Answer:
[tex]\huge\boxed{\bf\:1}[/tex]
Step-by-step explanation:
At first, let's factorise the given three numbers.
[tex]12\\= 4 * 3*1\\= \underline {2*2*3*1}[/tex]
[tex]15\\= \underline{5*3*1}[/tex]
[tex]20\\= 4*5*1\\=\underline {2*2*5*1}[/tex]
Here, from the given factors, we can see that the three numbers (12, 15 & 20) don't have any common factors except for 1.
•°• The least numbers divisible by 12, 15 & 20 is 1.
[tex]\rule{150pt}{2pt}[/tex]
Which expression is the factored form of x2 – 7x 10? (x 3)(x 4) (x – 3)(x – 4) (x – 2)(x – 5) (x 2)(x 5)
The expression x^2 -7x + 10 can be written in factored form as given by Option C: (x-2)(x-5)
How to find the factors of a quadratic expression?If the given quadratic expression is of the form [tex]ax^2 + bx + c[/tex]
then its factored form is obtained by two numbers alpha( α ) and beta( β) such that:
[tex]b = \alpha + \beta \\ ac =\alpha \times \beta[/tex]
Then writing b in terms of alpha and beta would help us getting common factors out.
Sometimes, it is not possible to find factors easily, so using the quadratic equation formula can help out without any trial and error.
For this case, we're provided the expression:
[tex]x^2 -7x + 10[/tex]
We can write 10 as multiple of -5 and -2 and
we can write -7 as sum of -5 and -2. Thus, we get:
[tex]x^2 -7x + 10 = x^2 -5x - 2x + 10 = x(x-5+ -2(x-5) = (x-2)(x-5)[/tex]
Thus, the expression x^2 -7x + 10 can be written in factored form as given by Option C: (x-2)(x-5)
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The directors of a dance show expect many students to participate but don’t yet know how many students will come. The directors need 7 students to work on the technical crew. The rest of the students work on dance routines in groups of 9. For the show to work, they need at least 6 full groups working on dance routines.
The inequality that represents the scenario given above in terms of the number of students is 9x + 7 ≥ 54
What is the Inequality?Inequality is known to be a statement that shows the step or order association either it is greater than, equal to, less than, etc., that exist between two or more numbers in an expression.
Note that 7 students are in the technical crew. Denote the number of students in a group as = x
We take the other students in dance routines in groups of 9 as 9x.
Therefore, we say that the total number of students = 9x + 7
Since 6 full groups are working on dance routines, we then multiply by the student dance groups = 9 x 6 = 54
Therefore, we can state that our inequality as:
9x + 7 ≥ 54
Then you collect like terms:
9x ≥ 54 - 7
9x ≥ 47
x ≥ 47/9
x ≥ 6
So therefore, I will write to directors that the number of students they need in each group should be at least 6 students.
See full question below
1. Write and solve an inequality to represent this situation.
2. Write a sentence to the directors about the number of students they need.
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Mrs. Johnson bought 12 pound of ham and used it to make 3 sandwiches. She uses the same amount of ham on each sandwich. What fraction of a pound of ham is on each sandwich
The fraction of a pound of ham that each sandwich has for the case when Mrs Johson used 12 pounds of ham to make 3 sandwiches is 4 pound per ham. or 4/1
How to interpret the division?When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get.
Thus, if 10 mangoes are there, and 2 people, then 10 ÷ 2 is the number of mangoes each person would get, which is 5.
Division, thus, can be interpreted as equally dividing the number that is being divided in total x parts, where x is the number of parts the given number is divided.
Thus, [tex]a \div b =[/tex] a divided in b equal parts.
Also, we can write: [tex]a \div b = a \times \dfrac{1}{b}[/tex]
(it is since a = a times 1 so [tex]a/b = 1 \times (a/b) = (1/b) \times a[/tex])
For this case, we're specified that:
Total ham Mrs. Johnson bought = 12 poundsTotal sandwiches that she makes of that amount of ham = 312 pound of ham is divided in 3 parts for 3 sandwiches (assuming equally divided).
That means:
Amount of ham each sandwich gets = 12 divided by 3 = 12/3 = 4 pounds.
To find the fraction of a pound of ham that is on each sandwich, we find what part of a pound is 4 pounds.
If we take 4 times a pound, then we get 4 pounds.
Thus, 4 of a pound = 4 pound
In fraction, we have: 4 pounds = 4/1 fraction of a pound.
Thus, the fraction of a pound of ham that each sandwich has for the case when Mrs Johson used 12 pounds of ham to make 3 sandwiches is 4 pound per ham. or 4/1 fraction of a pound
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KADS, Inc. Has spent $400,000 on research to develop a new computer game. The firm is planning to spend $200,000 on a machine to produce the new game. Shipping and installation costs of the machine will be capitalized and depreciated; they total $50,000. The machine has an expected life of three years, a $75,000 estimated resale value, and falls under the MACRS 7-year class life. Revenue from the new game is expected to be $600,000 per year, with costs of $250,000 per year. The firm has a tax rate of 35 percent, an opportunity cost of capital of 15 percent, and it expects net working capital to increase by $100,000 at the beginning of the project.
What will the cash flows for this project be? (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places. )
The cash flows for this project will be -$560,450 (negative amount indicated by a minus sign).
To calculate the cash flows for this project, we need to consider the initial investment, operating cash flows, and terminal cash flows over the project's life.
Initial Investment:
Research and development cost: -$400,000
Machine cost: -$200,000
Shipping and installation cost: -$50,000
Net working capital increase: -$100,000
Total Initial Investment: -($400,000 + $200,000 + $50,000 + $100,000) = -$750,000
Operating Cash Flows:
The operating cash flows include revenue, costs, and depreciation for each year.
Revenue: $600,000 per year
Costs: $250,000 per year
Depreciation: Calculated using MACRS depreciation method for 7-year class life.
Year 1:
Depreciation: $200,000 (rounded to the nearest dollar) [MACRS depreciation for Year 1]
Operating Cash Flow: $600,000 - $250,000 - $200,000 = $150,000
Year 2:
Depreciation: $320,000 (rounded to the nearest dollar) [MACRS depreciation for Year 2]
Operating Cash Flow: $600,000 - $250,000 - $320,000 = $30,000
Year 3:
Depreciation: $192,000 (rounded to the nearest dollar) [MACRS depreciation for Year 3]
Operating Cash Flow: $600,000 - $250,000 - $192,000 = $158,000
Terminal Cash Flows:
Terminal cash flow includes the salvage value of the machine and the tax effect of selling the machine.
Salvage Value: $75,000
Tax Effect of Salvage Value: Taxable gain or loss on the sale of the machine = (Selling price - Book value)
Book Value: Accumulated depreciation at the end of Year 3 = $200,000 + $320,000 + $192,000 = $712,000
Selling price: $75,000
Taxable gain or loss: $75,000 - $712,000 = -$637,000
Tax on gain or loss: Tax rate (35%) * Taxable gain or loss = 0.35 * (-$637,000) = -$223,450
Terminal Cash Flow: Salvage Value + Tax on gain or loss = $75,000 + (-$223,450) = -$148,450
Now, let's sum up all the cash flows:
Cash Flows = Initial Investment + Operating Cash Flows + Terminal Cash Flow
Cash Flows = -$750,000 + $150,000 + $30,000 + $158,000 + (-$148,450)
Cash Flows = -$560,450
Therefore, the cash flows for this project will be -$560,450 (negative amount indicated by a minus sign).
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Please Answer Both Questions!
If your correct I'll mark you brainliest if someone else answers
Answer:
Card 3: 53.68 cm, Card 4: 150.72 sq. cm
Step-by-step explanation:
Card 3: First find the circumference, d(pi), 16(3.14)=50.24. Since the circle has 1/4 of it missing, we will divide by 4 then multiply by, 50.24/4=12.56, then multiply by 3 37.68. Lastly, we have to add 16 because of the cutout so 37.68+ 16=53.68
Card 4: Find the area of the circle, r^2(pi), 64(3.14)= 200.96. Then divide by 4 and then multiply by 3, 200.96/4=50.24, 50.24*3=150.72.
George works at Whataburger. He makes $8. 50 per hour and works a maximum of 25
hours per week. The equation e = 8. 50h can be used to determine the amount of money,
e, that George earns after h hours worked. What is the domain and range that represents
this situation?
A Domain: 0 Shs 25
Range: 0 ses 212. 50
B Domain: Oshs 212. 50
Range: 0 ses 25
C Domain: 8. 50 Range: 0 ses 212. 50
D Domain: Oshs 8. 50
Range: 0 ses 212. 50
Answer:
200 should be
Step-by-step explanation: mhm yes yes
What is the length of leg s of the triangle below?
Answer:
[tex]\bf F.\;8[/tex]
Step-by-step explanation:
[tex]\bf Sin (45^o)=\cfrac{5}{8\sqrt{2} }[/tex]
[tex]\bf \cfrac{1}{\sqrt{2} } =\cfrac{S}{8\sqrt{2} }[/tex]
[tex]\bf S=\cfrac{8\sqrt{2} }{\sqrt{2} }[/tex]
Cancel common factor:- √(2)
[tex]\bf S=8[/tex]
Therefore, your answer is f) 8.
What is the value of x?
Enter your answer in the box.
Answer:
its c
Step-by-step explanation:
On average, what value is expected for the f-ratio if the null hypothesis is true?.
The expected value of the f-ratio is the mean value
On average, the expected value for the f-ratio is 1.00 if the null hypothesis is true
How to determine the expected value?From the question, we understand that the null hypothesis is true and the distribution is the F-ratio
The above scenario means that:
The variance of the top and the bottom ratio are the same
When the ratios are the same and the null hypothesis is accepted, then the expected value is 1.00
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Triangle ABC is a right triangle. The lengths of the legs are 21 centimeters and 28 centimeters. What is the length of the hypotenuse in centimeters?
Which volcano erupted in the early 1980s in the Pacific states?
Mt. Mauna Kea
Mt. St. Helens
Mt. Katla
Mt. Etna
Mt. St. Helens
hope it helps...!!!
Find the measure of angle B.
A. 56°
B. 62°
C. 75°
D. 68°
Answer:
56
Step-by-step explanation:
for triangles, you have to have a total of 180 degrees also triangles have the same degrees every time
PLEASE HELP ASAP:)!!
Zachary's cornfields are irrigated in circular regions. Zachary records data on the corn production from various irrigated circular regions,
Radius (ft)
500
1,000
1,500
2,000
2. 500
Bushels of Corn
2,705
10,818
24 341
43,273
67,613
What type of function best models the given data set?
A constant
B. Exponential
C. Linear
D. Quadratic
Answer:
Quadratic
Step-by-step explanation:
2705/500 = 5.41
10,818/1000 = 10.818
24 341/1,500 =24.227
43,273/2000 = 21.6365
67,613/2500 = 27.0452
Rate of change changes
Susana is with a mobile phone provider that charges $0.27 per minute plus a connection fee of $0.20. How much will she be charged for a
call that lasts b minutes?
Answer:
The total monthly charge if one uses 769 minutes is $68.65
Step-by-step explanation:
Example: If we are at x = 310, y = 45.50 and we use one more
minute, x goes up by 1, y increases by .05, putting us
at x = 311, y = 45.55. Thus, usage of 311 minutes
incurs a monthly cost of $45.55.
The y intercept is the point where x = 0.
That point on our equation is (0, 30)
This means that if zero minutes are used during the month,
the total charge for the month will be $30... the flat fee.
c) Find total monthly cost for using 769 minutes
y = .05x + 30
y = .05(769) + 30
y = 38.45 + 30
y = $68.65
A cylindrical tank whose diameter and height are 2.1m and 4m respectively is filled with water whose density is 1g/cm^3.calculate the mass of the water in kg.
Step-by-step explanation:
I assume it means the task is filled completely.
diameter = 2.1 m
therefore, radius = diameter/2 = 2.1/2 = 1.05 m
height = 4 m
volume of a cylinder is
ground area × height, so
pi×r² × height = pi×1.05²×4 = 13.8544236... m³
1 cm³ is 1g
for 1 kg (remember, "k" stands for "kilo" and means 1000) we need therefore 1000 cm³ (which is a cube of 10 cm side length).
how many cm³ are in 13.8544236... m³ ?
1 m = 100 cm
1 m² = 1 m × 1 m = 100×100 = 10,000 cm²
1 m³ = 1 m × 1 m × 1 m = 100×100×100 = 1,000,000 cm³
that means a factor of 1,000,000 !
so, the volume of the cylinder is
13.8544236... × 1,000,000 = 13,854,423.6... cm³
to get the mass of kg of that much water we need now to divide by 1000 :
13,854,423.6... / 1000 = 13,854.4236... kg
which is, by the way, 13.8544236... tons.
yes, 1 m³ of water is 1 ton ...
I don't know, if you need to round the result.
if you e.g. only need full kg, then the answer would be
13,854 kg.
PLEASE HELP 100 POINTS MATH ASAP URGENT
Answer:
answer to number 1
Step-by-step explanation:
Find the zeros of denominator (x=-2)
-2|1 4 0 -9 -2
After Carrying down coefficients = Coefficients of number polynomial is 1, 2, -4, -1, and 0
Polynomial format: x^3+2x^2-4x-1
Hope this helps :)
The volume of a box that measures 3cm x 3 cm x 2 cm is:
Answer:
18 cm cubed (cm^3)
Step-by-step explanation:
2 x 3 x 3
Answer: 18 cm (cubed)
Step-by-step explanation: Volume of a cube or box -
Length x Width x Height = 3x3x2
PLEASE HURRY!!!!!
EXPLAIN why or why not.
Answer:
The graph is not a line of best fit as there are not an equal number of data points on each side of the line
Step-by-step explanation:
Brainliest would be appreciated
Mark wants to run his town's half marathon, which covers 13.1 miles. When runners have completed 65% of the course, they are challenged with a steep hill to climb. What distance, in miles, will Mark run before he gets to the foot of the hill? Round your response to the hundredths place.
Using proportions, it is found that Mark will run 8.52 miles before he gets to the foot of the hill.
What is a proportion?A proportion is a fraction of a total amount.
In this problem, the distance to the foot of the hill is 65% of 13.1 miles, hence:
d = 0.65 x 13.1 = 8.52 miles.
Mark will run 8.52 miles before he gets to the foot of the hill.
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A triangle has a perimeter of 16x + 4. If Side 1 is 3x + 2, Side 2 is 8x + 7, what is the measure of Side 3? Show your work
Answer:
Side 3 = a - 2
Step-by-step explanation:
Perimeter of a ∆ = sum of all the sides of a triangle
Perimeter of the given ∆ = 6a + 3 units
Side 1 = 2(a + 3)
Side 2 = 3a - 1
Side 3 = ?
Therefore:
Side 3 = Perimeter - sum of side 1 and 2
Thus:
Side 3 = 6a + 3 - [2(a + 3) + (3a - 1)]
Side 3 = 6a + 3 - [2a + 6 + 3a - 1]
Side 3 = 6a + 3 - [5a + 5]
Side 3 = 6a + 3 - 5a - 5
Side 3 = a - 2
Step-by-step explanation:
745
90M
24
F&
2
7
D%
D. 24
5
⅔5
Answer:E Sin 16= opposite side/hypotenuse =7/15
Step-by-step explanation: opposite side to the angle used/ hypotenuse.
URGENTLY NEEDING HELP!!!!
Answer:
(6,-1)
Step-by-step explanation:
it's given 2m and m is at point (4,-3) increasing each point by 2 = (6,-1).
not sure
simplify 2 + 5(1 + 8n)
Answer:
7+40n
Step-by-step explanation:
distribute 5 and get 5=40n then add the extra 2 for the awnser of 7=40n
Answer:
7+40n
Step-by-step explanation:
expand 5(1+8n)= 5+40n=
2+5+40n
= 7+40n
Which of the following is a possible equation of a parabola. Explain why.
Answer:
the answer is C
because for an equation to be an equation of a parabola, the coefficient of x^2 and y^2 has to be 1
PLS HELP FAST!!
What is the mean of this data set?
3, 5, 10, 11, 15
Answer:
8.8
Step-by-step explanation:
To find mean, add all of the numbers together, then divide that sum by how many numbers there are.
3 + 5 + 10 + 11 + 15 = 44
44 ÷ 5 = 8.8
hope this helps!
Step-by-step explanation:
3+5+10+11+15÷5=
44 divided by 5 which gives 8.4
therefore that is the mean hope this helps
DISTRIBUTE 4(-3X + 2)
Answer:
-12x+8 or 12x+8
Step-by-step explanation:
p please mark me brainlest
Please helppppppppppppp!!!!!!!!!!!!!!
Answer:
60°
Step-by-step explanation:
We know in a circle, the interior angle is half of the exterior angle.
Interior angle = exterior angle x 1/2Interior angle = 120° / 2Interior angle = 60°Determine if a triangle can be formed with given length if yes classify as acute right or obtuse
1) cos α = 0.8, cos β = 0.6, cos γ = 0. The triangle exists and is right.
2) cos α ≈ 0.882, cos β ≈ 0.471, cos γ ≈ 0.441. The triangle exists and is acute.
3) cos α ≈ 0.977, cos β ≈ 0.324, cos γ ≈ -0.115. The triangle exists and is obtuse.
4) cos α = 1, cos β = 1, cos γ = -1. The triangle does not exist.
How to determine if a triangle may exist and the existence of given angles
Triangles are geometric figures formed by three line segments and internal angles, whose sum is equal to 180°, which can be three acute angles or an obtuse angle and two acute angles or a right angle and two acute angles. The possibility is determined by applying the law of cosine:
[tex]\cos \theta = -\frac{x^{2}-y^{2}-z^{2}}{2\cdot y\cdot z}[/tex] (1)
The triangle if and only if the cosine of each angle is between -1 and 1 with the following characteristics:
If the cosine of the angle is between 0 and 1, then it is acute.If the cosine of the angle is 0, then it is right.If the cosine of the angle is between 0 and -1, then it is obtuse.Now we proceed to determine the existence of each triangle:
1) cos α = 0.8, cos β = 0.6, cos γ = 0. The triangle exists and is right.
2) cos α ≈ 0.882, cos β ≈ 0.471, cos γ ≈ 0.441. The triangle exists and is acute.
3) cos α ≈ 0.977, cos β ≈ 0.324, cos γ ≈ -0.115. The triangle exists and is obtuse.
4) cos α = 1, cos β = 1, cos γ = -1. The triangle does not exist.
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How many 15° angles are in a circle?
Enter your answer in the box.
angles
Answer:
24
Step-by-step explanation:
a circle is 360
we can divide 360 by 15
360 divided by 15 =
24
PLEASEEE HELP !!!!!!!!!!!
Answer:
22√3.
Step-by-step explanation:
The perimeter is the sum of the lengths of the 3 sides,
= 5√3 + 3√27 + 4√12
= 5√3 + 3*√9√3 + 4√4√3
= 5√3 + 3*3√3 + 4*2√3
= 5√3 + 9√3 + 8√3
= 22√3.