Serena has attached a 10 inch ribbon to the corners of a frame to hang it on the wall. The frame 9 inches wide. How far above the top of the frame will the hook need to be? Round
Answers
Answer: The hook would be 2.2 inches (approximately) above the top of the frame
Step-by-step explanation: Please refer to the picture attached for further details.
The top of the picture frame has been given as 9 inches and a 10 inch ribbon has been attached in order to hang it on a wall. The ribbon at the point of being hung up would be divided into 5 inches on either side (as shown in the picture). The line from the tip/hook down to the frame would divide the length of the frame into two equal lengths, that is 4.5 inches on either side of the hook. This would effectively give us two similar right angled triangles with sides 5 inches, 4.5 inches and a third side yet unknown. That third side is the distance from the hook to the top of the frame. The distance is calculated by using the Pythagoras theorem which states as follows;
AC^2 = AB^2 + BC^2
Where AC is the hypotenuse (longest side) and AB and BC are the other two sides
5^2 = 4.5^2 + BC^2
25 = 20.25 + BC^2
Subtract 20.25 from both sides of the equation
4.75 = BC^2
Add the square root sign to both sides of the equation
2.1794 = BC
Rounded up to the nearest tenth, the distance from the hook to the top of the frame will be 2.2 inches
To find the distance above the frame for hanging, use the Pythagorean theorem by considering the diagonal created by the ribbon. The hook needs to be approximately 5.39 inches above the top of the frame.
To find how far above the top of the frame the hook needs to be, we need to consider the diagonal of the frame created by the ribbon. Using the Pythagorean theorem, we can calculate this distance.
Width of the frame = 9 inchesLength of the ribbon attached diagonally = 10 inchesUsing Pythagorean theorem: (9)² + x² = (10)²x = square root of (10² - 9²)x = 5.39 inchesTherefore, the hook needs to be approximately 5.39 inches above the top of the frame.
Related Questions
Sharon has 72 beads. She has twice as many sphere beads as cylinder beads. How many of each kind of bead does Sharon have? How did you solve the problem? How can you check your check.
Answers
Answer:
Sphere=48 beads
Cylinder=24 beads
Step-by-step explanation:
Let the number of cylinder beads be y and since she has twice as many sphere beads, the sphere beads will be 2y
The sum of sphere and cylinder beads will be y+2y=3y
This sum is equivalent to the total number given as 72
Therefore, equating 3y to be equal to 72 we obtain the equation
3y=72
Dividing by 3 on both sides we obtain that
Y=72/3=24 beads for cylinder
Since the sphere is 2y then 2*24=48
To confirm, it is evident that 48+24=72
Also, the number 48 is double/twice the number 24
If you invest $12,000 and one year later your investment has grown to $13,188, then the rate of return on your investment was ____ %. (Round your answer to the nearest tenth of a percent.) Type in your numerical answer only; do not type any words or letters with your answer.
Answers
turn the decimal into a percentage
1.099 times 100= 109.9%
what makes 2 figures congruent
Answers
Two polygons are congruent if they are the same size and shape
What is 3/2 times 14
Answers
Answer:
21
Step-by-step explanation:
3/2×14=21
Answer:
21
Step-by-step explanation:
A data set includes 103 body temperatures of healthy adult humans having a mean of 98.9degreesf and a standard deviation of 0.67degreesf. construct a 99% confidence interval estimate of the mean body temperature of all healthy humans. what does the sample suggest about the use of 98.6 degreesf as the mean body temperature?
Answers
A 99% confidence interval for the mean body temperature can be calculated using the sample mean, standard deviation, and the t-score corresponding to the confidence level. The findings may suggest that the commonly accepted average body temperature of 98.6°F could be reconsidered if it does not fall within this interval.
Constructing a 99% Confidence Interval
To construct a 99% confidence interval for the mean body temperature of all healthy humans, we use the sample mean, standard deviation, and the t-distribution since the population standard deviation is not known. With a mean of 98.9°F, a standard deviation of 0.67°F, and a sample size of 103, we can calculate the margin of error using a t-score that corresponds to the 99% confidence level.
First, we find the t-score from the t-distribution table for 102 degrees of freedom (n-1) that corresponds to a 99% confidence level. Then, we calculate the margin of error using the formula:
Margin of Error (E) = t-score * (standard deviation / sqrt(n))
This margin of error is then added and subtracted from the sample mean to obtain the confidence interval:
Lower Limit = Mean - Margin of Error
Upper Limit = Mean + Margin of Error
This confidence interval provides a range within which we can be 99% confident that the true mean body temperature of all healthy humans lies.
Implications for 98.6°F as Average Body Temperature
The sample suggests that the mean body temperature of 98.6°F might not be accurate for all individuals. If the constructed 99% confidence interval does not contain the traditional mean of 98.6°F, it could indicate that the average body temperature is different than what has been historically taught.
The 99% confidence interval estimate of the mean body temperature of all healthy humans is approximately (98.7294, 99.0706) degrees Fahrenheit.
To construct a 99% confidence interval for the mean body temperature of all healthy humans, we'll use the formula:
[tex]\[ \text{Confidence Interval} = \bar{x} \pm z \left( \frac{s}{\sqrt{n}} \right) \][/tex]
Let's calculate the confidence interval:
[tex]\[ \text{Confidence Interval} = 98.9 \pm 2.576 \left( \frac{0.67}{\sqrt{103}} \right) \]First, let's calculate \(\frac{s}{\sqrt{n}}\):\[ \frac{s}{\sqrt{n}} = \frac{0.67}{\sqrt{103}} \approx 0.0662 \][/tex]
Now, we can find the margin of error:
[tex]\[ \text{Margin of Error} = 2.576 \times 0.0662 \approx 0.1706 \]Finally, construct the confidence interval:\[ \text{Confidence Interval} = 98.9 \pm 0.1706 \][/tex]
So, the 99% confidence interval estimate of the mean body temperature of all healthy humans is approximately (98.7294, 99.0706) degrees Fahrenheit.
jazzy...respond pls..A box contains different-colored marbles that are all the same size. The table below shows the colors and amount of each marble in the box:
Color of Marble Number
Red 4
Blue 8
Green 3
Pink 5
Allen selects a marble from the box randomly, without looking, and then tosses a fair coin. What is the probability that Allen will select a red marble and the coin will land heads up?
Answers
Answer:
well is a 50 50 chains that Allen will get a red marble and
a 50 50 that the coin will land heads up.
Step-by-step explanation:
If (x, y) is a solution to the system of equations, what is the value of x?
5
2
x + y = 2
x +
2
3
y = 4
A) 4
B) -4
C) 12
D) -12
Answers
Answer:
B) -4
Step-by-step explanation:
(5/2)x + y = 2
x + (2/3)y = 4
y = 2 - (5/2)x
x + (2/3)(2 - (5/2)x) = 4
x + 4/3 - (5/3)x = 4
(-2/3)x = 8/3
-2x = 8
x = -4
All tickets for a concert are the same price as the ticket agency as a fixed fee to every order a person who orders five tickets pays $93 a person who orders three tickets pays $57 a hint you'll need to calculate the slope of your first line. what is the cost per ticket?
Answers
Answer:
$18 is the cost per ticket ordered
Step-by-step explanation:
We proceed as follows;
Let the cost per ticket be $x while the fixed fee be $y
For the person that ordered 5 tickets, we can have his mathematical representation as;
5(x) + y = 93 •••••••••(i)
For the person that ordered 3 tickets, we can have his mathematical representation as;
3(x) + y = 57 ••••••••(ii)
From the first equation, we can have;
y = 93 - 5x
Let’s plug this into ii
3x + 93 - 5x = 57
-2x = 57 -93
2x = 36
x = 36/2
x = $18
This means that the cost per ticket ordered is $18
The length of the base edge of a pyramid with a regular hexagon base is represented as x. The height of the pyramid is 3 times longer than the base edge. The height of the pyramid can be represented as . The of an equilateral triangle with length x is units2. The area of the hexagon base is times the area of the equilateral triangle. The volume of the pyramid is x3 units3.
Answers
Answer: 1: 3x
2: area
3: six
4: 3/2
Step-by-step explanation:
The height of the pyramid can be represented as 3x, The area of the hexagon base is six times the area of the equilateral triangle, and the volume is 3/2 times √3 x³.
What is a pyramid that has a hexagonal base?The pyramid has a hexagonal base with six isosceles triangular faces known as a hexagonal base pyramid. It is also called a heptahedron.
We have,
The length of the base edge of a pyramid = x units
The height of the pyramid is three times longer than the base edge ie.
The height of the pyramid = 3x
The area of an equilateral triangle with base length x units is [tex]\rm x\sqrt{3}[/tex] square units square(let's assume)
Then the area of the hexagon base = 6×[tex]\rm x\sqrt{3}[/tex] ⇒ 6[tex]\rm x\sqrt{3}[/tex] square units.
Because the hexagon base has a six-equilateral triangle.
Let's assume the area of a hexagonal base is Y times the equilateral triangle.
[tex]\rm 6x\sqrt{3} = Y \times x\sqrt{3}[/tex]
Y = 6 times
We know the volume of a hexagonal pyramid = [tex]\frac{\sqrt{3} }{2} a^2h[/tex]
Where a is the base length and h is the height of the hexagonal pyramid.
Here a = x units and h = 3x units
Then Volume:
[tex]\frac{\sqrt{3} }{2} x^2(3x)\\\\\frac{{3} }{2} \sqrt{3}x^2[/tex]
Thus, the height of the pyramid can be represented as 3x, The area of the hexagon base is six times the area of the equilateral triangle, and the volume is 3/2 times √3 x³.
Learn more about the pyramid here:
https://brainly.com/question/17615619
A coin is flipped and a normal dice is rolled.
a)
How many possible outcomes are there?
b)
What is the probability of getting a tail and a five?
c)
What is the probability of getting a number less than five and a head?
Answers
b) (1/2)(1/6) = 1/12 = .083
c) (1/2)(4/6) = 1/3 = .33
Total possible outcomes if a coin is flipped and a normal dice is rolled are 12
Probability of getting a tail and a five will be 1/12
The probability of getting a number less than five and a head is 1/3
What is probability?Probability is the chance of happening of an event.Probability is always ≤ 1How to find out how many possible outcomes are there?If a coin is tossed 2 possible outcomes will be there. Either it will be a Head or a Tail.If a normal dice is rolled 6 possible outcomes will be there.∴ Total possible outcomes = (6 x 2) = 12
How to know the probability of getting a tail and a five?As we know that there will be 12 possible outcomes .Getting a five and a tail will be one of those possible outcomes.∴ Probability of getting a tail and a five will be 1/12
How to know the probability of getting a number less than five and a head?We know that probability of getting a head when a coin is flipped is 1/2 Probability of getting a number less than five is a dice is rolled is = 4/6∴ The probability of getting a number less than five and a head = (1/2)(4/6) = 4/12 = 1/3
Find more about "Probability" here : https://brainly.com/question/25870256
#SPJ2
At time t is greater than or equal to zero, a cube has volume V(t) and edges of length x(t). If the volume of the cube decreases at a rate proportional to its surface area, which of the following differential equations could describe the rate at which the volume of the cube decreases?
A) dV/dt=-1.2x^2
B) dV/dt=-1.2x^3
C) dV/dt=-1.2x^2(t)
D) dV/dt=-1.2t^2
E) fav/dt=-1.2V^2
Answers
Answer:
A) dV/dt=-1.2x^2
Step-by-step explanation:
The rate of change of volume is given by dV/dt. Surface area is proportional to x^2. Since the volume is decreasing, the constant of proportionality between surface area and rate of volume change will be negative. Hence a possible equation might be ...
dV/dt = -1.2x^2
Answer:
C
Step-by-step explanation:
V(t) = [x(t)]³
A(t) = 6[x(t)]²
dV/dt = k × 6[x(t)]²
Where k < 0
From the options,
taking k = -0.2
dV/dt = -1.2[x(t)]²
You have 16 socks in your drawer. 4 are black, 6 are white, 4 are blue, and 2 are gray. Suppose you randomly choose a sock, replace it, and randomly choose another. What is the probability that either the first sock is blue or the second sock is gray?
Answers
Answer:
11/32
Step-by-step explanation:
4/16 + 2/16 - 1/32
simplify and solve
What is circumference? Please select all that apply:
A) distance around the circle
B) the space inside the circle
C) To find the circumference C of a circle if you know the diameter d is to multiply pi by the diameter
D) To find the circumference if you know the radius, replace d with 2r in the formula
E) the formula for circumference is C=pi + r
Answers
Answer:
A, C and D are correct.
\
Step-by-step explanation:
A is correct.
B is false; that space is the "area" of the circle.
C is true. C = πd
D is true. C = 2πr
E is false. Way off.
Final answer:
Circumference is the distance around a circle, calculated as C = πd or C = 2πr, depending on whether the diameter or radius is known. (Option A,C,D)
Explanation:
Circumference is the term used to describe the distance around a circle. When calculating the circumference, you can use different formulas depending on the information you have about the circle. If you know the diameter (d), the circumference (C) can be found by multiplying the diameter by pi (π), using the formula C = πd. Alternatively, if you know the radius (r) of the circle, you can use the formula C = 2πr since the diameter is twice the radius (d = 2r).
The correct answers to the question are:
A) distance around the circleC) To find the circumference C of a circle if you know the diameter d is to multiply pi by the diameterD) To find the circumference if you know the radius, replace d with 2r in the formulaIt's important to note that the space inside the circle is referred to as the area, not the circumference, and the formula for circumference is not C = pi + r as stated in option E, but rather C = πd or C = 2πr.
Which graph shows the solution set for Negative 4.4 greater-than-or-equal-to 1.6 x minus 3.6?
A number line going from negative 3 to positive 3. A closed circle is at negative 0.5. Everything to the left of the circle is shaded.
A number line going from negative 3 to positive 3. A closed circle is at negative 0.5. Everything to the right of the circle is shaded.
A number line going from negative 7 to negative 1. A closed circle is at negative 5. Everything to the left of the circle is shaded.
A number line going from negative 7 to negative 1. A closed circle is at negative 5. Everything to the right of the circle is shaded.
Answers
Answer:
A
Step-by-step explanation:
right on Edge.2020
The graph that shows the solution set for -4.4 ≥ 1.6x - 3.6 is A number line going from negative 3 to positive 3. A closed circle is at negative 0.5. Everything to the left of the circle is shaded, the correct option is A.
What is an Inequality?An Inequality is a statement that is formed when two expressions are joined using an inequality operator.
-4.4 ≥ 1.6x - 3.6
The value of x is
-4.4+3.6 ≥ 1.6x
x ≤ -0.5
The number line of any length, which has a closed circle at -0.5 and the left side of the point -0.5 is shaded is the graph of the inequality.
To know more about Inequality
https://brainly.com/question/20383699
#SPJ5
A net has a square at the center and 4 triangles on the sides. The square has side lengths of 4 millimeters. The triangles have a base of 4 millimeters and height of 7 millimeters. Complete the statements about the net of this pyramid. The net will have square face(s). The net will have triangular face(s). The triangular faces are . The net will have a total of faces.
Answers
Answer:
The net will have 1 square face
The net will have 4 triangular faces
The triangular faces are identical
The net will have a total of 5 faces.
Step-by-step explanation:
If you look at the picture, count the triangular faces, you will see 4.
Count the square on the bottom, its 1.
All the triangular faces are identical, if they weren't the picture would be all over the place.
Add 1+4 and it equals 5. The net will have a total of 5 faces.
(Hope you got it right, cause I took it and got it right!! Also I'm not good at explaining math lol)
Stay safe and social distance :DD
The net will have one square face, four triangular faces, the triangular faces are identical.
The net will have a total of five faces.
What is a square pyramid?"It is a three-dimensional geometric shape that has a square base and four triangular sides that are joined at a vertex."
What is net?"It is a two-dimensional structure which forms a three-dimensional geometric structure by folding."
According to the problem,
The base of the square pyramid has a square and if a three dimensional structure of a net formed into a pyramid is looked at, we can see 1 face of the square at the base.
A pyramid is comprised of 4 triangles joined together at the vertex.
Again, if a three dimensional structure of a pyramid is looked at, we can see 4 faces of the pyramid.
Now in order to align into a single unit to be joined at the vertex, the triangles have to be identical. They will have similar faces with the same base and slant height.
Therefore, 1 square face and 4 triangular faces adds up to five total faces.
Hence, we can conclude that the net will have one square face, four triangular faces and a total of five faces with the triangular faces being similar.
Learn more about net here:
https://brainly.com/question/12032061
#SPJ2
we started something new and I'm competely lost
Answers
Given:
Triangle ABC is similar to triangle XYZ.
The measures of the sides are AB = 6 cm, BC = 18 cm and XY = 12 cm
We need to determine the measure of side YZ.
Measure of YZ:
Since, ABC and XYZ are similar triangles, by using similar triangles property, we have;
[tex]\frac{AB}{XY}=\frac{BC}{YZ}[/tex]
Let the length of YZ be x.
Substituting the values, we get;
[tex]\frac{6}{12}=\frac{18}{x}[/tex]
Cross multiplying, we get;
[tex]6x=12 \times 18[/tex]
[tex]6x=216[/tex]
Dividing both sides by 6, we have;
[tex]x=36[/tex]
Thus, the value of x is 36.
Hence, the measure of the side YZ is 36 cm.
What is the length of BC given that CG is 2.5 inches and GB is 253 inches? Round to the nearest tenth.
3.5 inches
8.8 inches
9.1 inches
10.8 inches
Answers
Answer 3.5 inches
Step-by-step explanation:
Answer:
A. 3.5
Step-by-step explanation:
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 8 large boxes and 3 small boxes has a total weight of 187 kilograms. A delivery of 2 large boxes and 5 small boxes has a total weight of 102 kilograms. How much does each type of box weigh?
Answers
Answer:
Weight of large box = 18.5 Kg
Weight of small box = 13 Kg
Step-by-step explanation:
Let the weight of large box be X kg
Let the weight of small box be Y kg
So weight of 8 large boxes = 8X
weight of 3 small box be = 3Y
According to question
8 large boxes and 3 small boxes has a total weight of 187
mathematically it can be represented as
8X + 3 Y = 187
_________________________________________________
Second condition
weight of 2 large boxes = 2X
weight of 5 small box be = 5Y
According to question
2 large boxes and 5 small boxes has a total weight of 102 kilograms
mathematically it can be represented as
2X + 5Y = 102
--------------------------------------------------------------------------
we have two equation
8X + 3 Y = 187 -------------------A
2X + 5Y = 102 -------------------B
multiplying equation B with 4 on both side of equation we have
4*(2X + 5Y) = 4*102
=> 8X + 20Y = 408 -------------------C
Now subtracting equation A and C on both sides we have
8X + 3 Y - (8X + 20Y ) = 187 -408
8X - 8X + 3 Y - 20Y = -221
-17Y = -221
=> Y = -221/-17 = 13
Now substituting value of Y in equation B we have
2X + 5*13 = 102
=> 2X + 65 = 102
=> X = (102-65)/2 = 18.5
______________________________
Weight of large box = 18.5 Kg
Weight of small box = 13 Kg
The large box weighs 17 kg and the small box weighs 13 kg.
Explanation:Let's denote the weight of a large box as x and the weight of a small box as y. We can set up a system of equations to solve for the weights:
8x + 3y = 187 (equation 1)
2x + 5y = 102 (equation 2)
To solve the system, we can multiply equation 1 by 2 and equation 2 by 8 to eliminate x:
16x + 6y = 374 (equation 3)
16x + 40y = 816 (equation 4)
Subtracting equation 3 from equation 4, we get:
34y = 442
Solving for y, we find y = 13.
Substituting this value back into one of the original equations, we find x = 17.
Therefore, the large box weighs 17 kilograms, and the small box weighs 13 kilograms.
Learn more about weights here:https://brainly.com/question/33928093
#SPJ3
Frank has twice as many CDs as Vanessa. Lois has 4 less than 2 times as many CDs as Frank. If there is a total of 115 CDs for all 3 people, how many CDs does each person have?
Answers
Answer:
Frank, Vanessa, Lois have 34, 17, 64 disks respectively
Step-by-step explanation:
In this question, we are to calculate the number of disks each of the 3 has.
Let the number of disks owned by Frank be x
for vanessa, she has half of what frank has and that would be x/2
Lois has 4 less than 2 times what Frank has, that would be 2x - 4
adding the 3, we have a total of 115 disks
This means that;
x + x/2 + (2x-4) = 115
Multiply throughout by 2;
that gives;
2x + x + 4x - 8 = 230
7x -8 = 230
7x = 230+ 8
7x = 238
x = 238/7
x = 34 disks
Frank has 34
Vaness has 34/2 = 17
Lois have 2x - 4 = 2(34) - 4 = 68 - 4 = 64 disks
Answer:
So Frank has 34 CDs, Vanessa has 17 CD's and Lois has 64 CDs
Step-by-step explanation:
Let's call the amount of CDs that Frank has by 'F', that Vanessa has by 'V' and that Lois has by 'L'. Then, we can write the following equations:
F = 2*V
L = 2*F - 4
F + V + L = 115
If we use the values of F and L in the third equation, we have that:
2*V + V + 2*(2*V) - 4 = 115
7*V = 119
V = 17 CD's
Now we can find F:
F = 2*V = 34 CDs
And then we find L:
L = 2*F - 4 = 68 - 4 = 64 CDs
So Frank has 34 CDs, Vanessa has 17 CD's and Lois has 64 CDs
Line I and line m are straight lines , which statements are true regarding the angles in the figure!! Select 2 options .
Answers
Answer:2(B) and 4(D) are your answers!!
Step-by-step explanation:
hope this helped youu!!have a terrific Tuesday!
The university is on a bearing of 050 degrees from the stadium and 300 degrees from the hospital. Mark the position of the university on the map with a cross
Answers
The position of the university marked x is shown in the attachment.
Given that university is on a bearing of 050 degrees from the stadium and 300 degrees from the hospital.
so we can say that the university position is gotten relative to the the position of the stadium and hospital.
The university is 50° from the stadium and then 350° from the hospital.
I.e it is N 50° E from the stadium and N 60° W from hospital.
The angle forms will be 50+60 = 110°
The point where the two lines intersect is the position of the university. Mark this point with a cross on the map.
Learn more about diagrams here;
https://brainly.com/question/16670962
#SPJ12
Help please please help
Answers
Answer:
A, 61 degrees
Step-by-step explanation:
Since the two angles are supplementary, this means that they add up to 180 degrees. m=180-119=61 degrees, or option A. Hope this helps!
Answer:
A. 61
Step-by-step explanation:
The line AOB is a 180 degree line. That means that both the angles have to add up to 180. Angle AOc is 119. 180-119= 61. You can check by doing 119 + 61 does it equal 180.
Hope this helps!
Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour
of use to rent a paddle boat. Write an equation to find out how many
hours, h, they rented the Boat if the total cost was $33,
Answers
Answer:
y=2x+15
Step-by-step explanation:
h=9
The equation to find the number of hours the boat was rented is $33 = $15 + ($2 imes h). After subtracting the deposit fee and dividing by the cost per hour, the solution is h = 9, indicating the boat was rented for 9 hours.
The equation to find out how many hours, h, the boat was rented for when the total cost was $33 can be represented as follows:
Total cost = Deposit fee + (Cost per hour imes Number of hours)
Substituting the given values, we have:
$33 = $15 + ($2 imes h)
To solve for h, we subtract $15 from both sides of the equation:
$33 - $15 = $15 - $15 + ($2 imes h)
So, $18 = $2 imes h
Next, we divide both sides of the equation by $2 to solve for h:
$18 \/ $2 = ($2 imes h) \/ $2
h = 9
This means they rented the boat for 9 hours.
How to solve a quadrilateral
Answers
Answer:
You give it a nudge and it solves itself.
Step-by-step explanation:
Answer: Here is an example.
Step-by-step explanation:
Given: parallelogram ABCD, sides as marked.
Find AD.
Solution: 6x - 10 = 3x + 5 (opposite sides)
3x - 10 = 5; 3x = 15; x = 5
AD = 4x - 5 = 4(5) - 5 = 15
Remember:
• This is where the properties of a parallelogram are needed. You know the opposite sides of a parallelogram are congruent, so set the opposite sides equal to one another.
• Be sure to pair up the opposite sides correctly. The side labeled 4x - 5 will not be used when solving for x, but will be used to solve for AD.
There are 12 employees at the sub shop. How many ways can the manager choose 4 for the Sunday evening shift? Permutation or combination and the answer?
Answers
Answer:
It is a combination answer
495 ways
Step-by-step explanation:
In this question, we are tasked with calculating the number of ways in which a manager can select 4 people out of 12 for the Sunday evening shift.
Firstly, the question talks about selecting a particular number from a mix, this is a combination question since the key word SELECT is mentioned.
Now, how do we go about it? To select a partial number from a mix , we use the combination formula as stated.
Mathematically, say we are selecting a number r from a total of numbers n, the number of ways we can do this is nCr = n!/(n-r)!r!
In this case however, we are simply selecting 4 out of 12
Our combinational equation thus becomes 12C4 = 12!/(12-4)!4! = 12!/8!4! = 495 ways
Final answer:
The manager can choose 4 from 12 employees in 495 different ways for the Sunday evening shift, using a combination rather than a permutation since the order of selection does not matter.
Explanation:
To determine the number of ways the manager can choose 4 out of 12 employees for the Sunday evening shift, we need to decide whether the order in which the employees are chosen matters. If the order does not matter, we will use a combination. If the order does matter, we would use a permutation. In this case, because the task is simply to choose 4 employees and the order in which they are chosen does not affect the outcome, we use a combination.
The formula for finding the number of combinations when choosing k objects out of a total of n objects without repetition is given by:
C(n, k) = n! / (k! * (n-k)!)
In this situation, we have n=12 and k=4, so we calculate:
C(12, 4) = 12! / (4! * (12-4)!) = 12! / (4! * 8!) = (12*11*10*9) / (4*3*2*1) = 495
Therefore, there are 495 different ways for the manager to choose 4 employees for the Sunday evening shift.
In which number does the digit 8 have a value that is 1,000 times greater than the digit 8 in the number 349,257.83?
Answers
Answer:
349,257,830
Step-by-step explanation:
Multiply 349,257.83 by 1000
The required number where the digit 8 has a value that is 1,000 times greater than the digit 8 in the number 349,257.83 is 349,257,830.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let the number x,
According to the question, [An approximate calculation]
x / 1000 = 349,257.83
x = 1000 [349,257.83]
x = 349,257,830
Thus, the required number where the digit 8 has a value that is 1,000 times greater than the digit 8 in the number 349,257.83 is 349,257,830.
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ6
Rewrite the expressie
sohe.
1) 6(5 + 3)
Answers
Answer:
48
Step-by-step explanation:
6*5+6*3=30+18=48
distubutive property
Una Sección, compuesta por 18 soldados y 2 suboficiales, entra en combate y gasta la quinta parte del total de la munición de dicha Sección. Si la cantidad de cartuchos gastados por los soldados excede en 424 cartuchos al número de cartuchos gastados por los suboficiales. ¿Cuántos cartuchos gastaron los soldados y cuántos los suboficiales sabiendo que la dotación completa por cada hombre es de 175 cartuchos?
Answers
V=3Bh
What is the radius of the cone?
What is the area of the base of the cone?
aft?
What is the volume of the
The soldiers used 562 cartridges in combat, while the subofficers used 138, using the total amount of ammunition and the difference between cartridges used.
Explanation:The total amount of ammunition for the section is 175 per soldier for a total of 20 soldiers, so we have 175 * 20 = 3500 cartridges. A fifth of this ammunition is used in combat, that is, 3500/5 = 700 cartridges. According to the question, the number of cartridges used by the soldiers exceeds that of the subordinates by 424 cartridges, so we can establish a system of equations:
The total ammunition, 700, is the sum of the cartridges used by soldiers (x) and subofficers (y): x + y = 700The number of cartridges used by soldiers (x) is greater than the ammunition used by subofficers (y) by 424: x = y + 424We can then solve this system and find that the soldiers used 562 cartridges and the subofficers used 138.
Learn more about System of Equations here:https://brainly.com/question/35467992
#SPJ2
What single decimal multiplier would you use to increase by 7% followed by a 9% increase?
Answers
Answer:
The decimal multiplier is 1.1663
Step-by-step explanation:
Since the increases are done successively we can find decimal numbers for each one and multiply both to have a single decimal representing the whole operation. When there's a increase this means that we have the original value (100%) summed by some other value, in this case 7%, so the new value would be 100% + 7% = 107%, we can transform this to a decimal number by dividing it by 100, so 107/100 = 1.07. The same applies to the 9% increase, so we would have 109/100 = 1.09. We can now multiply both to obtain a single decimal multiplier, we have:
1.07*1.09 = 1.1663
A jet departs from an airport flying east. At the same time, a second jet departs from the same airport flying west at a speed of 20 miles per hour slower than the first jet. After 1.5 hours, the planes are 1,500 miles apart. What is the speed in miles per hour of the jet traveling east?
A. 300
B. 750
C. 510
D. 490
Answers
Answer:
490mph and 510mph
Step-by-step explanation:
Let x mph and x+20 mph be the speeds of the planes. The rate at which their distance from each other increases will be the sum of their speeds which is 2x+20 mph.
Their distance from each other after three hours is ( 1.5 hours)*(2x+20 mph) = 3x+30 miles. We are given that this is 1500 miles so we can solve for x.
3x+30 = 1500
3x = 1500 - 30
3x = 1470
x = 1470/3
x = 490mph
For the second jet :
x +20 = 490+20
x = 510
Thus the speeds of the two planes are 490 mph and 510mph.
Answer:
510 miles
Step-by-step explanation:
Please kindly check the attached file for explanation.