting the first Pike resident, there are now 17 customers left.
- There are now 7 Pike residents remaining.
- So, the probability that the second customer is a Pike resident, given the first was a Pike resident, is:
[tex]\[ \frac{7}{17} \][/tex]
3. Calculate the combined probability:
- Since the selections are dependent events (one customer is selected after another without replacement), multiply the probabilities of each step:
[tex]\[ \left( \frac{4}{9} \right) \times \left( \frac{7}{17} \right) \][/tex]
4. Simplify the multiplication:
- Multiply the numerators: [tex]\(4 \times 7 = 28\)[/tex]
- Multiply the denominators: [tex]\(9 \times 17 = 153\)[/tex]
- So, the combined probability is:
[tex]\[ \frac{28}{153} \][/tex]
If angle DAB measures 34 degrees, what is the measure of arc DB
Calculate 40^13 (mod85)
50% of all cakes. Jenny baked that week were party cakes. 1-5 we're fruit cakes, and the remainder were sponge cakes. What percentage of cakes were sponge cakes
I think by 1-5 you mean 1/5??
1/5 = 0.20 = 20%
50% + 20% = 70%
100-70 = 30
so 30% were sponge cakes
Tanisha opened a bank account. She deposited $74.50 into her account every month for 10 months. She used $32.50 every month to pay for painting classes. After 10 months, she used 1 over 2 of the total money left in her account to go to a summer camp for painters. What is the total amount of money Tanisha spent to go to the summer camp?
Answer:
A
Step-by-step explanation:
Write an equation of the line that has a slope of 5 and y-intercepts 3 in slope-intercept form.
Need help asap with number 4
Find the sum of the three expressions and choose the correct answer.
-2u 3 v + 5uv - 1
7u 3 v - 2u 2 v 2
5u 2 v 2 - uv + 6
The answer choices are.....
A. 5u3v + 3u2v2 + 4uv + 5
B. -5u3v - 3u2v2 + 4uv + 7
C. 5u3v - 3u2v2 + 4uv - 5
A radio active isotope decays according to the exponential decay equation where t is in days. Round to the thousandths place. For the half life: The half life is the solution (t) of the equation : a2=ae−7.571t a 2 = a e − 7.571 t
Which point represents a solution to the system y ≤ (1)/(5)x y > 4x-3 select all that apply
(5,1)
(0,0)
(-2,-3)
(2,5)
can you help me with this question and explain how you got the answer please and thank you ! this is very important !!!!!!!!!
help please thank you
If a Rubik’s Cube has a volume of 384 cubic centimeters, how long is one side of the cube?
Jim paddles from one shore of a lake 3 miles wide at 4 mph, and John paddles from the opposite shore at 5 mph. How long will they travel before they meet?
A. 3 hours
B. 1 hour, 24 minutes
C. 27 minutes
D. 20 minutes
Answer:
Option D. 20 minutes.
Step-by-step explanation:
It has been given in the question that distance between the shore of a lake is 3 miles.
Speed of Jim is 4 mph and speed of John is 5 mph.
Let they meet after time t hours.
Therefore distance traveled by Jim in t hours = 4×t miles
and distance traveled by John in t hours = 5×t miles
Total distance they cover = 3 miles.
Now 4t + 5t = 3
9t = 3
t = 3/9 hours.
t = (3×60)/9 minutes.
t = 20 minutes.
Answer is they will meet after 20 minutes.
Y=-x+Use the rule y= -x+7 to fill in the blank.
If (1,y) is on the graph, then y=
Answer:
y=6
Step-by-step explanation:
The taxable earnings column of a payroll register records
Final answer:
The taxable earnings column of a payroll register records the amount of earnings that are subject to taxes.
Explanation:
The taxable earnings column of a payroll register records the amount of earnings that are subject to taxes. In payroll, taxable earnings refer to the portion of an employee's wages or salary that is subject to various taxes, such as income tax and Social Security tax.
For example, if an employee earns $1,000 per week and the income tax rate is 20%, the taxable earnings would be $800 ($1,000 - $200).
It's important to note that not all earnings may be taxable. Some types of income, such as certain reimbursements or non-taxable fringe benefits, may be excluded from taxable earnings.
Quadrilateral ABCD is a rhombus. Suppose measure of angle A decreases. Which of the following changes would also need to happen in order for ABCD to still be a rhombus?
If angle A of a rhombus decreases, angle C must also decrease and the side length of the rhombus must remain the same for it to still be a rhombus.
Explanation:When angle A of a rhombus decreases, there are two changes that need to happen in order for the rhombus to still be a rhombus.
The opposite angle, angle C, must also decrease by the same amount in order to maintain the opposite angles of a rhombus being equal. The side length of the rhombus must remain the same, as all sides of a rhombus are congruent.
Therefore, if angle A decreases, angle C must also decrease by the same amount, and the side length of the rhombus must remain the same in order for ABCD to still be a rhombus.
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10 times the sum of half a number and 6 is 8
What is the degree of 6x5 - 4x2 + 2x3 - 3 + x?
Answer:
55555555555555555555
Step-by-step explanation:
The degree is 5.
what is degree of polynomial?The degree of a polynomial is the highest power of the variable in a polynomial expression.
Given function:
6x5 - 4x2 + 2x3 - 3 + x
as, the function have powers 2, 3 and 5.
Among which the highest power is 5.
So, degree of the polynomial is highest power of the variable present in an equation.
Hence, the degree of polynomial is 5.
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John needs to make a scale drawing of his school building for art class. If the building is 256.25 meters long, and John scales it down using a ratio of 25 meters to 1 inch, how long will the building be in the sketch?
My question is what do I start with first. Divide, multiply. and what numbers. My math is on line and I have not worked math problems in 30 years
Raul has $640 saved, and jaime has $320 saved. They each begin a new job on the same day and save all of their money. Raul earns $180 per day and jaime earns $200 per day. In how many days will they have an equal amount of money
In 16 days will they have an equal amount of money.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Raul has $640 saved, and jaime has $320 saved.
Raul earns $180 per day and jaime earns $200 per day.
let the be number of days they both have same amount
640 + 180x = 320 + 200x
320 = 20x
x= 16
Hence, 16 days will they have an equal amount of money.
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Waylon played defense in 12 soccer games. This was 60% of the total number of games he played. How many games did Waylon play?
Which statement is true for the equation 3x − 3x − 2 = −2?
It has no solution.
It has one solution.
It has two solutions.
It has infinitely many solutions.
The equation will have infinitely many solutions.
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
This equation has infinitely many solutions.
3x - 3x - 2 = - 2
3x - 3x = 0
3x = 3x
This equals each other meaning infinite solutions.
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PLEASE HELP!!!! Show steps and explain how to get the answer please
Solve 5x-16=4(x-8)-3x
5x-16 = 4(x-8)-3x
first expand what is in parenthesis
4(x-8) = 4x-32
so now you have 5x-16 = 4x-32-3x
subtract 3x from 4x on the right side of equation 4x-3x = x
5x-16 = x -32
subtract 1x from each side to get
4x-16 = -32
add 16 to both sides to get 4x=-16
x = -16/4 = -4
x=-4
Solve for x: 4 over 5 x + 4 over 3 = 2x x = __________________ Write your answer as a fraction in simplest form. Use the "/" symbol for the fraction bar. Answer for Blank 1:
each leg of a 45 45 90 triangle has a length of 6 units. what is the length of its hypotenuse ?
Answer: [tex]6\sqrt{2}\ in[/tex]
Step-by-step explanation:
Given: In a 45-45-90 triangle, the length of one of the legs= 6 in.
Let h be the hypotenuse of the given right triangle.
Since the two angles are equal (45°) in the given right triangle,Moreover in a triangle the side opposite to the equal angles are equal.
Therefore, the other leg of given right triangle = 6 in.
Thus by Pythagoras theorem, we get
[tex]h^2=6^2+6^2=36+36\\\\\Rightarrow\ h^2=72\\\\\Rightarrow h=\sqrt{72}\\\\\Rightarrow h=6\sqrt{2}\ in[/tex]
Hence, the length of its hypotenuse = [tex]6\sqrt{2}\ in[/tex]
Points D, E, and F are not in a line. To construct a circle through points D, E, and F, begin by drawing line segments ("DE" ) ̅ and ("EF" ) ̅. Then construct the perpendicular bisectors of ("DE" ) ̅ and ("EF" ) ̅, and name the point of intersection of the perpendicular bisectors O. How do you know that point O is the center of the circle that passes through the three points?
Point O is the center of the circle passing through points D, E, and F because it is equidistant from all these points. This is proven by the construction of the perpendicular bisectors of DE and EF and their intersection at point O.
Explanation:The point O is the center of the circle that passes through the three points D, E, F because it is equally distanced from each of them. Here's why: When you draw perpendicular bisectors of lines DE and EF, you're effectively finding the midpoint of each line. Then, when these bisectors intersect at point O, point O is equidistant from points D and E (due to being on the bisector of DE), and from points E and F (due to being on the bisector of EF).
By definition, the center of a circle is a point that is equidistant from all points on the circle's circumference. Hence, because points D, E, and F are on the circumference and are equidistant from O, O is the center of the circle passing through points D, E, and F.
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Point O is the center of the circle passing through points D, E, and F because it is equidistant from the vertices of triangle DEF, which is confirmed by the properties of the perpendicular bisectors of line segments DE and EF that intersect at point O.
Explanation:To determine that point O is the center of the circle passing through points D, E, and F, we use the properties of perpendicular bisectors in a triangle. When we draw the line segments DE and EF, we are essentially drawing two sides of the triangle DEF. Constructing the perpendicular bisectors of these sides involves finding the midpoint of each side and then drawing a line that is perpendicular to that side at its midpoint.
The point where these two perpendicular bisectors intersect, point O, is equidistant from the vertices of the triangle (D, E, and F). This is because the perpendicular bisector of a line segment has the property that every point on the bisector is equidistant from the two endpoints of the segment. In the case of triangle DEF, point O is equidistant from D and E, since it lies on the bisector of DE, and is also equidistant from E and F, since it lies on the bisector of EF.
Since point O is equidistant from all three vertices of the triangle, it can serve as the circle's center, with the radii to the vertices being equal. This circle that we have created by using this method is also known as the circumcircle of triangle DEF, and point O is referred to as the circumcenter.
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The top base of a trapezoid is 18 inches and the bottom base is 22 inches. The height of the trapezoid is 8.5 inches. What is the area of the trapezoid
Final answer:
The area of the trapezoid with top base 18 inches, bottom base 22 inches, and height 8.5 inches is calculated using the formula (1/2) × (base1 + base2) × height, resulting in an area of 170 square inches.
Explanation:
To calculate the area of the trapezoid, you can use the formula for the area of a trapezoid, which is A = (1/2) × (base1 + base2) × height. In this case, the top base (base1) is 18 inches, the bottom base (base2) is 22 inches, and the height is 8.5 inches.
Using the formula, we get:
A = (1/2) × (18 inches + 22 inches) × 8.5 inches
A = (1/2) × 40 inches × 8.5 inches
A = 20 inches × 8.5 inches
A = 170 square inches
So, the area of the trapezoid is 170 square inches.
Find the area of a circle, in terms of pi, if the radius is 20 ft.
Find the common ratio of the sequence 2,8,32,128..
A ball is dropped from a height of 5 ft and bounces to 60% of its previous height on each subsequent bounce. Which statement is true regarding the vertical distance the ball has traveled when it hits the ground for the fourth time?
A) 10.88 ft vertical distance traveled total
B) 16.76 ft vertical distance traveled total
C) 18.06 ft vertical distance traveled total
D) 21.76 ft vertical distance traveled total
Answer:
the answer is 16.76 ft option B
Step-by-step explanation:
The vertical distance the ball has traveled when it hits the ground for the fourth time is 16.76m.
What is the percentage?The Percentage is the value per hundred.
Distance traveled by the ball when it hits the ground first time =5m
After the first hit, it bounces to 60% of its previous height
60% of 5m =3m
This means ball goes 3m up and then 3m down before hitting for the second time.
So, the vertical distance traveled by the ball till the second hit=5+3+3 =11m
After the second hit, it bounces to 60% of its previous height
60% of 3m =1.8m
This means ball goes 1.8m up and then 1.8m down before hitting for the third time.
So, the vertical distance traveled by the ball till the third hit=11+1.8+1.8 = 14.6m
After the third hit, it bounces to 60% of its previous height
60% of 1.8m =1.08m
This means ball goes 1.08m up and then 1.08m down.
So, the vertical distance traveled by the ball till the fourth hit=14.6+1.08+1.08 = 16.76m
Hence, the vertical distance the ball has traveled when it hits the ground for the fourth time is 16.76m.
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