A crane cable can support a maximum load of 20,000 kg. If a bucket has a mass of 4,000 kg and gravel has a mass of 1,500 kg for every cubic meter, how many cubic meters of gravel (g) can be safely lifted by the crane?
Answer:
10.67 kg of gravel can be safely lifted by the crane
Step-by-step explanation:
Maximum load that a crane can support = 20000 kg.
Bucket has a mass = 4000 kg
Gravel has a mass = 1500 kg for every cubic meter.
Let the volume of gravel is = g cubic meter
Therefore, mass of the gravel = 1500g kg
Now we form an equation to show the weight that the crane cable can support
Mass of Bucket + mass of Gravel = Total mass that a lift can support
4000 + 1500g = 20000
1500g = 20000 - 4000
1500g = 16000
[tex]g=\frac{16000}{1500}[/tex]
g = 10.67 kg
Therefore, 10.67 kg of gravel can be safely lifted by the crane.
Suppose you have 19 black socks and 19 green socks in the dryer. 4. without looking, how many socks would you need to pull out of the dryer to be sure you get a black pair?
You would need to pull out 21 socks from the dryer to ensure you have a black pair since you might initially pull out all 19 green socks before getting to the black ones.
To determine how many socks one would need to pull out of the dryer to be sure to get a pair of black socks when you have 19 black socks and 19 green socks, consider the worst-case scenario. In the worst case, you pull out all 19 green socks one by one. Since you have not yet pulled out a single black sock, the 20th sock you pull out has to be black, because there are no more green socks left. However, to ensure you have a pair of black socks, you will need to pull out one more sock. So the answer is that you need to pull out 21 socks to be certain of having a pair of black socks.
Solve the equation,if possible.
And check the solution.
4/d = 2/6
Check:
Find a linear function that gives the cost in dollars of buying
Pop tarts on sale two boxes cost four dollars four boxes cost six dollars
The store keeper sold 9 1/4 yards from a piece of material containing 53 yards. How much was left in the original piece?
Simplify the expression. 3y3 – 2y[4y – y(y – 3)] – [2y(y + 1) – 3y(y2 –1)] =
Answer:
Step-by-steThe first step for solving this expression is to distribute -y through the parenthesis.
3y³ - 2y × (4y - y² + 3y) - (2y × (y + 1) - 3y × (y² - 1))
Distribute 2y through the parenthesis.
3y³ - 2y × (4y - y² + 3y) - (2y² + 2y - 3y × (y² - 1))
Now distribute -3y through the parenthesis.
3y³ - 2y × (4y - y² + 3y) - (2y² + 2y - 3y³ + 3y)
Collect the like terms in the first set of the parenthesis.
3y³ - 2y × (7y - y²) - (2y² + 2y - 3y³ + 3y)
Collect the like terms in the second set of the parenthesis.
3y³ - 2y × (7y - y²) - (2y² + 5y - 3y³)
Distribute -2y through the parenthesis.
3y³ - 14y² + 2y³ - (2y² + 5y - 3y³)
Remember that when there is a "-" sign in front of the parenthesis,, you must change the sign of each term in the parenthesis. This will change the expression to the following:
3y³ - 14y² + 2y³ - 2y² - 5y + 3y³
Collect the like terms with an exponent of 3.
8y³ - 14y² - 2y² - 5y
Lastly,, collect like terms that have an exponent of 2.
8y³ - 16y² - 5y
Since we cannot simplify the expression any further,, the correct answer is going to be 8y³ - 16y² - 5y.
Let me know if you have any further questions.
Find the values of x and y that make k || j and
m || n.
x =
y =
Answer:
x= 80
y= 130
Step-by-step explanation:
The correct values of x and y that make k || j and m || n are x = 130 and y = 130.
To find the values of x and y, we need to use the fact that if two lines are parallel, their corresponding angles are equal.
Given that k is parallel to j, we have:
x = 50 (corresponding angles)
Since m is parallel to n, we have:
y + 80 = 210 (corresponding angles)
Solving for y:
y = 210 - 80
y = 130
Now, we have the value of x as 50 and the value of y as 130. However, we also know that the angles x and y are supplementary because they form a straight line. Therefore, their sum must be 180 degrees.
x + y = 180
50 + y = 180
y = 180 - 50
y = 130
This confirms that y is indeed 130 degrees. Since x and y are supplementary and both equal to 130 degrees, we have a contradiction because the sum of x and y should be 180 degrees.
To resolve this contradiction, we must re-evaluate our initial assumption that x = 50 degrees. Since x and y are supplementary, and we have correctly determined that y = 130 degrees, we must have:
x + y = 180
x + 130 = 180
x = 180 - 130
x = 50
This is incorrect because we initially assumed x = 50 degrees based on corresponding angles, but we did not consider that the angle adjacent to x on line k is not given and could be different from the corresponding angle of 50 degrees on line j.
To correct this, we should consider the angle adjacent to x on line k, which must sum up with x to 180 degrees because of the straight line. Let's call this angle x'. Since k is parallel to j, x' corresponds to the angle of 130 degrees on line j. Therefore, we have:
x' + x = 180
130 + x = 180
x = 180 - 130
x = 50
Now, considering that x and y are supplementary:
x + y = 180
50 + y = 180
y = 180 - 50
y = 130
Thus, we have x = 50 degrees and y = 130 degrees, which are indeed the values that make k || j and m || n. However, since x and y are supplementary, they must both be 130 degrees to satisfy the conditions of the problem.
Therefore, the correct values are x = 130 degrees and y = 130 degrees.
1. The radius, r, of a circle is one-half of the length of its diameter, d.
r = d
2r = d
+ r = d
r=d
r=
Answer:
2r=d stands as correct
Step-by-step explanation:
At a rate of 36 miles per hour, it takes Henry 15 minutes to drive from the library to his house. Show how to find the distance that Henry traveled. Include units in your calculation.
Let point C be between V and W on VW. Given that VW = 61, VC = z + 13, and CW = z + 8, solve for z. A. 18 B. 19 C. 20 D. 21
A flat rectangular piece of aluminum has a perimeter of 70 inches. The length is 11 inches longer than the width. Find the width. A. 34 inches B. 35 inches C. 23 inches D. 12 inches
perimeter = 2L +2w
L = w+11
70 = 2(w+11) +2w
70 = 2w+22+2w
70= 4w + 22
48 = 4w
w=48/4 = 12
width = 12
length = 12+11 = 23
2x12 = 24
2x23 = 46
46+24 = 40
length = 23 inches, width = 12 inches
Answer is D
Answer:
The answer is the option D
[tex]12\ inches[/tex]
Step-by-step explanation:
we know that
The perimeter of a rectangle is equal to
[tex]P=2L+2W[/tex]
where
L is the length side of the rectangle
W is the width side of the rectangle
In this problem we have
[tex]P=70\ in[/tex]
so
[tex]70=2L+2W[/tex] ------> equation A
[tex]L=W+11[/tex] ------> equation B
Substitute equation B in equation A and solve for W
[tex]70=2[W+11]+2W[/tex]
[tex]70=2W+22+2W[/tex]
[tex]4W=70-22[/tex]
[tex]W=48/4[/tex]
[tex]W=12\ in[/tex]
Justify the last two steps of the proof.
Given MN is congruent to segment PO and MO is congruent to PN
Prove MNO is congruent to PON
Proof:
1. MN is congruent to segment PO _______ 1. Given
2.MO is congruent to PN_______ 2. Given
3. NO is congruent to ON ________ 3. ?
4.MNO is congruent to PON___ 4. ?
*Symmetric Property of congruent to; SAS
*Reflexive Property of congruent to; SAS
*Symmetric Property of congruent to; SSS
*Reflexive Property of congruent to; SSS
Based on the information, the correct option is 4. Reflexive Property of congruent to; SSS
What is congruence?The reflexive property of congruence states that any geometric figure is congruent to itself. In other words, any shape or object is congruent to itself.
For example, if we have a triangle ABC, we can say that triangle ABC is congruent to triangle ABC. This is because all the corresponding sides and angles of the two triangles are equal, and they represent the same geometric figure.
NO and ON are the same line. They are congruent by the reflexive property (a line segment is a reflection of itself). Shape MNO and shape PON are congruent by side-side-side since:
side PN = side MO
side MN = side PO
side NO = side ON
Learn more about congruence
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A fracture in the left femoral region that is 5 centimeters proximal to the patellar region and 30 centimeters distal to the coxal region will be __________.
A fracture in the left femoral region that is 5 centimeters proximal to the patellar region and 30 centimeters distal to the coxal region will be located in the midshaft of the femur.
The femur is the long bone in the thigh, and it has distinct regions:
Coxal Region (Hip Region):
This refers to the upper end of the femur, which articulates with the hip bone (coxal bone).
A fracture occurring here would typically be near the hip joint.
Patellar Region (Knee Region):
This refers to the lower end of the femur, where it articulates with the patella (knee cap).
A fracture here would typically involve the knee joint.
Midshaft of the Femur:
This is the region between the coxal and patellar regions.
A fracture that is 5 centimeters proximal (closer to the hip) to the patellar region and 30 centimeters distal (away from the hip) to the coxal region would be located in the midshaft of the femur.
Fractures in the midshaft of the femur can vary in severity, and treatment may depend on factors such as the type of fracture (e.g., simple, comminuted), the extent of displacement, and the patient's overall health.
These fractures are often serious and may require surgical intervention, such as the placement of pins, screws, or a metal rod to stabilize the bone and promote proper healing.
Rehabilitation and physical therapy are also crucial for recovery and restoring function.
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A rectangle has perimeter 80 m and length 27 m. What is the width?
For f(x)=-3x+6, find f(-4)
What is the distributive property of 60 - 50?
In a college of exactly 2740 students, exactly 55 % are male. what is the number of female students? express your answer as an integer.
In a college of exactly 2740 students, exactly 55 % are male. 1233 is the number of female students.
What is percentage?
A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
In a college of exactly 2740 students,
exactly 55 % are male.
i.e. female students = 45%
so, the number of female students = 2740*45%
=1233
Hence, In a college of exactly 2740 students, exactly 55 % are male. 1233 is the number of female students.
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Find the inverse of f(x)= -x + 3
what is( ×+4 /6)=(18/12)
x + y = 12
x - y = 10
What is the value of the x-determinant for the system shown?
(A.) -22
(B.) -12
(C.) -2
Final answer:
The value of the x-determinant for the system of equations is (C) -2, which is found by evaluating the determinant of the system's coefficient matrix.
Explanation:
To find the x-determinant for the system of equations given below:
x - y = 10
We can set up the coefficient matrix for these equations:
Matrix [A] =
| 1 1 |
| 1 -1 |
The determinant of this matrix is calculated by multiplying the diagonal elements and then subtracting the product of the off-diagonal elements. Hence, the determinant (det A) = (1)(-1) - (1)(1) = -1 - 1 = -2.
Therefore, the value of the x-determinant is (C) -2.
What is the sector area created by the hands of a clock with a radius of 9 inches when the time is 4:00? 6.75π in.2 20.25π in.2 27π in.2 81π in.2?
we know that
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
where
r is the radius of the circle
In this problem we have
[tex]r=9\ in[/tex]
substitute in the formula
[tex]A=\pi*9^{2}=81 \pi\ in^{2}[/tex]
The area of the complete circle subtends [tex]360\ degrees[/tex]
When the time is 4:00 the angle formed by the hands of a clock is [tex]120\ degrees[/tex]
so by proportion
Find the area of the sector area
[tex]\frac{81\pi}{360} \frac{in^{2}}{degree} =\frac{x}{120} \frac{in^{2}}{degree} \\ \\x=120*81 \pi /360\\ \\x=27 \pi\ in^{2}[/tex]
therefore
the answer is the option
[tex]27 \pi\ in^{2}[/tex]
How to write a standard form equation with an undefined slope?
What is the union of the following sets?
G = {12, 14, 16, 18}
H = {13, 15, 17, 18}
A. {18}
B. {12, 13, 14, 15, 16, 17}
C. { }
D. {12, 13, 14, 15, 16, 17, 18}
Answer: D. {12, 13, 14, 15, 16, 17, 18}
Step-by-step explanation:
The union of two sets A and B is the set of elements which are in A, in B, or in both A and B, without repetition.
In this case, the union of the sets G and H will be the set of elements in G= {12, 14, 16, 18} and then the set of elements in H= {13, 15, 17, 18}, excluding those that already were in G, which in this case is the number 18.
Then:
G ∪ H={12, 13, 14, 15, 16, 17, 18}
Only individuals over the age of 60 need to create an estate plan? True or False
Answer: False
Step-by-step explanation: People of any age over 21 need to complete an estate plan or a will. If you don't complete an estate plan or a will, anything you have could be left to the government. Regardless of your age or income, you always want to have a plan to distribute your money should you die unexpectedly.
The square root of 2.25 is
A.15
B.1.5
C.0.15
D.irrational
Mark draws one card from a standard deck of 52. he receives $ 0.35 for a heart, $ 0.55 for a jack and $ 0.85 for the jack of hearts. how much should he pay for one draw
To find out how much Mark should pay for one draw, calculate the expected value by multiplying the payouts for a heart, a jack, and the jack of hearts by their respective probabilities. Sum these values to find the amount Mark should pay per draw to make the game fair, which is $0.135.
To determine how much Mark should pay for one draw from the deck of 52 cards, we need to calculate the expected value (EV) of one draw. The EV is calculated by multiplying each outcome by its probability and summing these products.
The deck has 13 hearts, so the probability of drawing a heart (excluding the jack of hearts) is 12/52 or 3/13. Drawing any jack other than the jack of hearts has 3 possible outcomes in the remaining 51 cards; the probability is 3/52. The jack of hearts is a single card with a probability of 1/52. The remaining 36 cards are neither hearts nor jacks and yield no payout.
The EV is calculated as follows:
(12/52 × $0.35) for a heart
(3/52 × $0.55) for a jack
(1/52 × $0.85) for the jack of hearts
Adding these up we get: (3/13 × $0.35) + (3/52 × $0.55) + (1/52 × $0.85) = $0.13538. To ensure the game is fair and the host neither loses nor gains money in the long term, Mark should pay $0.135 per draw.
M is the midpoint of CF for the points C(1, 2) and F(7, 10). Find MF.
To calculate the length of MF, find the midpoint M of CF using the midpoint formula, then use the distance formula to determine the length of MF, which is 5.0 cm.
Explanation:To find the length of the segment MF, we must first determine the coordinates of the midpoint M of the segment CF. Since C has coordinates (1, 2) and F has coordinates (7, 10), we use the midpoint formula which is ( (x1 + x2)/2, (y1 + y2)/2 ). Calculating this for C and F gives us the coordinates of M as:
x-coordinate of M = (1 + 7)/2 = 4y-coordinate of M = (2 + 10)/2 = 6Therefore, M has coordinates (4, 6). Now, to find the distance MF, we use the distance formula between points M and F:
MF = √[(x2 - x1)² + (y2 - y1)²] where (x1, y1) are the coordinates of M and (x2, y2) are the coordinates of F.
Replacing with the known values:
MF = √[(7 - 4)² + (10 - 6)²]
MF = √[3² + 4²] = √[9 + 16] = √25 = 5.0 cm
Thus, the length of the segment MF is 5.0 cm.
Find an equation of the sphere with points p such that the distance from p to a(−3, 6, 4) is twice the distance from p to b(5, 3, −2).
How to put 33 into 4:7
Please help me . I don't get it