Answer:
A. n ≥ 11
Step-by-step explanation:
You have a triangle with sides (n), (n-3), and 2(n-2). Its perimeter is at least 37 units, and you want to know the value of n.
PerimeterThe perimeter is the sum of the side lengths:
P = (n) +(n -3) +2(n -2)
P = n + n -3 +2n -4
P = 4n -7
ConstraintThe perimeter is at least 37, so we have ...
P ≥ 37
4n -7 ≥ 37
4n ≥ 44 . . . . . . . add 7
n ≥ 11 . . . . . . . divide by 4
The value of n is at least 11.
observations 1 2 3 4 5 6 num. of defects 10 18 13 15 9 12the number of runs up and down for the preceding data is:
The number of runs up and runs down for the preceding data is 5.
What is runs up ?Runs up refers to the number of observations that are higher than the number of observations before them.
What is runs down ?Runs down refers to the number of observations that are lower than the number of observations before them.
As 2nd observation is higher than 1st observation, 4th observation is higher than 3rd observation and 6th observation is also higher than 5th observation so 2nd, 4th,6th observation should be included in runs up.
Therefore,
Runs up = 2nd + 4th + 6th observations
= 3
As 3rd observation is lower than 2nd observation,5th observation is also lower than 4th observation so 3rd,5th observation should be included in the runs down
Therefore,
Runs down= 3rd +5th observations
=2
Therefore,
Runs up + Runs down =3+2
=5
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Segment BD bisects angle ABC measure angle ABC equals 7x. The measure angle ABD equals 3x+25. Find the measurement of angle DBC
The measurement of angle DBC is 100°. It can be obtained by the properties of bisector of an angle and algebriac multiplication.
What is angle bisector?
An angle bisector is the ray or line segment that divides the angle into two equal parts.
Since the segment BD bisects angle ABC hence,
∠ABC = ∠ABD+∠DBC ..... (1)
Also, since segment BD bisects angle ABC hence,
∠ABD = ∠DBC
Use this fact in equation (1)
∠ABC = ∠ABD+∠ABD
∠ABC =2 ∠ABD
Now, substitute values and use algebriac multiplication.
7x = 2(3x+25)
7x = 6x+50
7x - 6x= 50
x=50
Now, substitute the value of x in the expression of ∠ABD.
∠ABD = 3x+25
∠ABD = 3(50)+25
∠ABD = 100
Now, since ∠ABD = ∠DBC hence, ∠DBC = 100.
Hence, the measurement of angle DBC is 100°.
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Givenf(x)=4x^2 - 1, and g(x) = 2x - 1, find g(f(2)).
Given f(x) = x^2 and g(x)=x - 1, write each composite function.State the domain of each:2.f(g(x)) 3.g(f(x))
The value of the function g(f(2)) is 29 and 2.f(g(x)) is (x - 1)(2x - 2).
What is a composite function?When the output of one function is given to the input of another function they are called composite functions.In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).
Given, f(x) = 4x² - 1. and g(x) = 2x - 1.
Now, g(f(2)) is the output of f(2) is the input of g(x).
∴ f(2) = 4(2)² - 1.
f(2) = 15.
Now, g(f(2)) = 2(15) - 1.
g(f(2)) = 29.
Also given,
f(x) = x² and g(x) = x - 1.
Now, 2.f(g(x)).
2.f(g(x)) = 2.f(x- 1).
2.f(g(x)) = 2(x - 1)².
2.f(g(x)) = 2(x² - 2x + 1).
2.f(g(x)) = 2x² - 4x + 2.
2.f(g(x)) = 2x² - 2x - 2x + 2.
2.f(g(x)) = 2x(x - 1) - 2(x - 1).
2.f(g(x)) = (x - 1)(2x - 2).
There is no restriction to the domain of this quadratic function.
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the sum of two number 12 when three times the first number is added to 5 times the second number the results is 44
Answer:
one number is 8 and other is 4
Step-by-step explanation:
So we can say x+y=12.
And 3x+5y=44
For x+y=12, we can subtract x to get: y=12-x
Plug that in to get 3x+5(12-x)=44
3x+60-5x=44
Subtract 44: -2x+16=0
2x=16
x=8
12-8=4.
Bob bad $50. he spent $28.67 for a new backpack. How much money does he have left?
Answer: $21.33
Step-by-step explanation: 50 - 28.67 = 21.33
1. Write two equivalent expressions to represent the area of this rectangle.
2. Write two equivalent expressions to represent the perimeter of this rectangle.
(pls add an explanation)
The perimeter of a rectangle is 2x+6 units and the area of a rectangle is 5x-10 square units.
Given that, the breadth of a rectangle =5 units and the length of a rectangle =(x-2) units.
What is the perimeter of a rectangle?The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).
Here, perimeter =2(x-2+5)
= 2(x+3)
= 2x+6 units
Area of a rectangle =length × width
= (x-2) × 5
= 5x-10 square units
Therefore, the perimeter of a rectangle is 2x+6 units and the area of a rectangle is 5x-10 square units.
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Gianna can wash 6 cars in 2 hours. At this rate, how many cars can Gianna wash in 5 hours?
Gianna washes 15 cars in 5 hours as her rate of washing cars is 3 cars per hour.
What is unitary method?
The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
According to the given question:
Gianna can wash 6 cars in 2 hours
Therefore, in 1 hour she can wash 6/2 cars which is 3 cars.
Gianna's rate of washing cars is 3 cars per hour
Hence by unitary method, Gianna at this rate can washes 5 x 3 cars that is 15 cars.
Gianna washes 15 cars in 5 hours as her rate of washing cars is 3 cars per hour.
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Answer to this question
In the picture
[tex]tan(\alpha - \beta) = \cfrac{tan(\alpha)- tan(\beta)}{1+ tan(\alpha)tan(\beta)} \\\\[-0.35em] ~\dotfill\\\\ cos(\alpha )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\qquad \textit{let's find the opposite} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]
[tex]\pm\sqrt{5^2 - 3^2}=b\implies \pm 4=b\implies \stackrel{IV~Quadrant}{-4=b}~\hfill tan(\alpha)=\cfrac{\stackrel{opposite}{-4}}{\underset{adjacent}{3}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]tan(\alpha - \beta) \implies \cfrac{\stackrel{tan(\alpha)}{-\frac{4}{3}}- \stackrel{tan(\beta)}{\frac{4}{3}}}{1+ \stackrel{tan(\alpha)}{\left( -\frac{4}{3} \right)}\stackrel{tan(\beta)}{\left( \frac{4}{3}\right)}}\implies \cfrac{~~ \frac{-8 }{3 } ~~}{1-\frac{16}{9}}\implies \cfrac{~~ \frac{-8 }{3 } ~~}{\frac{-7}{9}} \\\\\\ \cfrac{-8}{3}\cdot \cfrac{9}{-7}\implies \cfrac{24}{7}\implies {\Large \begin{array}{llll} 3\frac{3}{7} \end{array}}[/tex]
In the figure below, points D, B, E, F, and lie in plane X.
Points A and C do not lie in plane X.
For each part below, fill in the blanks to write a true statement.
The blanks are filled as below
(b) G and E are distinct points that are collinear.(c) F, D, B, and G are distinct points that are coplanar.(d) Suppose line AD is drawn on the figure. Then AD and AC are distinct lines that intersect.What are collinear points?Collinear points are those that are situated along a single straight line.
Collinear points are those that are on a line either close to or far from another point, it can be more than two points.
While coplanar points imply lying on the same plane
In the diagram,
E, F, and G are collinear points
D, B, E, F, and G are coplanar points
A, B, and C are another collinear points
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The soccer field is 105 meters long. The football field is 120 yards long. Which is longer?
The football field is longer than soccer field.
What is a expression? What is a mathematical equation? What is unit conversion?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.
We have a soccer field that is 105 meters long and a football field is 120 yards long.
In one yard, we have -
1 yard = 0.9144 meters
Then, in 120 yards, we will have -
120 x 0.9144 = 109.728 meters
Now, 109.728 meters > 105 meters.
Therefore, the football field is longer than soccer field.
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REASONING 11. Can the value of o*g_{2}(- 4) * befounc ? What about the value of log ? Why or why not ? What does this tell you about the domain of log ?
In 1972, about 22 crushed beverage cans weighed one pound. In 2002, beverage cans were lighter and about 34 crushed beverage cans weighed one pound. Every minute of every day, an average of 113,204 beverage cans are recycled. A: About how many pounds of beverage cans are recycled in an hour?
B: About how many tons of beverage cans are recycled in an average day?
C: About how many kilograms of beverage cans are recycled in a day?
A) The number of pounds that the beverage cans are recycled in an hour is 119772 pounds
B) The number of tons that the beverage cans are recycled in an average day is 2397 ton
C) The number of Kilograms that the beverage cans are recycled in a day is 57528000 kg
What is a pound?The pound is the main unit of sterling, and the term "pound" is frequently used to refer to British currency in general, which is often qualified in foreign contexts as the British pound or the pound sterling.
In 2002 about 34 beverages can weigh one pound.
In one minute 113204 beverage cans are recycled.
In one hour, 60 minutes number of beverage cans recycled=113204×60
=6792240
34 beverage cans weight 1 pound
1 beverage cans weight=1/34 pounds
A) 6792240 beverage can weigh=1
=(1/34)(6792240) pound
=119771.765 pound
≈119772 pound
B) So, In 24 hours, no. of pounds recycled
=119772×24 pound
=119772×24×0.0005 ton
=2397.26 ton
≅2397 ton in one day.
C) So, In 24 hours, no. of tons recycled
=2397×24 ton
=2397×24×1000 kg
=57528000 kg
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If you roll a standard six-sided die a thousand times and add up the total number of pips, which approximate sum could you reasonably expect to end with?
1) 16.7% probability of rolling 10+.
2) 50% probability an odd number is rolled.
3) 7 is the most likely total result.
These are all the possible outcomes:
(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)
(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)
(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)
(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)
(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)
(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)
There are 36 possible outcomes
1) what is the probability of rolling 10+?
There are 6 possible outcomes in which 10+ is rolled:
(4,6), (5,5),(5,6), (6,4), (6,5),(6,6).
So there is a 6/36 = 0.167 = 16.7% probability of rolling 10+.
2) what is the probability of rolling an odd number?
There are 18 possible outcomes in which an odd number is rolled.
So there is a 18/36 = 0.5 = 50% probability an odd number is rolled.
3) what is the total that is most likely to result?
There are 6 outcomes in which 7 is rolled.
So 7 is the most likely total result.
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PLEASE HELP 50 POINTS
The trigonometric expression cos 3x / (sin x · cos x) is equivalent by trigonometric formulas to the trigonometric expression csc x · cos 2x - sec x · sin 2x. (Correct choice: A)
How to find an expression equivalent to another trigonometric expressionIn this problem we find the definition of a trigonometric expression, whose equivalent expression must be found by using algebra properties and trigonometric formulas. First, write the trigonometric function:
cos 3x / (sin x · cos x)
Second, use trigonometric formulas:
cos (x + 2x) / (sin x · cos x)
(cos x · cos 2x - sin x · sin 2x) / (sin x · cos x)
cos 2x / sin x - sin 2x / cos x
csc x · cos 2x - sec x · sin 2x
The equivalent trigonometric expression is csc x · cos 2x - sec x · sin 2x.
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18 Which expression uses the greatest common factor and distributive property to write 18 + 24 as a product? Circle the letter of the correct answer.
The expression that uses the greatest common factor and distributive property to write the given expression, 18 + 24, is 6(3 + 4)
Writing an expression using the Greatest common factor and distributive propertyFrom the question, we are to determine the expression that uses the greatest common factor and the distributive property to write the given expression.
The given expression is
18 + 24
First, we will determine the greatest common factor of 18 and 24
18 = 2 × 3 × 3
24 = 2 × 2 × 2 × 3
Thus,
The greatest common factor is 2 × 3 = 6
Now, we will write the expression using the greatest common factor and the distributive property
18 + 24
6(3 + 4)
Hence, the expression is 6(3 + 4)
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5 divided by 19 vvchgdvbdvvvdbbxbvxvvdhhsjjshhhdbhshhhdhhshshhshdggdhshgdgfduhf
If X is the midpoint of TV, TV bisects RS, and TR is parallel to VS, state five pairs of objects (segments or angles) that must be congruent and give a reason why for each pair.
According to the Alternate Interior Angles Theorem, when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.
Alternate Interior Angle Theorem?According to the Alternate Interior Angles Theorem, when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.Is it true or false that different interior angles are always congruent? Although untrue, this assertion is a typical misunderstanding. Keep in mind that when the lines are parallel, alternate inner angles are congruent.Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposing sides of the transversal when two lines are crossed by another line (referred to as the Transversal). These two pairs of alternate interior angles in this illustration are c and f.To learn more about Congruent refer to:
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After the consumption of an alcoholic beverage, the concentration of alcohol in the bloodstream (blood alcohol concentration, or BAC) surges as the alcohol is absorbed, followed by a gradual decline as the alcohol is metabolized. The function C(t) = 1. 35te−2. 802t † models the average BAC, measured in mg/mL, of a group of eight male subjects t hours after rapid consumption of 15 mL of ethanol (corresponding to one alcoholic drink). A. What is the maximum average BAC during the first 3 hours? (Round your answer to three decimal places. ) mg/mL b. When does it occur? (Round your answer to two decimal places. ) h
The maximum average BAC during the first 6 hours is about 0.177 mg/ml.
What is average ?
The middle number in a group of numbers is the average value, which is determined by dividing the sum of all the values by the variety of values.
When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.
The maximum is found where the derivative of C(t) is zero.
dC/dt = 1.35e^(-2.802t) -(1.35t)2.802e^(-2.802t) = 0
Solving for t gives ...
t = 1/2.802
So, the maximum C(t) is ...
C(1/2.802) = 1.35/2.802e^(-1) ≈ 0.177 . . . . . mg/mL
The maximum average BAC during the first 6 hours is about 0.177 mg/mL.
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2 websites sell the same type of headphone cost of headphone in website A is 49.95 and the postage is 4.39. The headphones in website B is 47.68 and the postage is 6.95. Including the postage which website is cheaper and by how much
Answer:
Website A is cheaper by 29 cents
Step-by-step explanation:
A
49.95 + 4.39 = 54.34
B
47.68 + 6.95 = 54.63
54.63 - 54.34 = 0.29
Answer:
the difference is 0.29 cents
website A is cheaper
Step-by-step explanation:
(47.68 + 6.95) - (49.95 + 4.39)
54.63 - 54.34 = 0.29
Help please help help please help help me
Answer:
103
Step-by-step explanation:
angle 1 and angle 5 are the same as each other.
A cylindrical rod of steel (e = 207 gpa) having a yield strength of 310 mpa is to be subjected to a load of 11,100 n. If the length of the rod is 500 mm, what must be the diameter to allow an elongation of 0. 38 mm?.
the diameter to allow an elongation of 0. 38 mm therefore required diameter is 7.65 mm
Given the data in the question;
F = 11100 N
l₀ = 310 mm = 0.31 m
E = 207 GPa = 207 × 10⁹ N/m²
Δl = 0.38 mm = 0.0005 m
So, lets assume the deformation is elastic;
d₀ = √( [4l₀F] / [πEΔl] )
we substitute
d₀ = √( [4 × 0.38 × 11100] / [π × (207 × 10⁹) × 0.0005]] )
d₀ = √( 10123.2 / 172787595.947 )
d₀ = √( 5.85875 × 10⁻⁵ )
d₀ = 0.007654 m
d₀ = ( 0.007654 × 1000 )mm
d₀ = 7.65 mm
Therefore, required diameter is 7.65 mm
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2(x-4 1/2)=-6.1 hellllllppppp meeeee
Answer:
[tex]x=1.45[/tex]
Step-by-step explanation:
[tex]2\left(x-4 \frac{1}{2} \right)=-6.1 \\ \\ 2\left(x-\frac{9}{2} \right)=-6.1 \\ \\ 2x-9=-6.1 \\ \\ 2x=2.9 \\ \\ x=1.45[/tex]
Write an inequality that could be used to represent all solutions for x: the quotient of a number and three minus twelve is less than 12
We can write the given statement as inequality as -
-(x/9) < 12
What is linear inequality? What is the law of Reversal and law of Trichotomy? What is the general equation of a Straight line?Linear inequalities are defined as expressions in which two linear expressions are compared using the inequality symbols.
y > mx + cy < mx + cy ≥ mx + cy ≤ mx + cReversal property : If (a > b) then (b < a) and if (a < b) then (b > a).
Law of Trichotomy : The "Law of Trichotomy" says that - only one of the following is true : (a < b) or (a = b) or (a > b).
The general equation of a straight line is y = mx + c
Other possible equations of lines are -
(y - y₁) = m(x - x₁) {Point - slope form}(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁) {Two point - slope form}x/a + y/b = 1 {intercept form}x cos(β) + y sin(β) = L {Normal form}We have the following statement -
"the quotient of a number and three minus twelve is less than 12".
We can write the inequality as -
-(x/9) < 12
Therefore, we can write the given statement as inequality as -
-(x/9) < 12
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A shopping mall has 226 stores on 4 levels. Each level of the mall has about the same number of stores. Which of the following are reasonable estimates for the number of stores on each level
The number of stores in each level of the shopping mall are 56 stores.
How to solve an equation?An equation is an expression that can be used to show the relationship between variables and numbers. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
Let x represent the number of stores on each level.
A shopping mall has 226 stores on 4 levels. If there are same number of stores in each level:
(4 × x) = 226
4x = 226
Divide
x = 226 / 4
x = 56.5
There are about 56 stores per level.
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Can anybody help me with this?
The Height of trees are equal after 4 years and the height is 54 inches.
What is linear equation?A linear equation is a equation which draws straight line on the plot
when plotted.
Given,
Height of tree A at the time of planting = 38 inches
Height of tree B at the time of planting = 22 inches
Each year tree A grow = 4 inches
Each year tree B grow = 8 inches
Let's make an equation for the height of the trees,
H = 38 +4t
H = 22+8t
Now the time when height of both the trees will equal
38 + 4t = 22 + 8t
4t = 16
t = 4
Hence , After 4 years the height of both the trees will equal and the height of both the trees after 4 years will be 54 inches.
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Find the perimeter of a quadrilateral with the following vertices.
(−6, −2), (0, −10), (5, 2), (−1, 10)
a.40
b.52
c.23
d.46
The perimeter of the quadrilateral is 46 units, so the correct option is d.
How to find the perimeter of the quadrilateral?The perimeter is equal to the sum of the lengths of all the sides of the quadrilateral.
Remember that the length of a segment whose endpoints are (x₁, y₁) and (x₂, y₂) is:
L = √( (x₁ - x₂)^2 + (y₁ - y₂)^2)
The length between the first two vertices: (−6, −2), (0, −10)
L₁ = √( (-6 - 0)^2 + (-2 + 10)^2) = 10
The length between the second two vertices: (0, −10), (5, 2)
L₂ = √( (0 - 5)^2 + (-10 - 2)^2) = 13
The length between the third two vertices: (5, 2), (−1, 10)
L₃ = √( (5 + 1)^2 + (2 - 10)^2) = 10
The length between the fourth two vertices: (−1, 10), (−6, −2)
L₄ = √( (-1 + 6)^2 + (10 + 2)^2) = 13
Then the perimeter is:
P = 10 + 13 + 10 + 13 = 46
The correct option is D.
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A game consists of drawing three cards at random from a deck of playing cards. You win $3 for each red card that is drawn. It costs $2 to play. For one play of this game, the sample space S for the net amount you win (after deducting the cost of play) is
Select one:
a. S = {$0, $1, $2, $3}
b. S = {$0, $3, $6, $9}
c. S = {-$2, $1, $4, $7}
The sample space S for the net amount you win (after deducting the cost of pay) is S = {-$2, $1, $4, $7}.
What is cost?
A cost is the worth of money that has been expended in the production or delivery of a good or service and is therefore no longer accessible for use in accounting, retail, research, or accounting. In business, the cost may be one of acquisition, in which case the cost is the sum of the money used to obtain it.
Let, a game consists of drawing three cards at random from a deck of playing cards.
You win $3 for each red card that is drawn.
It costs $2 to play.
After deducting the cost of pay the amount will start from -$2.
For first red card drawn you win $3.
So, the amount becomes, -$2 + $3 = $1.
For second red card drawn you again win $3.
So, the next amount becomes $1 + $3 = $4.
For third red card drawn the amount becomes,
$4 + $3 = $7.
Hence, the sample space S for the net amount you win is
S = {-$2, $1, $4, $7}.
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Simplify. Rewrite the expression in the form y^n. y^5/y^3=
Answer:
y^2
Step-by-step explanation:
a^m/a^n = a^(m - n)
y^5/y^3 = y^2
Give a number in the form of a/b o that when it i divided by 100, the reult would be 0. 014 (write in fraction in reduce form)
The reduced form of the fraction would be 2.8/2.
What is a fraction?
A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters.
Given that a/b is a fraction and when it is divided by 100 it will result in 0.014.
So we can write,
[tex]\frac{\frac{a}{b} }{100}=0.014\\\\ \frac{a}{b}=0.014*100\\\\\frac{a}{b}=1.4\\[/tex]
Now 1.4 can be written as
a/b = 2.8/2
Hence, the reduced form of the fraction would be 2.8/2.
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Four more than twice the sum of a number and three is negative 5
Answer: It is A
Step-by-step explanation:
