Answer:
5817 Newtons.
Step-by-step explanation:
Total mass of the cage + the miners = 700 Kg which is a downward force of 700g N.
The net downward force = 700g - T where T is the tension (force) in the cable. The g = acceleration due to gravity = 9.81 m s-2.
We calculate the acceleration of the cage by using an equation of motion:
Distance = ut + 1/2 a t^2 where u = initial velocity , t = time and a = acceleration:
75 = 0(t) + 1/2 a (10^2)
50a = 75
a = 1.5 m s-2.
So using Newtons second law of motion
Force = mass * acceleration:
700*9.81 - T = 700 * 1.5
T = 700 * 9.81 - 700*1.5
= 5817 N.
The force in the cable during the first 10 seconds is 7930N. This was determined using the formulas s = ut + 1/2at² (to calculate acceleration) and F = ma + mg (to calculate the force).
Explanation:The subject of this question is Physics, specifically dealing with forces and acceleration. The total weight of the miners and the cage equals the sum of the miners' weight and the cage's weight, giving a total of 700kg, using the formula weight = mass x gravity (assumed to be 9.8m/s²). Therefore, the total weight is 700kg x 9.8m/s² = 6860N.
Then, we'd calculate the acceleration. The formula used is s = ut + 1/2at², where s is distance, u is initial velocity, a is acceleration, and t is time. Given that initial velocity is 0, the formula is simplified to s = 1/2at². After rearranging, we get acceleration (a) = 2s/t² = 2*75/10² = 1.5m/s².
Finally, we can determine the force on the cable using the formula F = ma + mg (F = force, m = mass, a = acceleration, g = gravity). Substituting, we get F = 700kg x 1.5m/s² + 700kg x 9.8m/s² = 7930N. Therefore, the force in the cable during the first 10 seconds is 7930N.
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What are the dimensions of the rectangle shown on the coordinate plane?
On a coordinate plane, a rectangle has points (0, 3), (0, negative 1), (negative 5, negative 1), (negative 5, 3).
The base is 5 units and the height is 4 units.
The base is 5 units and the height is 5 units.
The base is 5 units and the height is 3 units.
The base is 5 units and the height is 6 units.
Answer:
A
Step-by-step explanation:
count the lines on the bottom and top
The dimensions of the rectangle shown on the coordinate plane are : The base is 5 units and the height is 4 units.
What is a coordinate plane?A coordinate plane is a two-dimensional plane or region formed by the intersection of two number lines.
One number line is horizontal and called the x-axis, and the other number line is vertical and called the y-axis.
The point where they meet is called the origin. Points on a coordinate plane can be located by using numbers on the x-axis and the y-axis.
Given that a rectangle shown on the coordinate plane, we need to find the dimensions of the same,
So, if we see the figure we are going to have that, the base is of 5 units, (no matter if the base is -5 we will consider it as 5 units)
And the height is about 4 units.
Hence, the dimensions of the rectangle shown on the coordinate plane are : The base is 5 units and the height is 4 units.
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What is the converse of the following statement?
If you study in front of the television, then you do not
score well on exams.
F. If you do not study in front of the television, then you
score well on exams.
G. If you score well on exams, then you do not study in
front of the television.
H. If you do not score well on exams, then you study in
front of the television.
J. If you study in front of the television, then you score
well on exams.
Final answer:
The converse of the given statement switches the hypothesis and conclusion, leading to 'If you do not score well on exams, then you study in front of the television', which corresponds to option H.
Explanation:
The question asks for the converse of a given statement, which is a key concept in logical reasoning and mathematics. The original statement is If you study in front of the television, then you do not score well on exams. To find the converse, you switch the hypothesis and conclusion of the statement. Therefore, the converse is: If you do not score well on exams, then you study in front of the television. This means the correct answer is option H.
If you don't score well on exams, then you study in front of the television.
To find the converse of a conditional statement, we simply switch the hypothesis and the conclusion.
The original statement is: "If you study in front of the television, then you do not score well on exams."
The converse of this statement would be: "If you do not score well on exams, then you study in front of the television."
So, the correct answer is: "If you do not score well on exams, then you study in front of the television."
What two decimals give you a product close to 5.5?
Product of 4.21 and 1.31 gives 5.5
Product of 3.21 and 1.72 gives 5.5
Solution:
Given that,
We have to find two decimals that gives a product close to 5.5
So, when the two decimals are added, the product must be close to 5.5
Let us consider the following two decimals
4.21 and 1.31
Let us multiply 4.21 and 1.31 and check if their product is close to 5.5
[tex]4.21 \times 1.31 = 5.5151 \approx 5.5[/tex]
Thus, product of 4.21 and 1.31 gives a product close to 5.5
Similarly, consider two decimals 3.21 and 1.72
Let us multiply 3.21 and 1.72 and check if their product is close to 5.5
[tex]3.21 \times 1.72 = 5.5212 \approx 5.5[/tex]
Thus product of 3.21 and 1.72 gives 5.5
How do you solve 44 ÷ 0.5
Answer:
88
Step-by-step explanation:
44 / 0.5 = 44*2 = 88
Answer:
Step-by-step explanation:
0.5 is the same as 5/10 which reduces to 1/2. Half of 44 is 22! The answer is 22!
What is 5/5 multiplied by nine
Answer:
9
Step-by-step explanation:
5/5 = 1
1 x 9 = 9
Answer:
9
Step-by-step explanation:
The graph of the quadratic function y = ax^2 + bx + c is given.
Find a + b + c.
Answer:
[tex]\frac{145}{24}\approx 6[/tex]***
Answers may vary depending on the person reading the graph.
It is hard to tell what they think crosses nicely.
For example, I decided that the graph crossed nicely at the following points:
[tex](0,3)[/tex]
[tex](2,8)[/tex]
[tex](6,5)[/tex]
Step-by-step explanation:
I see that the graph crosses at [tex](0,3)[/tex],[tex](2,8)[/tex], and [tex](6,5)[/tex].
The equation [tex]y=ax^2+bx+c[/tex] tells us the [tex]y[/tex]-intercept is [tex]c[/tex] since when [tex]x=0[/tex] we have [tex]y=a(0)^2+b(0)+c=0+0+c=c[/tex].
The [tex]y[/tex]-intercept for our graph is [tex]3[/tex]. Therefore, [tex]c=3[/tex].
So far we have the equation:
[tex]y=ax^2+bx+3[/tex].
Let's enter the other points creating a system of linear equations to solve:
[tex]8=a(2)^2+b(2)+3[/tex]
[tex]5=a(6)^2+b(6)+3[/tex]
Let's simplify:
[tex]8=4a+2b+3[/tex]
[tex]5=36a+6b+3[/tex]
Let's subtract 3 on both sides:
[tex]5=4a+2b[/tex]
[tex]2=36a+6b[/tex]
I choose to solve the system by elimination.
Let's multiply the top equation by -3:
[tex]-15=-12a-6b[/tex]
[tex]2=36a+6b[/tex]
Now adding the equations results in:
[tex]-13=24a[/tex]
Divide both sides by 24:
[tex]\frac{-13}{24}=a[/tex]
Now using one of the equations we can find [tex]b[/tex]:
[tex]5=4a+2b[/tex] with [tex]a=\frac{-13}{24}[/tex]
[tex]5=4\frac{-13}{24}+2b[/tex]
[tex]5=\frac{-13}{6}+2b[/tex]
Add 13/6 on both sides:
[tex]5+\frac{13}{6}=2b[/tex]
[tex]\frac{30+13}{6}=2b[/tex]
[tex]\frac{43}{6}=2b[/tex]
Divide both sides by 2:
[tex]\frac{43}{2(6)}=b[/tex]
[tex]\frac{43}{12}=b[/tex]
So we have the equation:
[tex]y=\frac{-13}{24}x^2+\frac{43}{12}+3[/tex]
Let's evaluate [tex]a+b+c[/tex] now:
[tex]\frac{-13}{24}+\frac{43}{12}+3[/tex]
[tex]\frac{-13+86+72}{24}[/tex]
[tex]\frac{73+72}{24}[/tex]
[tex]\frac{145}{24}[/tex]
How many fractions are there between 1/4 and 1/2?
Answer:
none
Step-by-step explanation:
you cant multiply or divide to make them equivalent
Emily has 6 cans of pain. She uses 3 5/8 cans. How many cans she have left
Answer: the answer is 2.375 and as a mixed fraction is 2 3/8
Step-by-step explanation: first you subtract 3 5/8 from 6 so 6-3= 3 and in order to get the 3/8 you have to make one more number divisible by 1 which in this case was
Over 8 so then you do 8/8 which gives you a whole then you subtract the 5-8/8 which is 3/8 plus the 2 you had left
In a bag there are 2 red, 3 yellow, 4 green, and 6 blue marbles. What is the probability of P (blue)?
Answer:
6/15
Step-by-step explanation:
First we are going to need to add the total number of marbles.
2+3+4+6=15
So the denominator will be 15.
It asks us to find the probability of blue marbles so we put how many blue marbles there is inside of the bag.
There are six blue marbles.
So the probability is 6/15.
Or you could write it 6:15
Or percentage but that's no fun..
Final answer:
The probability of drawing a blue marble from a bag containing 2 red, 3 yellow, 4 green, and 6 blue marbles is 2/5, or 40%.
Explanation:
Calculating the Probability of Choosing Blue Marbles
The question asks about the probability of choosing a blue marble from a bag containing various colored marbles. With 2 red, 3 yellow, 4 green, and 6 blue marbles, the total number of marbles in the bag is 2 + 3 + 4 + 6 = 15. To find the probability of choosing a blue marble (P(blue)), we need to divide the number of blue marbles by the total number of marbles in the bag: P(blue) = Number of blue marbles / Total number of marbles = 6/15.
After simplifying, we get P(blue) = 2/5. Therefore, the probability of drawing a blue marble from the bag is 2/5, which can also be expressed as 0.4 or 40%.
Maria has an 8-sided die that is numbered from 1 to 8. She rolls the die 96 times. About how many times can she expect to roll an 8?
Answer:
12
Step-by-step explanation:
Final answer:
Maria can expect to roll an 8 around 12 times after rolling her eight-sided die 96 times, as calculated by multiplying the probability of rolling an 8 (⅓) by the number of rolls (96).
Explanation:
The student is asking about the expected number of times a specific outcome will occur when rolling an eight-sided die multiple times. In Maria's case, she is rolling the die 96 times and wants to know how many times she can expect to roll an 8.
To calculate this, we'll use the principle of theoretical probability, which states that the expected frequency for any event is the product of the total number of trials and the probability of the event occurring in a single trial. Since the die is fair and has eight sides, the probability of rolling an 8 on any given throw is ⅓ (or 1 out of 8).
Calculate the probability of rolling an 8: P(8) = ⅓.Multiply this probability by the total number of rolls: Expected frequency = P(8) × 96 throws = ⅓ × 96.Perform the calculation: Expected frequency = 12.Therefore, Maria can expect to roll an 8 about 12 times in 96 rolls of the die.
5 more than the product of 23 and the number n
Answer:
5+(23xN)
I think this is right. Sorry if I'm wrong.
Mike has 4 soccer balls and 2 footballs what fraction if the balls are footballs
Answer:2/6
Step-by-step explanation:
Answer:
2/1
Step-by-step explanation:
If we use ratios, it would be 4:2 which is the same as 4/2. But, we can simplify them both by 2. So 4/2=2 and 2/2=1. So the fraction would be 2/1
Joe walks over on a treadmill at constant rate the equation below describes the relationship between t the time he walks in hours and d the distance he walks in miles d=4t
The graph in option A (refer attachment) represents the relationship between the amount of time Joe walks and the distance he walks
Step-by-step explanation:
Given scenario is "Joe walks over on a treadmill at constant rate"
The equation which describes the relationship between' t' the time he walks in hours and ;d' the distance he walks in miles
d = 4 t
Now, we have to find the graph which indicates correctly about the relationship between the amount of time Joe walks and the distance he walks. Refer attachment to find the graph.
According to the given equation,
when t = 1 s so 'd' would would be 4 miles
when t = 2 s so 'd' would would be 8 miles
The above shows the plotting points in graph (t,d) = (1,4) (2,8). Hence, concluded that graph in option A (refer attachment) would be the right answer.
Because, others are not satisfying the equation d = 4 t
graph in option B shows the plotted points (t,d) = (4,1) (8,2)
graph in option C shows the plotted points (t,d) = (4,4) (8,8)
graph in option D shows the plotted points (t,d) = (4,4) (4,8)
Which of the following is a graph of y = x2?
The only option that is a graph of the function y = x² is: Second Graph
How to find the graph of the Quadratic Function?The general formula for a quadratic function is:
y = ax² + bx + c
Where a ≠ 0
We are given the quadratic function as:
y = x²
When x = -2, we have:
y = (-2)² = 4
When x = -1, we have:
y = (-1)² = 1
When x = 0, we have:
y = (0)² = 0
When x = 1, we have:
y = (1)² = 1
When x = 2, we have:
y = (2)² = 4
Looking at the graphs, the only one with these coordinate values is Graph 2
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The price of a television was reduced from $250 to $200. By what percentage was the price of the television reduced? (F 20%) (G 25%) (H 80%) (J 50%)
Do you guys know what y=2x is ?
Answer:
Graph the line using the slope and y-intercept, or two points.
Slope:
2
y-intercept: 0 x y 0 0 1 2
Step-by-step explanation:
Evaluate the expression: 5 + 3 × (5 - 2) 2
16
32
36
72
Using the order of operations (PEMDAS), the expression 5 + 3 × (5 - 2) 2 evaluates to 32.
Explanation:The expression to be evaluated is 5 + 3 × (5 - 2) 2. In mathematics you should always follow the order of operations, often remembered by the acronym PEMDAS which stands for: Parentheses, Exponents (i.e. Powers and Square Roots, etc.), Multiplication and Division, Addition and Subtraction. So in this case you should first evaluate the expression inside the parentheses (5 - 2), which equals 3. Then, 3 is squared to get 9 and is multiplied by 3 to get 27. Finally we add 5 to get a final answer of 32.
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Sabrina is catering a friend's party. A pan of chicken will feed 28 guests and a tray
of Turkey wraps will feed 42 guests. In total, the pans of food must feed at least 428
guests.
Part A: Write an inequality to represent the situation.
Part B: If she prepares 7 pans of chicken, what is the minimum number of trays of turkey wraps she must prepare for the party? Why?
Answer:
A : 428 ≤ 28x+42y B : 5.5238 trays
Step-by-step explanation:
X stands for # of pans of chicken and y stands for # of pans of wraps. Multiply 28 by 7 pans to get 196. then subtract the total guests by 196 to get 232. then divide that by how many a turkey wrap tray feeds so you get 5.5238
Final answer:
To ensure at least 428 guests are fed, using the given food pan capacities, Sabrina must prepare at least 6 trays of turkey wraps if she already plans on preparing 7 pans of chicken, according to the inequality 28x + 42y ≥ 428.
Explanation:
To solve this problem, we need to approach it in two parts. Let's tackle each part systematically.
Part A: Writing the Inequality
Let's let x represent the number of pans of chicken and y represent the number of trays of turkey wraps. Given that a pan of chicken feeds 28 guests and a tray of turkey wraps feeds 42 guests, and we need to feed at least 428 guests, we can write the following inequality:
28x + 42y ≥ 428
Part B: Finding the Minimum Number of Turkey Wraps Required
Given Sabrina prepares 7 pans of chicken, we need to find the minimum number of turkey wraps required. Substituting x = 7 into our inequality gives us:
28(7) + 42y ≥ 428
Solving for y gives:
196 + 42y ≥ 428
42y ≥ 232
y ≥ 5.5238
Since Sabrina cannot prepare a fraction of a tray, she must prepare at least 6 trays of turkey wraps to meet the minimum requirement, ensuring she has enough food to feed at least 428 guests.
Bank robber holds up a bank and speeds off at 71 mph. Police start chasing him 10 minutes later going 78 mph. How long will it take to catch up to them?
Answer:
It takes 1.68 hours to catch up to them.
Step-by-step explanation:
The speed of robber = 71 mph
The speed of police = 78 mph
The police start 10 minutes later
by that time robber would have travelled
[tex]distance = \frac{speed}{time}[/tex]
10 minutes =0.166667 hours
then the distance = 11.8 mph
Let them meet at distance x from the bank.
time taken by police to reach x , time =[tex]\frac{ x}{78}[/tex]----------------------(1)
time taken by robber in the same time = [tex]\frac{x-11.8}{71}[/tex]---------------(2)
Equating (1) and (2)
[tex]\frac{x}{78} =\frac{ x-11.8}{71}[/tex]
[tex]71 x = 78(x - 11.8)[/tex]
71x =78x - 920.4
920.4 = 78x - 71x
920.4 = 7x
x = 131.48
The distance where they catch up with the robber from the bank is 131.48 miles
speed of police = 78 mph
distance = 131.48 miles
time they catch up = [tex]\frac{131.48}{78}[/tex]
= 1.68 hours
You make $750 and 24% is taken out for taxes.
How much are the taxes?
A silversmith combined pure silver that cost $33.48 per ounce with 51 oz of a silver alloy that cost $24.35 per ounce. How many ounces of pure silver were used to make an alloy of silver costing $27.87 per ounce?
Answer:
$38.31
Step-by-step explanation:
Given:
Pure silver that cost $33.48 per ounce used to form $24.35 alloy/ounce.
Question asked:
How many ounces of pure silver were used to make an alloy of silver costing $27.87 per ounce?
Solution:
At cost $24.35/ounce, pure silver is mixed = $33.48
At cost $1/ounce, pure silver is mixed = [tex]\frac{33.48}{24.35}[/tex]
At cost $27.87/ounce, pure silver is mixed = [tex]\frac{33.48}{24.35}[/tex][tex]\times 27.87 = \frac{933.08}{24.35} = 38.31[/tex]
Thus, $38.31 ounces of pure silver were used to make an alloy of silver costing $27.87 per ounce.
copy and complete the table of values for the relation y equal to 3 x square - 5 x - 7
Answer:
x y
0 -7
1 -9
2 -5
3 5
Step-by-step explanation:
The give function is [tex]y=3x^2-5x-7[/tex]
Assuming the domain is :{0,1,2,3} then we substitute these values into the function and solve for the range.
When x=0, [tex]y=3(0)^2-5(0)-7=-7[/tex]
When x=1, [tex]y=3(1)^2-5(1)-7=-9[/tex]
When x=2, [tex]y=3(2)^2-5(2)-7=-5[/tex]
When x=3, [tex]y=3(3)^2-5(3)-7=5[/tex]
The table then becomes:
x y
0 -7
1 -9
2 -5
3 5
For what reason would we use the distance formula to determine the type of quadrilateral?
O Sides/diagonals are congruent
O Diagonals are bisected
O Sides are parallel
O Sides are perpendicular (right angles are formed)
Answer:
Sides/diagonals are congruent
Step-by-step explanation:
If the distance formula is used to determine the type of quadrilateral, then we are interested in knowing whether the opposite sides are congruent or adjacent sides are congruent.
We can also use the length of diagonals to determine which type of quadrilateral.
For instance the square has all sides equal.
The diagonals of the rectangle are congruent.
The attendance at a seminar in year 1 was 500. In year 2, the attendance changed by 100. What was the percent change in attendance
Answer:
The answer is 20% :)
A cargo container 9‘ x 12‘ x 7.5‘ is to be given a coat of paint on all surfaces inside and out. If 1 L of paint covers 30 ft.², how many 3 L tins of paint are required.
Answer: 18
Step-by-step explanation: 9 x 12 x 7.5 = 810
since it is inside out 810 x 2 = 1620
1620 divided by 90 = 18
Hope this helps
Chris is purchasing a house and needs to finance a $150,000 mortgage from the bank with an annual percentage rate (APR) of 3.8% He is financing it over 30 years and making monthly payments. what is the monthly payment?
answer choices:
$416.67
$698.94
$833.33
$1393.88
$698.94
Step-by-step explanation:
M = P [r (1 + r) ∧n / ( (1 + r) ∧n) - 1) ]
P = the principal loan amount = $150,000
Annual percentage rate = 3.8%
r = monthly interest rate = 0.038 / 12 = 0.003166
Term in years = 30
n = number of payments over the loan’s lifetime monthly = 30 * 12 = 360
M = the total monthly mortgage payment
Using the formula,
M = 150,000 [0.003166 (1 + 0.003166)∧360 / ((1 + 0.003166)∧360) - 1]
M = 150,000 [(0.003166 * 3.120394) / (3.120394 - 1)]
M = 150,000 [0.009880 / 2.120394]
M = 150,000 * 0.004660 = $699 (rounded up value)
As per mortgage calculator we get the exact value
M = $698.94
How to solve in elimination
x=2y+1
-8x+2y=6
Answer:
look at the picture shown
What is the area of a triangle with a base of 3.2 cm and a height of 9.6 cm? Question 5 options: 6.4 cm² 12.8 cm² 15.36 cm² 30.72 cm²
Step-by-step explanation:
[tex]Area \: of \: triangle = \frac{1}{2} \times base \times height \\ = \frac{1}{2} \times 3.2 \times 9.6 \\ = 1.6 \times 9.6 \\ = 15.36 \: {cm}^{2} \\ [/tex]
If Charles rides 4 miles in 20 minutes on his bike, which ratio shows the number of miles per minute he can ride
A
24:1
B
1:4
C
4:24
D
1:5
Answer:
D
Step-by-step explanation:
what does orgin means in math terms
Answer:
The point from which measurements are made. The point where all coordinate values are zero.
Step-by-step explanation:
In the Newtonian/Euclidean universe, the laws of geometry and physics are the same everywhere. Hence, in order to tell one place from another, we define a point of origin from which all coordinates are measured. Then, every point in space can be named in terms of its coordinates relative to the origin.