Answer:
9
Step-by-step explanation:
according to the condition it is possible to make up a system of two equations (if to suppose 'l' - the larger number and the 's' - is the smaller one):
1. 'two numbers have a sum of 7' means s+l=7;
2. 'When the smaller number is subtracted from twice the larger number, the result is 20' means 2*l-s=20.
3. the system of two equations is:
[tex]\left \{ {{s+l=7} \atop {2l-s=20}} \right. \ => \left \{ {{s=-2} \atop {l=9}} \right.[/tex]
4. the larger number is 9.
The larger number would be as follows:
[tex]9[/tex]
What are numbers?Let the two numbers (larger and smaller) be [tex]= x ; y[/tex] respectively.
[tex]x + y = 7[/tex]
So, [tex]y = 7 - x[/tex]
Given that,
The Smaller number subtracted from twice large number gives 20. Thus,
[tex]2x - y = 20[/tex]
Putting the value of [tex]y, 2x - (7 - x) = 20[/tex]
[tex]2x - 7 + x = 20[/tex]
[tex]3x - 7 = 20[/tex]
[tex]3x = 27[/tex]
[tex]x = 27 / 3[/tex]
∵ [tex]x = 9[/tex] [The larger Number]
The smaller number [tex]'y' = 7 - 9 = -2[/tex]
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simplify (0.125)⅓(0.25)-½
Answer:
0.125⅓×0.25½
(125/1000)⅓×(25/100)½
(5³/10³)⅓ × (5²/10²)½
5/10 × 5/10
1/2×1/2
1/4
Classify the indicated triangular shape by its sides and by its angles.
acute scalene
equangular equilateral
acute isosceles
obtuse isosceles
Step-by-step explanation:
step 1. all the side length are different therefore all of the internal angles are different.
step 2. a triangle with all different angles is scalene.
step 3. all of the angles are less than 90°
step 4. a triangle with all angles less than 90° is acute.
solve for x and y, show your work with your answer.
Answer and Step-by-step explanation:
This problem involves the use of trigonometric functions.
First, we will use the tangent trig function, and then the sine trig function.
[tex]tan(32) = \frac{x}{15}[/tex]
We solve for x by multiplying both sides by 15.
15(tan(32)) = x
Put this into a calculator and solve.
x = 9.373
Now, we solve for y.
[tex]sin(32) = \frac{9.373}{y}[/tex]
We multiply by y on both sides first.
y(sin(32)) = 9.373
Now, we divide each side by sin(32).
[tex]y = \frac{9.373}{sin(32)}[/tex]
Put this into a calculator and solve.
y = 17.6877
x = 9.373
y = 17.6877
These are your answers.
#teamtrees #WAP (Water And Plant)
Suppose the probability of an IRS audit is 3.8 percent for U.S. taxpayers who file form 1040 and who earned $100,000 or more. What are the odds that such a taxpayer will be audited? (Round your answers to the nearest whole number.) What are the odds against such a taxpayer being audited? (Round your answers to the nearest whole number.)
Find the slope of the following graphs ?
Answer:
slope=2
Step-by-step explanation:
the line is negative since it's downwards, and the slope goes 2 down and 1 right to meet the next point. -2/1=-2
The slope of the given graph is -2.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Points from the graph (1, 0) and (0, 2).
So, the slope of line
= ( 2- 0) / (0 -1)
= 2 / (-1)
= -2/1
= -2
Hence, the slope of graph is -2.
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Write the percent as a fraction and as a decimal.
5% tax
Answer:
The answer would be 0.05
Step-by-step explanation:
This is because it is PER Cent so 5% is 0.05 of 1
Answer:
1/20 and 0.05
Step-by-step explanation:
Is x = -4 a solution to these equations? Show your work and write YES or NO.
1. 3(2x-4) = -36
2. 5x - 6x - x = 18
3. 5 - 2(3x - 1) = 31
Answer:
1. Yes
2. No
3. Yes
Step-by-step explanation:
We have three equations where x is equal to -4. We are then asked if -4 are a solution to these equations.
To solve we need to substitute the x in every equation for -4. Start :
1.
3(2(-4) - 4) = -36
3(-8 - 4) = -36
-24 - 12 = -36
Therefore -4 is a solution.
2.
5(-4) - 6(-4) - (-4) = 18
-20 + 24 + 4 = 18
4 + 4 = 18
8 ≠ 18
Therefore -4 is not a solution.
3.
5 - 2(3(-4) - 1) = 31
5 - 2(-12 - 1) = 31
5 - 2(-13) = 31
5 + 26 = 31
Therefore -4 is a solution.
The function f(x) is defined below. What is the end behavior of f(x)?
Answer:
D
Step-by-step explanation:
Because the term 7x^3 is to the third power, the curve moves like x^3. This means that as x approaches infinity and -infinity, it approaches infinity and -infinity respectively. The answer is D.
please please begging please help me with this i’m giving a lot of poiints just please answer all these!!
Answer:
1) 7 x (6+y)
2)( y x 6) + (y x 7)
3) 6(y+7)
4) (y x 6) + y^2
I hope im right !
Step-by-step explanation:
( 7 * 6 ) + ( 7 * y) ➡ 7 (6 +y)
y(6 + 7) ➡ ( y * 6 ) + ( y * 7)
( 6 * y) + ( 6 * 7) ➡ 6 ( y + 7)
y( 6 + y) ➡ ( y * 6 ) + y²
Hope it will help :)
In a carnival game, there are six identical boxes, one of which contains a prize. A contestant wins the prize by selecting the box containing it. Before each game, the old prize is removed and another prize is placed at random in one of the six boxes. Is it appropriate to use the binomial probability distribution to find the probability that a contestant who plays the game five times wins exactly twice?
A) Yes. The five trials are independent, have only two outcomes, and have the same P(success); n = 5, r = 2, p = 1/5.
B) Yes. The five trials are independent, have only two outcomes, and have the same P(success); n = 2, r = 5, p = 1/6.
C) No. The five trials are independent, but have more than two outcomes.
D) Yes. The five trials are independent, have only two outcomes, and have the same P(success); n = 5, r = 2, p = 1/6.
Answer:
D) Yes. The five trials are independent, have only two outcomes, and have the same P(success); n = 5, r = 2, p = 1/6.
Step-by-step explanation:
The Number of boxes = 6
Box containing a prize = 1
Probability of success, p = box containing a price / number of boxes = 1 /6
Number of trials = 5
Probability of success on exactly 2 trials, r = 2
Hence,
P(r = 2) = nCr * p^r * (1-p)^(n-r)
n = 5 ; r = 2 ; p = 1/6
Using a binomial probability calculator :
P(r = 2) = 0.1608
Ana has won a lottery. She was offered two options to receive the award: She can either take it in five installments of $60,000 annually, starting from now; or she can take a lump-sum of $255,000 now. Assuming (a) interest at an annual rate of 5% compounded annually, or (b) interest at an annual rate of 6% compounded continuously, which option should she choose under the consideration of cash value only?
A) If the interest is at the annual rate of 5%, compounded annually, then the present value of the five installments is $______. B) If the interest is at the annual rate of 6%, compounded continuously, then the present value of the five installments is $______.
Answer:
Results are below.
Step-by-step explanation:
Giving the following information:
She can either take it in five installments of $60,000 annually, starting from now; or she can take a lump-sum of $255,000 now.
First, we determine the value of the 5 installments using a 5% annual compounded rate.
We calculate the future value, and then the present value:
FV= {A*[(1+i)^n-1]}/i
A= annual payments
FV= {60,000*[(1.05^5) - 1]} / 0.05
FV= $331.537.88
PV= FV/(1+i)^n
PV= $259,768.60
At an annual rate of 5% compounded annually, she should choose the five installments instead of the $255,000.
Now, if the annual rate is 6% continuously compounded.
First, we need to calculate the effective interest rate:
r= e^i - 1
r= effective inerest rate
r= e^0.06 - 1
r= 0.0618
FV= {60,000*[(1.0618^5) - 1]} / 0.0618
FV= 339,443.23
PV= 339,443.23/1.0618^5
PV= $251,509.01
At an annual rate of 6% compounded continuously, she should choose the $255,000.
Chancellor Manufacturing makes two pumps for use in household reef aquariums. The Standard pump (Model A) requires 4.5 lbs of stainless steel while the Deluxe lightweight pump (Model B) 3.0 lbs of stainless steel. There are 63 lbs of stainless steel available during this production period. The combined production of both pumps must be at least 12 pumps. There are orders for at least 6 of the lightweight Model B. Lastly, management has decided that no more than 15 Model B pumps be produced.
Required:
a. Write the LP formulation which provides the optimal production schedule for the standard and deluxe pumps such that the cost is minimized.
b. Write the above LP formulation in Standard Form.
c. Using your grid page, graph the above LP formulation. Be sure to label axes, constraints, and the feasible region.
Answer:
The answer is below
Step-by-step explanation:
Chancellor Manufacturing makes two pumps for use in household reef aquariums. The Standard pump (Model A) requires 4.5 lbs of stainless steel while the Deluxe lightweight pump (Model B) 3.0 lbs of stainless steel. There are 63 lbs of stainless steel available during this production period. The combined production of both pumps must be at least 12 pumps. There are orders for at least 6 of the lightweight Model B. Lastly, management has decided that no more than 15 Model B pumps be produced.
The cost to produce one Standard pump is $150 and to produce one Deluxe pump is $210.
Solution:
a) Let x represent model pump A and let y represent model pump B.
Since There are 63 lbs of stainless steel available, hence:
4.5x + 3y ≤ 63
Both pumps must be at least 12 pumps. Therefore:
x + y ≤ 12
There are orders for at least 6 of the lightweight Model B:
y ≥ 6
Also, no more than 15 Model B pumps be produced:
y ≤ 15
The cost to produce one Standard pump is $150 and to produce one Deluxe pump is $210. The cost equation is:
Minimize Cost = 150x + 210y
b)
Hence the LP formation is:
Minimize Cost = 150x + 210y
4.5x + 3y ≤ 63
x + y ≤ 12
y ≥ 6
y ≤ 15
x ≥ 0.
c) The LP problem was solved using geogebra online graphing tool.
The points that satisfy the problem are:
(0, 6), (0,12), (6, 6)
At (0,6); cost = 150(0) + 210(6) = 1260
At (0,6); cost = 150(0) + 210(12) = 2520
At (6,6); cost = 150(6) + 210(6) = 2160
Hence the minimum cost is at (0, 6)
CEOLATIONS AND INEQUALITIES
Finding angle measures of a triangle given angles with variables
In the triangle below, suppose that m U=(x+9)°, m = (2x+1), and mW=(7x)".
Find the degree measure of each angle in the triangle.
Answer:
∠U = 26°
∠V = 35°
∠W = 119°
Step-by-step explanation:
Given:
∠U = (x+9)°
∠V = (2x+1)°
∠W = (7x)°
Find:
Value of each angle
Computation:
Using angle sum property
∠U + ∠V + ∠W = 180°
(x+9)° + (2x+1)° + (7x)° = 180°
10x + 10 = 180
x = 17
So,
∠U = (x+9)° = 17 + 9 = 26°
∠V = (2x+1)° = 34 + 1 = 35°
∠W = (7x)° = 7 x 17 = 119°
Rearrange the equation to isolate b
-5b=10a please help i dont get it
Answer:
b = -2aExplanation:
-5b = 10a
Divide Both Sides By -5-5b / -5 = 10a / -5
b = - 2aBelow is a table of the breaking strength in pounds of 20 pieces of Douglas fir.33,190 31,860 32,590 26,520 33,28032,320 33,020 32,030 30,460 32,70023,040 30,930 32,720 33,650 32,34024,050 30,170 31,300 28,730 31,920Give the five-number summary of the distribution of breaking strengths. Match your results below. Make sure that you calculate the quartiles manually exactly as defined in the text. Do not rely on results from calculators or software since they may use alternative definitions for the quartiles.1. 23,040 5. 31,860 9. 32,030 13. 32,465 17. 32,7002. 26,520 6. 31,890 10. 32,320 14. 32,590 18. 32,7203. 30,315 7. 31,920 11. 32,330 15. 32,645 19. 33,0204. 30,460 8. 31,975 12. 32,340 16. 32,710 20. 33,650Enter the number of the term that corresponds to each choice:MinimumQ 1MedianQ 3Maximum
Answer:
Minimum = 23,040
Q1 = 30315
Q2 = 31975
Q3 = 31975
Maximum = 33650
Step-by-step explanation:
Ordered data:
23040, 24050, 26520, 28730, 30170, 30460, 30930, 31300, 31860, 31920, 32030, 32320, 32340, 32590, 32700, 32720, 33020, 33190, 33280, 33650
The five number summary :
Minimum = 23,040
Lower quartile (Q1) = 1/4(n+1)th term
n = 20
Q1 = 1/4* (21)th term
Q1 = 5.25 ; (5th + 6th) term / 2
Q1 = (30170 + 30460) / 2 = 30315
Median (Q2) :
Q2 = 1/2* (21)th term
Q2 = 10.5 ; (10th + 11th) term / 2
Q2 = (31920 + 32030) / 2 = 31975
Upper Quartile (Q3) :
Q3 = 3/4* (21)th term
Q3 = 15.75 ; (15th + 16th) term / 2
Q 3 = (32700 + 32720) / 2 = 32710
Maximum : 33650
A homeowner is building a flower bed in the backyard. He plans to put a layer of fertilizer over the entire flower bed.The diagram shows the flower bed and its dimensions in feet.
4w2 + 3w - 1
5w - 2.
Which expression represents the area in square feet that the homeowner will cover with fertilizer?
Answer:
The answer is 4w^2 + 8w - 3
Step-by-step explanation:
Umm I hope it's right
Below are three different types of slopes. Directions: Drag the colored boxes on the bottom of the page upward and place them under the appropriate slope. Then explain why you chose your answer. Left Left Left Right Right Right Explain: Explain: Explain: Negative Slope Positive slope NO Slope
Answer:
The left graph is a positive slope (yellow box)
The middle graph has no slope (green)
The right graph has a negative slope (purple)
Step-by-step explanation:
The left graph has a positive slope because the slope increases left to right. We can see this because the line starts at the origin at zero (0, 0), and increases.
The right graph has a negative slope because the slope decreases left to right. We can see this because it starts a value greater than zero, and gradually decrease to zero.
The middle graph contains no slope because it is a straight horizontal line. If we were to calculate the slope, (rise/run) of two points, the slope is the same in every point. It is constant.
The correct answer is,
The left graph is a positive slope (yellow box)
The middle graph has no slope (green)
The right graph has a negative slope (purple)
What is slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.
Here, we have.
The left graph has a positive slope because the slope increases left to right. We can see this because the line starts at the origin at zero (0, 0), and increases.
The right graph has a negative slope because the slope decreases left to right. We can see this because it starts a value greater than zero, and gradually decrease to zero.
The middle graph contains no slope because it is a straight horizontal line. If we were to calculate the slope, (rise/run) of two points, the slope is the same in every point. It is constant.
Hence, The correct answer is,
The left graph is a positive slope (yellow box)
The middle graph has no slope (green)
The right graph has a negative slope (purple)
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Help pls!!!!!!!!!!!!!!!!!
Answer: just turn them into decimals and use a calculator then turn them back into fractions in simplified form
Step-by-step explanation:
Hi please help me as soon as possible for a heart, a 5 star rating, comment and maybe brainiest - you only get this after you give the right answer:
Rimo spends £588 on a plane ticket and $130 on airport tax. Using £1 = $1.34, what percentage of the total cost does Rimo spend on airport tax?
Give your answer rounded to 1 dp.
Need help ASAP!
I have no idea how to do this
Answer:
the last one 3(x+4) = 3x + 12
Step-by-step explanation:
Which expression is equivalent to -3m+7.5?
Answer:
-3m+7.5=4.5m
Step-by-step explanation:
What is the approximate sum of this series?
A.
0.185
B.
134.83
C.
69.279
D.
184.77
Answer:
Step-by-step explanation:
For all Plato users.
We have to find the sum of the series has been given as.
[tex]\sum_{k=1}^{8}5(\frac{4}{3} )^{k-1}[/tex] -----(1)
If the series has been given as,
[tex]\sum_{n=1}^{k}a(r)^{n-1}[/tex] -------(2)
It's a geometric series with first term 'a' and common ratio 'r'.
Comparing both the expressions (1) and (2),
[tex]a=[/tex] 5
[tex]r=\frac{4}{3}[/tex]
Number of terms 'n' = 8
Sum of the k terms of this series is given by,
Sum = [tex]\frac{a(r^k-1)}{r-1}[/tex]
= [tex]\frac{5[(\frac{4}{3})^8-1)]}{\frac{4}{3}-1 }[/tex]
= [tex]\frac{5(9.98872-1)}{\frac{1}{3}}[/tex]
= [tex]\frac{44.9436}{\frac{1}{3} }[/tex]
= 134.83
Therefore, Option (B) is the correct option.
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the perimeter of a playing field for a certain sport is 262 ft. the field is a rectangle and the length is 41 ft longer than the width. find the dimensions
Answer: The width of the playing field = 45 ft
length of playing fiels = 86ft
Step-by-step explanation:
Step 1
Perimeter of rectangular field is given as 2 ( L+ b)
Let the width be represented as x
such that the length = 41 ft longer than the width be x+ 41
To find the length and breadth
Step 2
Perimeter = 2( L+ b)= 2l + 2b
Perimeter = 2 (x+41 ) + 2 x = 262
2x + 82 + 2x= 262
4x+ 82= 262
4x= 262 - 82
4x= 180
x= 180/4
x= 45
width= 45 ft
length = x+ 41= 45+ 41= 86ft
What is the slope of this graph
Answer: positive I think
Step-by-step explanation:
which equation shows that 9 is a factor of 72
Answer:
8 times 9 or 72 devide 9 is 8
Step-by-step explanation:
that th answer
Answer:
The factors of 72 are 1,2,3,4,6,8,9,12,18,24,36,72
Step-by-step explanation:
9 is a factor of 72 because 9×8=72
Please find the area of D, E, and F.
This would be appreciated :)
Answer:
Using graph for units
D=1/2(6)(9)=27 sq units
E=1/2(7)(6)=21 sq units
F=1/2(6)(8)=24 sq units
Step-by-step explanation:
Answer:
D=27 units, E=21 units, F=24 units
Step-by-step explanation:
The formula for area of a triangle is (BASE * HEIGHT)/2
For triangle D, the base is 9 units and the height is 6 units. Then you can apply the formula and do 9*6 which is 54 and then do 54/2 which is 27 units.
Similarly, the base for E is 6 units, and the height is 7 units. So you do 6*7 which is 42 and then do 42/2 which is 21 units.
Again, the base for F is 6 units, and the height is 8 units. Then again, using the formula, we can do 6*8 which is 48 and then do 48/2, which is 24 units.
Hopefully this helped!
please help me understand this
Answer:
whats your snap ill help
Step-by-step explanation:
The value of 2^0 ??
Answer:
1
Step-by-step explanation:
. It is read as 2 raised to zero. Now let see how to solve such problem For example 3^5 then it means 3×3×3×3×3 = 243 Now back to question Anything raised to zero is always 1 Hence 2^0= 1
You and classmate have volunteered to contact everyembervof your class by phone to inform them of an upcoming event you can complete the calls in 6 days od you woek alonw id u work togehwr you can complwte the calls in 2.4 days how long would it takw your classmate to make call alon
Answer:
what
Step-by-step explanation:
did you have a stroke?
You buy a new graphing calculator for $125. Graphing calculators hold their value very well, and only depreciate
at a rate of 0.5% per year. How much will your calculator be worth in 5 years when you are done using it in
college?
Depreciation formula :
Amount x (1-rate)^time
125 x (1-0.005)^5
124 x 0.995^5 = 121.91
Answer: $121.91