plot on a number line 8 2/5 away from 2 3/4
Answers
Now, let's represent the mixed numbers given in the problem.
Let's start with 8 2/5: This mixed number is located between 8 and 9. The numerator 2 of the fractional part, tells us how far from 8 it will be located and the denominator 5 indicates how many parts we must divide the space between these two numbers (8 and 9).
Now, to plot 2 3/4 on the number line, we have to follow the same proccedure: It is located between the numbers 2 and 3. The numerator 3 of the fractional part, tells us how far from 2 it will be located and the denominator 4 indicates how many parts we must divide the space between 2 and 3.
Related Questions
Suppose that △ XYZ is isosceles with base YZ . Suppose also that = m ∠ X + 2 x 52 ° and = m ∠ Y + 4 x 34 ° . Find the degree measure of each angle in the triangle.
Answers
If A(0, 0), B(3, 4), C(8, 4), and D(5, 0) are the vertices of a quadrilateral, do the points form a rhombus? Justify your answer.
Answers
The given points do not form a rhombus.
What is a rhombus?A rhombus is a quadrilateral that has four equal sides.
Some of the properties we need to know are:
- The opposite sides are parallel to each other.
- The opposite angles are equal.
- The adjacent angles add up to 180 degrees.
We have,
To determine if the given points form a rhombus, we need to check if the sides are congruent (have equal length) and if the opposite angles are congruent (have equal measure).
First, we can find the lengths of all four sides of the quadrilateral using the distance formula:
AB = √((3 - 0)² + (4 - 0)²) = 5
BC = √((8 - 3)² + (4 - 4)²) = 5
CD = √((5 - 8)² + (0 - 4)²) = 5
DA = √((0 - 5)² + (0 - 4)²) = 5
Since all four sides have the same length of 5 units, the quadrilateral satisfies the property of having congruent sides.
Next, we need to check if the opposite angles are congruent.
We can do this by finding the slopes of the two diagonals and checking if they are perpendicular. If the slopes are perpendicular, then the opposite angles are congruent.
The slope of diagonal AC can be found as:
m(AC) = (4-0)/(8-0) = 1/2
The slope of diagonal BD can be found as:
m(BD) = (0-4)/(5-3) = -2/2 = -1
Since the product of the slopes is:
m(AC) x m(BD) = (1/2) x (-1) = -1/2
which is not equal to -1, the diagonals are not perpendicular and the opposite angles are not congruent.
Therefore,
The given points do not form a rhombus.
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In the 2005 regular season, the Chicago White Sox won 28 more games than the Detroit Tigers. Together, they won a total of 170 games. How many games did each team win?
Answers
In the 2005 regular season, the Chicago White Sox won 99 games and the Detroit Tigers won 71 games.
Explanation:In the 2005 regular season, let's denote the number of games won by the Chicago White Sox as 'x' and the number of games won by the Detroit Tigers as 'y'. We know that the Chicago White Sox won 28 more games than the Detroit Tigers, so we can write x = y + 28.
Together, they won a total of 170 games, so we can write x + y = 170.
Now we can solve the system of equations:
Substitute the value of x from the first equation into the second equation: (y + 28) + y = 170
Combine like terms: 2y + 28 = 170
Subtract 28 from both sides: 2y = 142
Divide by 2: y = 71
Substitute the value of y into the first equation to find x: x = 71 + 28 = 99
Therefore, the Chicago White Sox won 99 games and the Detroit Tigers won 71 games.
The Chicago White Sox won 99 games and the Detroit Tigers won 71 games in the 2005 regular season.
Explanation:To find out how many games each team won, we need to set up a system of equations using the given information. Let x represent the number of games won by the Chicago White Sox and y represent the number of games won by the Detroit Tigers.
We are given two pieces of information:
1. The White Sox won 28 more games than the Tigers, so we have the equation x = y + 28.
2. Together, both teams won a total of 170 games, so we have the equation x + y = 170.
We can use these equations to solve for the values of x and y. Substituting the first equation into the second equation, we get (y + 28) + y = 170. Combining like terms, we have 2y + 28 = 170. Subtracting 28 from both sides, we get 2y = 142. Dividing both sides by 2, we find that y = 71.
Now we can substitute the value of y back into the first equation to find x. x = 71 + 28, so x = 99. Therefore, the Chicago White Sox won 99 games and the Detroit Tigers won 71 games.
In this problem we consider an equation in differential form mdx+ndy=0. the equation (4y+(5x^4)e^(?4x))dx+(1?4y^3(e^(?4x)))dy=0 in differential form m˜dx+n˜dy=0 is not exact. indeed, we have m˜y?n˜x= for this exercise we can find an integrating factor which is a function of x alone since m˜y?n˜xn˜= can be considered as a function of x alone. namely we have ?(x)= multiplying the original equation by the integrating factor we obtain a new equation mdx+ndy=0 where m= n= which is exact since my= nx= are equal. this problem is exact. therefore an implicit general solution can be written in the form f(x,y)=c where f(x,y)= finally find the value of the constant c so that the initial condition y(0)=1. c= .
Answers
[tex]\underbrace{(4y+5x^4e^{-4x})_{M(x,y)}\,\mathrm dx+\underbrace{(1-4y^3e^{-4x})}_{N(x,y)}\,\mathrm dy=0[/tex]
then the ODE will be exact if [tex]M_y=N_x[/tex]. We have
[tex]M_y=4[/tex]
[tex]N_x=16y^3e^{-4x}[/tex]
and so indeed the equation is not exact. So we look for an integrating factor [tex]\mu(x,y)[/tex] such that
[tex]\mu M\,\mathrm dx+\mu N\,\mathrm dy=0[/tex]
is exact. In order for this to occur, we require
[tex](\mu M)_y=(\mu N)_x\implies\mu_yM+\mu M_y=\mu_xN+\mu N_x[/tex]
[tex]\implies\mu_yM-\mu_xN=\mu(N_x-M_y)[/tex]
Now if [tex]\mu[/tex] is a function of either [tex]x[/tex] or [tex]y[/tex] alone, then this PDE reduces to an ODE in either variable. Let's assume the first case, so that [tex]\mu_y=0[/tex]. Then
[tex]\mu_x N=\mu(M_y-N_x)\implies\dfrac{\mathrm d\mu}\mu=\dfrac{M_y-N_x}N\,\mathrm dx[/tex]
So in our case we might consider using
[tex]\dfrac{\mathrm d\mu}\mu=\dfrac{4-16y^3e^{-4x}}{1-4y^3e^{-4x}}\,\mathrm dx=4\,\mathrm dx[/tex]
[tex]\implies\displaystyle\int\frac{\mathrm d\mu}\mu=4\int\mathrm dx[/tex]
[tex]\implies\ln|\mu|=4x[/tex]
[tex]\implies\mu=e^{4x}[/tex]
Our new ODE is guaranteed to be exact:
[tex](4ye^{4x}+5x^4)\,\mathrm dx+(e^{4x}-4y^3)\,\mathrm dy=0[/tex]
so we can now look for our solution [tex]f(x,y)=C[/tex]. By the chain rule, differentiating with respect to [tex]x[/tex] yields
[tex]\dfrac{\mathrm df}{\mathrm dx}=\dfrac{\partial f}{\partial x}\dfrac{\mathrm dx}{\mathrm dx}+\dfrac{\partial f}{\partial y}\dfrac{\mathrm dy}{\mathrm dx}=0[/tex]
[tex]\implies\dfrac{\partial f}{\partial x}+\dfrac{\partial f}{\partial y}\dfrac{\mathrm dy}{\mathrm dx}=0[/tex]
[tex]\implies\dfrac{\partial f}{\partial x}\,\mathrm dx+\dfrac{\partial df}{\partial y}\mathrm dy=0[/tex]
Now,
[tex]\dfrac{\partial f}{\partial x}=\mu M=4ye^{4x}+5x^4[/tex]
[tex]\implies f=ye^{4x}+x^5+g(y)[/tex]
Differentiating with respect to [tex]y[/tex] gives
[tex]\dfrac{\partial f}{\partial y}=\mu N[/tex]
[tex]\implies e^{4x}+\dfrac{\mathrm dg}{\mathrm dy}=e^{4x}-4y^3[/tex]
[tex]\implies\dfrac{\mathrm dg}{\mathrm dy}=-4y^3[/tex]
[tex]\implies g(y)=-y^4+C[/tex]
So the general solution is
[tex]f(x,y)=ye^{4x}+x^5-y^4+C=C[/tex]
[tex]\implies f(x,y)=ye^{4x}+x^5-y^4=C[/tex]
Given that [tex]y(0)=1[/tex], we get
[tex]f(0,1)=1-1^4=0=C[/tex]
so the particular solution is just
[tex]ye^{4x}+x^5-y^4=0[/tex]
how dpyou find the area of a trapizoid
Answers
A = (1/2)×(b₁ +b₂)×h
where b₁ and b₂ are the lengths of the parallel bases, and h is the height (the perpendicular distance between the bases)
_____
This is one of several area formulas it pays to memorize.
Answer:
add the parallel sides and divide by 2
then multiply it by the perpendicular side so
Step-by-step explanation:
A=side one+side two x2
2
Find the general solution of the given second-order differential equation. 3y'' + 2y' + y = 0
Answers
Final answer:
The general solution to the given second-order differential equation, 3y'' + 2y' + y = 0, is found using the characteristic equation method, resulting in complex roots. The solution is expressed in terms of sine and cosine functions multiplied by an exponential decay factor.
Explanation:
To find the general solution of the given second-order differential equation, 3y'' + 2y' + y = 0, we first convert it into its characteristic equation. This is done by substituting y = ert into the differential equation, where r is the root of the characteristic equation and t is an independent variable. This approach transforms the given differential equation into a quadratic equation.
The characteristic equation for this differential equation is 3r2 + 2r + 1 = 0. Solving this quadratic equation using the formula r = [-b ± sqrt(b2 - 4ac)] / 2a, where a=3, b=2, and c=1, gives the roots of the characteristic equation. In this case, the discriminant (b2 - 4ac) is less than zero, indicating complex roots.
The roots can be found to be r = -1/3 ± i(sqrt(2)/3). Therefore, the general solution to the differential equation is y(t) = e-t/3[C1cos(sqrt(2)t/3) + C2sin(sqrt(2)t/3)], where C1 and C2 are constants determined by initial conditions.
The general solution is [tex]\( y(t) = e^{-\frac{t}{3}} (C_1 \cos\left(\frac{\sqrt{2} t}{3}\right) + C_2 \sin\left(\frac{\sqrt{2} t}{3}\right)) \)[/tex].
To solve the second-order linear homogeneous differential equation [tex]\( 3y'' + 2y' + y = 0 \)[/tex], we follow these steps:
1. Write the characteristic equation associated with the differential equation.
2. Solve the characteristic equation for its roots.
3. Write the general solution based on the roots of the characteristic equation.
Step 1: Write the Characteristic Equation
The given differential equation is:
[tex]\[ 3y'' + 2y' + y = 0 \][/tex]
We assume a solution of the form [tex]\( y = e^{rt} \)[/tex]. Substituting [tex]\( y = e^{rt} \)[/tex] into the differential equation, we get:
[tex]\[ 3(r^2 e^{rt}) + 2(r e^{rt}) + e^{rt} = 0 \][/tex]
Dividing through by [tex]\( e^{rt} \)[/tex] (which is never zero), we obtain the characteristic equation:
[tex]\[ 3r^2 + 2r + 1 = 0 \][/tex]
Step 2: Solve the Characteristic Equation
The characteristic equation is a quadratic equation:
[tex]\[ 3r^2 + 2r + 1 = 0 \][/tex]
To find the roots of this quadratic equation, we use the quadratic formula:
[tex]\[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
where [tex]\( a = 3 \)[/tex], [tex]\( b = 2 \)[/tex], and [tex]\( c = 1 \)[/tex].
Substitute the values of [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] into the quadratic formula:
[tex]\[ r = \frac{-2 \pm \sqrt{2^2 - 4 \cdot 3 \cdot 1}}{2 \cdot 3} \][/tex]
[tex]\[ r = \frac{-2 \pm \sqrt{4 - 12}}{6} \][/tex]
[tex]\[ r = \frac{-2 \pm \sqrt{-8}}{6} \][/tex]
[tex]\[ r = \frac{-2 \pm 2i\sqrt{2}}{6} \][/tex]
[tex]\[ r = \frac{-1 \pm i\sqrt{2}}{3} \][/tex]
Thus, the roots of the characteristic equation are:
[tex]\[ r_1 = \frac{-1 + i\sqrt{2}}{3} \][/tex]
[tex]\[ r_2 = \frac{-1 - i\sqrt{2}}{3} \][/tex]
Step 3: Write the General Solution
Since the roots are complex conjugates [tex]\( r_1 = \alpha + i\beta \)[/tex] and [tex]\( r_2 = \alpha - i\beta \)[/tex] with [tex]\( \alpha = -\frac{1}{3} \)[/tex] and [tex]\( \beta = \frac{\sqrt{2}}{3} \)[/tex], the general solution to the differential equation is of the form:
[tex]\[ y(t) = e^{\alpha t} (C_1 \cos(\beta t) + C_2 \sin(\beta t)) \][/tex]
Substitute [tex]\( \alpha \)[/tex] and [tex]\( \beta \)[/tex]:
[tex]\[ y(t) = e^{-\frac{t}{3}} \left( C_1 \cos\left( \frac{\sqrt{2} t}{3} \right) + C_2 \sin\left( \frac{\sqrt{2} t}{3} \right) \right) \][/tex]
Thus, the general solution of the differential equation [tex]\( 3y'' + 2y' + y = 0 \)[/tex] is:
[tex]\[ y(t) = e^{-\frac{t}{3}} \left( C_1 \cos\left( \frac{\sqrt{2} t}{3} \right) + C_2 \sin\left( \frac{\sqrt{2} t}{3} \right) \right) \][/tex]
where [tex]\( C_1 \)[/tex] and [tex]\( C_2 \)[/tex] are arbitrary constants.
the measures of the legs of a right triangle can be represented by the expressions 6x^(2)y 9x^(2)y. Use the Pythagorean Theorem to find a simplified expression for the hypotenuse.
Answers
Answer:
h^2=a^2+b^2.
h^2=(6x^2y)^2+(9x^2y)^2.
h^2=36x^4y^2+81x^4y^2.
h^2=117x^4y^2.
h=sqrt(117x^4y^2).
=3 √13 x^2y
After applying Pythagoras' theorem the length of the hypotenuse we get is approximately 10.8 x²y unit.
Use the concept of the triangle defined as:
A triangle is a three-sided polygon, which has three vertices and three angles which has a sum of 180 degrees.
And the Pythagoras theorem for a right-angled triangle is defined as:
(Hypotenuse)²= (Perpendicular)² + (Base)²
Given that,
Base = 6x²y
perpendicular = 9x²y
Now apply the Pythagorean theorem,
(Hypotenuse)²= (6x²y)² + (9x²y)²
(Hypotenuse)²= 36x⁴y² + 81x⁴y²
(Hypotenuse)²= 117x⁴y²
Take square root on both sides we get,
Hypotenuse = √117 x²y
Hypotenuse ≈ 10.8 x²y
Hence,
The length of the hypotenuse is approximately 10.8 x²y unit.
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which equation represents an exponential function with an initial value of 500
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A box of 25 light bulbs is shipped to a hardware store.when it arrives,four of the bulbs are broken.predict the number of broken light bulbs in an order of 125 bulbs
Answers
Final answer:
The prediction method for the number of broken light bulbs in an order is based on a proportional relationship. Using the ratio from a smaller sample, it's calculated that an order of 125 light bulbs would result in 20 broken bulbs, assuming the breakage rate stays constant.
Explanation:
Given that 4 out of 25 light bulbs are broken in the initial order, we can predict the number of broken light bulbs in a larger order of 125 bulbs. The ratio of broken bulbs to total bulbs in the initial order is 4 broken bulbs for every 25 bulbs.
To find the predicted number of broken bulbs in a larger order, you multiply the total number of bulbs in the larger order by the ratio of broken bulbs in the smaller order. The calculation for the larger order of 125 bulbs would be:
(4 broken bulbs / 25 total bulbs) × 125 total bulbs in the larger order = 20 broken bulbs
Therefore, if 25 light bulbs yield 4 broken ones, an order of 125 light bulbs is predicted to have 20 broken bulbs, assuming the rate of breakage remains consistent.
What is the fifth term of the sequence?
an=5⋅2n−1
Enter your answer in the box.
a5=
Answers
Answer:
The fifth term of the sequence is:
49
Step-by-step explanation:
We are given the general term([tex]n^{th}[/tex] term) of the sequence as:
an=5.2n-1
We have to find the fifth term
i.e. we have to find the value of an for n=5
a5=5×2×5-1
=50-1
=49
Hence, the fifth term of the sequence is:
49
the average waiting time to be seated for dinner at a popular restaurant is 23.5 minutes with a standard deviation of 3.6 minutes assume the variable is normally distributed what is the probability that a patron Will Wait less than 18 minutes or more than 25 minutes
Answers
To determine the probability of a patron waiting less than 18 minutes or more than 25 minutes at a restaurant, we calculate the Z-scores for each time, look up the corresponding probabilities in a standard normal distribution table, and add the probabilities together.
To find the probability that a patron will wait less than 18 minutes or more than 25 minutes at a restaurant with an average waiting time of 23.5 minutes and a standard deviation of 3.6 minutes, assuming a normal distribution, we need to calculate two separate probabilities and then add them together.
First, we calculate the Z-score for 18 minutes, which is (18 - 23.5) / 3.6. Then, we find the corresponding probability from the standard normal distribution table. This gives us the probability of waiting less than 18 minutes.
Secondly, we calculate the Z-score for 25 minutes, which is (25 - 23.5) / 3.6. The corresponding probability gives us the probability of waiting more than 25 minutes. However, we want the probability of waiting longer, so we subtract this probability from 1 to find the probability of waiting more than 25 minutes.
Adding both probabilities gives us the total probability of a patron waiting either less than 18 minutes or more than 25 minutes.
How do I solve this?Help me please!!!
Answers
Ship M travels E 15 km, then N35E 27 km. Its sub travels down 48° 2 km from that location.
Ship F travels S75E 20 km, then N25E 38 km. The treasure is expected to be at this location 2.18° below horizontal from the port.
Find:
1a. The distance from port to Ship M
1b. The distance from port to the sub
1c. The angle below horizontal from the port to the sub
2a. The distance from port to Ship F
2b. The depth to the expected treasure location
2c. The distance from port to the expected treasure location
Solution:
It can be helpful to draw diagrams. See the attached. The diagram for depth is not to scale.
There are several ways this problem can be worked. A calculator that handles vectors (as many graphing calculators do) can make short work of it. Here, we will use the Law of Cosines and the definitions of Tangent and Cosine.
Part 1
1a. We are given sides 15 and 27 of a triangle and the included angle of 125°. Then the distance (m) from the port to the ship is given by the Law of Cosines as
m² = 15² +27² -2·15·27·cos(125°) ≈ 1418.60
m ≈ 37.66
The distance from port to Ship M is 37.66 km.
1b. The distance just calculated is one side of a new triangle with other side 2 km and included angle of 132°. Then the distance from port to sub (s) is given by the Law of Cosines as
s² = 1418.60 +2² -2·37.66·2·cos(132°) ≈ 1523.41
s ≈ 39.03
The distance from port to the sub is 39.03 km.
1c. The Law of Sines can be used to find the angle of depression (α) from the port. That angle is opposite the side of length 2 in the triangle of 1b. The 39.03 km side is opposite the angle of 132°. So, we have the relation
sin(α)/2 = sin(132°)/39.03
α = arcsin(2·sin(132°)/39.03) ≈ 2.18°
The angle below horizontal from the port to the sub is 2.18°.
Part 2
2a. We are given sides 20 and 38 of a triangle and the included angle of 100°. Then the distance (f) from the port to the ship is given by the Law of Cosines as
f² = 20² +38² -2·20·38·cos(100°) ≈ 2107.95
f ≈ 45.91
The distance from port to Ship F is 45.91 km.
2b. The expected treasure location is at a depth that is 2.18° below the horizontal from the port. The tangent ratio for an angle is the ratio of the opposite side (depth) to the adjacent side (distance from F to port), so we have
tan(2.18°) = depth/45.91
depth = 45.91·tan(2.18°) ≈ 1.748
The depth to the expected treasure location is 1.748 km.
2c. The distance from port to the expected treasure location is the hypotenuse of a right triangle. The cosine ratio for an angle is the ratio of the adjacent side to the hypotenuse, so we have
cos(2.18°) = (port to F distance)/(port to treasure distance)
(port to treasure distance) = 45.91 km/cos(2.18°) ≈ 45.95
The distance from the port to the expected treasure is 45.95 km.
Part 3
It seems the Mach 5 Mimi is the ship most likely to have found the treasure. That one seems ripe for attack. Its crew goes to a location that is 2.18° below horizontal. The crew of the FTFF don't have any idea where they are going. (Of course, the pirate ship would have no way of knowing if it is only observing surface behavior.)
Find the derivative of the function. f'(x)= arccsc 8x
Answers
Answer:
-1/x√64x^2-1
The derivative of the function f'(x)= arccsc 8x is f'(x)= -1/(|8x|√((8x)² - 1)). We achieved this result by using the rules for derivatives of arcsine, arcsecant and arccosecant along with the chain rule for differentiation of composite functions.
Explanation:To find the derivative of the function f'(x)= arccsc 8x, we will first need to understand that the derivative of the arcsine of x, also known as the inverse sine of x, is 1/(√(1 - x²)). Similarly, the derivative of arcsecant of x, known as the inverse secant of x, is 1/(|x|√(x² - 1)).
However, here we have arccosecant of x, known as the inverse cosecant of x. With this, we find that the derivative of arccosecant of x is -1/(|x|√(x² - 1)). Now in context of our function, where we replace x with 8x, we get f'(x)= -1/(|8x|√((8x)² - 1)).
We used the rules mentioned as well as the mutation rule ( df (u) = [du f(u)] dx ). This mutation rule is also known as the chain rule in differentiation, which allows us to differentiate composite functions. The function present here is a composite function where we have 8x in place of x in the arccosecant function.
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Determine whether the sequence is arithmetic, geometric, both or neither.
16, 8, 4, 2
A. arithmetic
B. Goemetric
C. Neither
D. Both
Answers
I think its both because An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. Consecutive means one after the other. The constant value is called the common difference. Another way to think about an arithmetic sequence is that each term in the sequence is equal to the previous term plus the common difference and also A geometric sequence is a sequence in which the ratio of any two consecutive terms is constant. This constant value is called the common ratio. Another way to think about a geometric sequence is that each term is equal to the previous term times the common ratio. So when u look at it check out if the 16, 8, 4, and 2 see if they fit these terms
The ratios are constant (0.5), so the sequence is geometric.
Since the sequence is not arithmetic but is geometric, the correct answer is: B. Geometric
To determine whether the sequence 16, 8, 4, 2 is arithmetic, geometric, both, or neither, let's analyze the differences between consecutive terms and the ratios between consecutive terms.
Arithmetic Sequence:
An arithmetic sequence is a sequence in which the difference between consecutive terms is constant.
Calculating the differences:
8 - 16 = -8
4 - 8 = -4
2 - 4 = -2
The differences are not constant, so the sequence is not arithmetic.
Geometric Sequence:
A geometric sequence is a sequence in which the ratio between consecutive terms is constant.
Calculating the ratios:
8 / 16 = 0.5
4 / 8 = 0.5
2 / 4 = 0.5
The ratios are constant (0.5), so the sequence is geometric.
Since the sequence is not arithmetic but is geometric, the correct answer is:
B. Geometric
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Jim is able to sell a hand-carved statue for $670 which was a 35% profit over his cost. How much did the statue originally cost him?
Answers
Mr. Maddox asked four students to create a number line to help find the sum of fractions 3 2/3 + 1 3/4 + 2/3
Answers
Answer with explanation:
Question asked by Mr.Maddox to find the sum of fractions with the help of number line :
[tex]\rightarrow 3 \frac{2}{3}+1 \frac{3}{4}+\frac{2}{3}\\\\ \text{Using Associative Property}\\\\\rightarrow a+(b+c)=(b+c)+a\\\\\rightarrow [\frac{2}{3}+ 1\frac{3}{4}]+3 \frac{2}{3}\\\\\rightarrow [\frac{2}{3}+\frac{7}{4}]+\frac{11}{3}\\\\\rightarrow \frac{21+8}{12}+ \frac{11}{3}\\\\\rightarrow\frac{29+44}{12}\\\\ \rightarrow\frac{73}{12}\\\\\rightarrow 6\frac{1}{12}[/tex]
To find the number of centimeters in 10 inches, multiply the number of inches given (10) by _____.
3.04
2.54
2.78
2.44
Answers
10 in--------X
x=10*2.54=25.4 cms
the answer is 2.54 cms
1 inch = 2.54 centimeters
We can make the following rule of three:
1 ---> 2.54
10 ----> x
Clearing x:
x = (10/1) * (2.54)
x = 25.4 cm
Answer:
multiply the number of inches given by
2.54
write 2/5 and 1/3 as equivalent fractions using a common denominator
Answers
The equivalent fractions with the same denominator are 6/ 15 and 5 /15.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the two fractions are 2/5 and 1/3. The two equivalent expressions with the common base will be written as:-
2/5 = ( 2 x 3 ) / ( 5 x 3 )
2//5 = 6 / 15
1/3 = ( 1 x 5 ) / ( 3 x 5 )
1 / 3 = 5 / 15
Therefore, the two fractions are 6/ 15 and 5 /15.
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a fish is 12 meters above the surface of the ocean. what is its elevation
Answers
the level of the surface of the ocean is level zero
therefore
the elevation of the fish is = 0+12=+12 meters (the positive sign tells me that it is above the surface of the ocean)
the answer is 12 meters
4 friends equally share 1/3 of a pan of brownies. How much of the whole pan of brownies does each friend get?
Answers
Question:
Evaluate each expression:
1. 9x + 8y, when x = 4 and y = 5
2. 2x + 8x, when x = 3
3. 4y + 7y, y = 5
4. 10x + 18y, when x = 4 and y = 5
5. x + 8y, when x = 2 and y = 1/4
6. 9x + 8y, when x = 1/3 and y = 1/4
7. 3x + 7y, when x = 8 and y = 4
8. 12x + 16y, when x = 1/4 and y = 5
Answers
1.) 9(4) + 8(5)
36 + 40 = 74
2.) 2(3) + 8(3)
6 + 24 = 30
3.) 4(5) + 7(5)
20 + 35 = 55
4.) 10(4) + 18(5)
40 + 90 = 130
5.) 2 + 8(1/4)
2 + 2 = 4
6.) 9(1/3) + 8(1/4)
3 + 2 = 5
7.) 3(8) + 7(4)
24 + 28 = 52
8.) 12(1/4) + 16(5)
4 + 80 = 84
Weights were recorded for all nurses at a particular hospital, the mean weight for an individual nurse was 135 lbs. with a standard deviation of 15. If 19 nurses are selected at random, find the probability that the mean weight is between 125 and 130 lbs
Answers
population mean, μ =135
population standard deviation, σ = 15
sample size, n = 19
Assume a large population, say > 100,
we can reasonably assume a normal distribution, and a relatively small sample.
The use of the generally simpler formula is justified.
Estimate of sample mean
[tex]\bar{x}=\mu=135[/tex]
Estimate of sample standard deviation
[tex]\s=\sqrt{\frac{\sigma^2}{n}}[/tex]
[tex]=\sqrt{\frac{15^2}{19}}=3.44124[/tex] to 5 decimal places.
Thus, using the normal probability table,
[tex]P(125<X<130)[/tex]
[tex]=P(\frac{125-135}{3.44124}<Z<\frac{130-135}{3.44124})[/tex]
[tex]=P(-2.90593<Z<-1.45297)[/tex]
[tex]=P(Z<-2.90593)=0.0018308[/tex]
[tex]=P(Z<-1.45297)=0.0731166[/tex]
Therefore
The probability that the mean weight is between 125 and 130 lbs
P(125<X<130)=0.0731166-0.0018308
=0.0712858
Which function has an inverse that is also a function?
Answers
{(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}
Answer:
C){(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}
Step-by-step explanation:
The one-to-one function has inverse where the inverse is also function.
That is, there should be unique output for each input values.
Look at the options, Option C) only has unique output for each input values.
Therefore, the answer C){(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}
Hope this will helpful.
Thank you.
Please can some body please help me with this math problem on IXL. I just want to get done with tthis IXL, because i have been doing it forever now
Answers
= 2(5 · u)
= (2 · 5)u
= 10u
= (2 * 5) u | associative property
= 10u | multiply
Hope this helps
a book normally costs $21.50. today it was on sale for 15.05. what percentage discount was offered during the sale?
Answers
Discounted Price / Original Price = 1 - Discount %
15.05 / 21.5 = 1 - Discount %
Subtract 15.05 / 21.5 from both sides and add Discount % to both sides to get the following equation.
Discount % = 1 - 15.05 / 21.5 = 1 - 0.7 = 0.3 = 30% discounted
Final answer:
To calculate the percentage discount of a book, subtract the sale price from the original price, divide by the original price, and multiply by 100. The detailed calculation shows that the book had a 30% discount during the sale.
Explanation:
The question asks how to calculate the percentage discount of a book that has been reduced from its normal price to a sale price. To find the percentage discount, we subtract the sale price from the original price, and then divide this difference by the original price. Finally, we multiply by 100 to get the percentage.
Step-by-Step Solution:
Calculate the difference in price: $21.50 (original price) - $15.05 (sale price) = $6.45 (amount discounted).Divide the discount by the original price: $6.45 / $21.50.Convert the result to a percentage: ($6.45 / $21.50) × 100 = 30%.The percentage discount offered on the book during the sale was 30%.
a rectangular corn hole area at the recreation center has a width of 5 feet and a length of 10 feet. if a uniform amount is added to each side, the area is increased to 84 square feet. what is the amount added to each side
Answers
x-------------> amount added to each side
A-------------> area increased----------> 84 ft²
we know that
A=(10+x)*(5+x)=84-----------> 10*5+10*x+5*x+x²
50+15x+x²=84----------> x²+15x-34=0
solving the second order equation
x1=-17
x2=2
the answer is x=2 ft
Answer:
the answer is add 2 feet on each side!
Step-by-step explanation:
The graph shows the function f(x)=2x
What is the value of x when the f(x)=4?
A. 3
B. 1
C. 0
D.2
Answers
2*2=4
X=4
Answer is 2
The value of x is option (D) 2
What is a function?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.
Given,
f(x) = [tex]2^{x}[/tex]
we have to find the value of x when f(x) =4
f(x) = [tex]2^{x}[/tex] =4
[tex]2^{x}=4\\ 2^{x}=2^{2}[/tex]
Therefore value of x is 2
Hence, the value of x is option (D) 2
Learn more about Function here
https://brainly.com/question/12431044
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Which system of linear inequalities is represented by the graph?
x – 3y > 6 and y > 2x + 4
x + 3y > 6 and y > 2x – 4
x – 3y > 6 and y > 2x – 4
x + 3y > 6 and y > 2x + 4
Answers
y = 2x +4
The shaded area is above the line, so it is the boundary of the inequality
y ≥ 2x + 4
The red dashed line has a slope of -1/3 and a y-intercept of 2. Its equation is
y = -1/3x + 2
The shaded area is above the line, so it is the boundary of the inequality
y > -1/3x + 2
or
x +3y > 6
The graph seems to represent the inequalities
x +3y > 6 and y ≥ 2x +4
Answer:
So the answer is D
Step-by-step explanation:
Suppose u = f(x, y) with x = r cos θ and y = r sin θ. find ∂u ∂r .
Answers
Calculate the rise and run and find the slope ( -9,2) and (-1,6)
Answers
Slope= Rise/Run or (y2-y1)/(x2-x1)
Put values
Slope=(6-2)/(-1-(-9))
Slope=4/(-1+9)
Slope=4/8
Slope=1/2
So here Rise=1 and Run=2
Answer: Slope= 1/2 , Rise= 1 and Run=2