Margret has $32.00 in a savings account. Margret wants to have a balance of $40.00 in the account. How much money does Margret need to deposit to reach this amount?
The amount of money that Margret needs to deposit to reach this amount is $8.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
Since Margret has $32.00 in a savings account. Margret wants to have a balance of $40.00 in the account, the amount needed will be:
= $40 - $32
= $8
She'll need $8 more.
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1. A painting crew bought 45 gallons of paint for a job. The crew members used 5 gallons of paint per hour until they used all the paint. Sketch a graph to represent the start to the end of the job, assuming all paint was used. Be sure to title your graph, label your axes, and label your intercepts. This must be graphed by hand or by using the tools in Word. You may not use a web-based graphing program.
The graph that shows the equation, y = -5x + 45, that represents the scenario given is shown in the attachment.
How to Graph a Linear Equation?Determine the slope (m) and the y-intercept (b), then input the values in the equation, y = mx + b, to write the equation of the line that would be graphed.
Given the information above, we have the following:
Let x = hours, and y = quantity of gallons of paint left
Slope (m) = -5
Y-intercept (b) = 45
Write the equation of the graph by substituting m = 5 and b = 45 into y = mx + b:
y = -5x + 45
The graph shown below for y = 5x + 45 would be labelled as follows:
x-axis = hours
y-axis = quantity of paint (in gallons)
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The letters that spell MISSISSIPPI are each written on separate tiles lying facedown on a table. A tile
is selected at random, the letter is recorded, and then the tile is placed facedown on the table. Then
the process repeats.
What is the theoretical probability of choosing a tile with the letter P?
0 11
01/11
Answer: 2/11
Step-by-step explanation: there are 11 letters and 2 of them are p so the chances of getting p is 2/11
Answer:
2/11
Step-by-step explanation:
The total amount of tiles is 11. There are only 2 tiles that have the letter P on them.
Theoretical probability is the probability that should occur over many, many trials.
Theoretical probability = favorable outcomes / total outcomes.
In this scenario, the favorable outcome is the letter P. which there are two of. The total outcomes would be all the letters that make up the word MISSISSIPPI, or 11.
So your theoretical probability would be 2/11.
Units help please due today 50 points
Answer:
12.8
Step-by-step explanation:
You can see that triangle DAF and BED are equal.
So lineAF is lineDE.
6.4*2=12.8.
Find the exact value of sin(u + v) given that sinu = 5/3 and cos v =-4/5. (Both u and v are in Quadrant I.)
The exact value of sin(u + v), obtained using trigonometric identities is for sine and cosine is 16/65
What are trigonometric identities?Trigonometric identities are equations that involve trigonometric functions that are valid for all values of the input variable.
The possible value of sin(u) obtained from a similar question posted online is; sin(u) = 5/13
Both u and v are in quadrant II
The trigonometric identity of the addition formula for the sine of the sum of two angles, indicates;
sin(u + v) = sin(u)·cos(v) + sin(v)·cos(u)
sin(u) = 5/13
cos(v) = -4/5
sin(v) = √(1 - (cos(v))²)
Therefore;
sin(v) = √(1 - (-4/5)²) = 3/5
cos(u) = √(1 - (sin(v))²)
Therefore;
cos(u) = √(1 - (5/13)²) = 12/13
Therefore;
sin(u + v) = (5/13) × (-4/5) + (3/5) × (12/13) = 16/65
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Consider all right circular cylinders for which the sum of the height and circumference is 60 cm. What is the radius of the one with maximum volume?.
By using the concept of maxima, it can be calculated that
Volume is maximum if the radius of the cone is 40 cm
What is maxima of a function?
Maxima of a function gives the maximum value of the function on a certain interval or on the whole domain.
Let the height of the cylinder be h and radius be r
Sum of height and circumference = h + 2πr
By the problem,
h + 2πr = 60
h = 60 -2πr
Volume(V) = π[tex]r^2[/tex] h
= π[tex]r^2[/tex](60 - r)
= 60π[tex]r^2[/tex] - π[tex]r^3[/tex]
[tex]\frac{dV}{dr} = 120\pi r - 3 \pi r^2[/tex]
For maximum volume
[tex]\frac{dV}{dr} = 0[/tex]
[tex]120\pi r - 3 \pi r^2 = 0\\[/tex]
[tex]3 r^2 = 120 r\\3r = 120 [r \neq 0]\\r = \frac{120}{3}\\r = 40 \ cm[/tex]
[tex]\frac{d^2V}{dr^2} = 120 \pi - 6 \pi r\\[/tex]
Putting r = 40
[tex]\frac{d^2V}{dr^2} = 120 \pi - 6 \pi \times 40\\\frac{d^2V}{dr^2} =120\pi - 240 \pi\\\frac{d^2V}{dr^2} = -120\pi < 0[/tex]
Hence Volume is maximum
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one thousand independent rolls of a fair die will be made. compute an approximation to the probability that the number 6 will appear between 150 and 200 times inclusively.
The probability that the number 6 will appear between 150 and 200 times inclusively is 0.926.
In the given question, one thousand independent rolls of a fair die will be made.
We have to compute an approximation to the probability that the number 6 will appear between 150 and 200 times inclusively.
Let n=1000 are independent trails.
The probability of success is constant, p=1/6
The probability of success is not constant,
q=1-1/6 = 5/6
let X be the number of times the die shows a 6.
μ = np
μ = 1000*1/6
μ = 166.7
σ=√npq
σ=√1000*1/6*5/6
σ=√5000/36
σ=11.785
Now we used the correlation continuity for finding the probability that number 6 will appear between 150 and 200 times is
P(150≤X≤200)=P(X≤200)-P(X<150)
P(150≤X≤200)=P(Z≤(200+0.5-166.7)/11.785)-P(Z≤(150-0.5-166.7)/11.785)
P(150≤X≤200)=P(Z≤2.87)-P(Z≤-1.46)
P(150≤X≤200)=0.998-0.072
P(150≤X≤200)=0.926
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A vehicle uses 1\frac{1}{8} gallons of gasoline to travel 13\frac{1}{2} miles. Create a rate to represent the miles the vehicle can travel per gallon of gasoline.
The vehicle can travel 12 miles per gallon of gasoline.
What is the Mixed fraction ?
A mixed fraction is one that is represented by both its remainder and quotient. Consequently, a mixed fraction is created by combining a whole number and a proper fraction.
What is the Rate ?
A rate is the comparison of two comparable amounts expressed in different units. If the ratio's denominator is written as a single unit of one of these quantities, and if it is assumed that this quantity can be modified systematically (i.e., is an independent variable), then the numerator of the ratio indicates the comparable rate of change in the other (dependent) variable.
The vehicle travels 13\frac{1}{2} by using 1\frac{1}{8} gallons of gasoline.
since the units are in mixed fraction, we can simplify it to simple fraction,
distance travelled= 13\frac{1}{2} = [(13 × 2) + 1] / 2 = 27/2 miles.
gasoline used= 1\frac{1}{8} = [(1×8)+1] /8 = 9/8 gallons.
∴ Miles per gallon of gasoline = distance travelled ÷ gasoline used
= 27/2 miles ÷ 9/8 gallons
= 12 miles per gallon of gasoline.
Hence, The rate of miles per gallon of gasoline is 12 miles/gallon of gasoline.
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A = 2(x + 3) y B = 3(13 + x)
h(x) = 4x-22 for h(12)
The value of h ( 12 ) is 26
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be A
Now , the value of equation A is
h ( x ) = 4x - 22 be equation (1)
Now , to find the value of h ( 12 ) , substitute the value of x = 12 in the equation , we get
h ( x ) = 4x - 22
h ( 12 ) = 4 x 12 - 22
On simplifying the equation , we get
h ( 12 ) = 48 - 26
= 22
Therefore , the value of h ( x ) when x = 12 is 22
Hence , The value of h ( 12 ) is 26
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He creates paths through the garden along line segment a b, line segment x y, and line segment z y. Which correctly compares the lengths of the paths?the path along line segment x y is longer than the path along line segment z y, and the path along line segment z y is longer than the path along line segment a b. The path along line segment a b is longer than the path along line segment z y, and the path along line segment z y is longer than the path along line segment x y. The path along line segment z y is longer than the path along line segment x y, and the path along line segment x y is longer than the path along line segment a b. The path along line segment z y is longer than the path along line segment a b, and the path along line segment a b is longer than the path along line segment x y.
The journey along Line segment X Y is longer than the path along Line segment Z Y, and the path along Line segment Z Y is longer than the path along Line segment A B, hence Option-A is the correct answer.
Given that,
He makes paths that follow Line segments A and B, X and Y, and Z and Y through the garden.
We have to find which accurately compares the pathways' lengths.
We know that,
The length of the third side in a triangle is proportional to the angle Ф if the lengths of the two sides that make up the angle Ф are fixed.
XY > YZ because XY's opposing angle (79°) is greater than YZ's (65°).
As before, YZ > AB because the opposing angle of YZ (65°) is greater than that of AB (36°).
Since both sides of the angle are the same length (8 feet),
As a result, assertion A. is accurate. (Answer)
Therefore, The journey along Line segment X Y is longer than the path along Line segment Z Y, and the path along Line segment Z Y is longer than the path along Line segment A B, hence Option-A is the correct answer.
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Answer:
It's A
Step-by-step explanation:
I got 100 on the quiz
and D are noncoplanar. △ABC,△ABC,△ACD, and △ABD are equilateral. X and Y are midpoints of AC¯¯¯¯¯¯¯¯ and and AD.Z is a point on AB¯¯¯¯¯¯¯¯. What kind of triangle is △XYZ? Explain.
ΔXYZ will also be an equilateral triangle.
What is equilateral triangle?
An equilateral triangle in geometry is a triangle with equal-length sides on all three sides. In the well-known Euclidean space, an equilateral triangle also is equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others. It's also referred to it as a regular triangle because it is a regular polygon.
As X,Y,Z are the midpoints of sides of equilateral triangle so when we will join the X,Y,Z we will find that distances XY=YZ=XZ are three are equal because this is proved by similarity of triangles which in itself is a detailed and vast topic
Hence XYZ will also be an equilateral triangle
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Type the correct answer in each box. Use numerals instead of words for numbers. If necessary, use / for the fraction bar(s). The amount of time it takes a water pump to empty a tank varies directly as the capacity of the tank. If it takes a water pump 2. 5 hours to empty a tank containing 60,000 gallons of water, how long does it take the same pump to empty a tank containing 108,000 gallons of water? it will take hours to empty the second tank.
An equation is formed when two equal expressions. The time the same pump will take to empty a tank containing 108,000 gallons of water is 4.5 hours.
What is an equation?When two equal expressions are added together with the aid of the equal sign "=," an equation is created.
Given that the time it takes a water pump to empty a tank directly correlates with the tank's capacity. Consequently, the relationship can be expressed as,
V ∝ T
V = kT
Substituting the volume and time in the equation,
60,000 gallons = 2.5 hours × k
Solving the equation for k,
k = 60,000 gallons / 2.5 hours
k = 24,000 gallons per hour
Now, the equation for the relationship can be written as,
V = 24,000 gallons per hour × T
Now, the time the same pump will take to empty a tank containing 108,000 gallons of water is,
V = 24,000 gallons per hour × T
108,000 gallons = 24,000 gallons per hour × T
108,000 gallons / 24,000 gallons per hour = T
T = 4.5 hours
Hence, the time the same pump will take to empty a tank containing 108,000 gallons of water is 4.5 hours.
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I can't theme to grasp these questions can someone please explain the steps ?
Answer:
(i) See below for proof.
(ii) x = 1.823, x = -0.823
Step-by-step explanation:
Part (i)Given equation:
[tex]\dfrac{x+2}{x+1}+\dfrac{3}{x}=3[/tex]
Make the denominators of the fractions the same:
[tex]\implies \dfrac{x+2}{x+1}\cdot \dfrac{x}{x}+\dfrac{3}{x}\cdot \dfrac{x+1}{x+1}=3[/tex]
[tex]\implies \dfrac{x(x+2)}{x(x+1)}+\dfrac{3(x+1)}{x(x+1)}=3[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]
[tex]\implies \dfrac{x(x+2)+3(x+1)}{x(x+1)}=3[/tex]
Multiply both sides of the equation by x(x + 1) to eliminate the denominator of the fraction on the LHS:
[tex]\implies x(x+2)+3(x+1)=3x(x+1)[/tex]
Expand the brackets:
[tex]\implies x^2+2x+3x+3=3x^2+3x[/tex]
[tex]\implies x^2+5x+3=3x^2+3x[/tex]
Subtract x² from both sides:
[tex]\implies 5x+3=2x^2+3x[/tex]
Subtract 5x from both sides:
[tex]\implies 3=2x^2-2x[/tex]
Subtract 3 from both sides:
[tex]\implies 0=2x^2-2x-3[/tex]
[tex]\implies 2x^2-2x-3=0[/tex]
Part (ii)[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]
To solve the quadratic equation [tex]2x^2-2x-3=0[/tex], use the quadratic formula.
Therefore:
a = 2b = -2c = -3Substitute these values into the formula and solve for x:
[tex]\implies x=\dfrac{-(-2) \pm \sqrt{(-2)^2-4(2)(-3)}}{2(2)}[/tex]
[tex]\implies x=\dfrac{2 \pm \sqrt{4+24}}{4}[/tex]
[tex]\implies x=\dfrac{2 \pm \sqrt{28}}{4}[/tex]
[tex]\implies x=\dfrac{2 \pm \sqrt{4 \cdot 7}}{4}[/tex]
[tex]\implies x=\dfrac{2 \pm \sqrt{4} \sqrt{7}}{4}[/tex]
[tex]\implies x=\dfrac{2 \pm 2 \sqrt{7}}{4}[/tex]
[tex]\implies x=\dfrac{1 \pm \sqrt{7}}{2}[/tex]
Therefore, the solutions correct to 3 decimal places are:
[tex]x=1.823,\;\; x= -0.823[/tex]
It has long been thought that the length of one's femur is positively correlated to the length of one's tibia. The following are data for a classroom of students who measured each (approximately) in inches. Femur Length Tibia Length 18.7 14.2 20.5 15.9 16.2 13.1 15.0 12.4 19.0 16.2 21.3 15.8 21.0 16.2 14.3 12.1 15.8 13.0 18.8 14.3 18.7 13.8 Regression Statistics Multiple R 0.9305 R Square 0.8659 Adjusted R Square 0.8510 Standard Error 0.5963 Observations ANOVA SS MS F Significance F Regression 1 20.6611 20.6611 58.0968 3.25116E-05 Residual 9 3.2007 0.3556 Total 10 23.8618 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 3.5850 1.4137 2.5359 0.0319 0.3871 6.7830 Femur Length 0.5899 0.0774 7.6221 0.0000 0.4148 0.7650 A strong linear correlation was found between the two variables. Find the standard error of estimate. Round answer to 4 decimal places.
The linear correlation between the given two variables be,
4.5y + 5.2x = 168.34
Given, data for a classroom of students who measured each (approximately) in inches.
Femur Length 18.7 14.2 20.5 15.9 16.2 13.1 15.0 12.4 19.0 16.2 21.3
Tibia Length 15.8 21.0 16.2 14.3 12.1 15.8 13.0 18.8 14.3 18.7 13.8
we have to find a linear correlation between the two variables,
linear correlation be,
(y - 15.8)/(x - 18.7) = (15.8 - 21.0)/(18.7 - 14.2)
(y - 15.8)/(x - 18.7) = (- 5.2)/4.5
4.5y - 71.1 = -5.2x + 97.24
4.5y + 5.2x = 168.34
So, the linear correlation between the given two variables be,
4.5y + 5.2x = 168.34
Hence, the linear correlation between the given two variables be,
4.5y + 5.2x = 168.34
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(pythagorean theorem mc) a right triangle has a leg length of square root of 11 and a hypotenuse length of 9. determine the length of the other leg of the right triangle. square root of 18 square root of 81 square root of 70 22
The length of the other leg of the given right triangle is [tex]\sqrt{70}[/tex].
RIGHT TRIANGLE
A triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.
The Pythagorean Theorem says (hypotenuse)²= (leg1)²+(leg2)². And the main trigonometric ratios are: sin (x) , cos (x) and tan (x) .
The question gives:
leg1=[tex]\sqrt{11}[/tex]hypotenuse = 9Therefore, from the Pythagorean Theorem, you will find the value of the other leg. See below.
[tex]9^2={\sqrt{11}^2 +{leg_2}^2[/tex]
[tex]81=11 +{leg_2}^2[/tex]
[tex]{leg_2}^2=81-11\\ \\ {leg_2}^2=70\\ \\ leg_2=\sqrt{70}[/tex]
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Diana spent 3 hours at the museum. For 1.418 hours she was watching a movie. The rest of the time she spent looking at exhibits. How longs did Diana spend looking at exhibits?
The time that Diana spent looking at the exhibits is given as follows:
1.582 hours.
How to obtain the time that Diana spent looking at the exhibits?As stated in the problem, the total time that Diana spent at the museum is given as follows:
3 hours.
The total time that Diana spent at the museum was divided into two activities, presented as follows:
Watching a movie.Looking at exhibits.The times of each activity are given as follows:
Watching a movie: 1.418 hours.Looking at exhibits: x hours.Then the time that Diana spent looking at exhibits is obtained as follows:
x + 1.418 = 3
The time is obtained by the subtraction of 3 by 1.418 as follows:
x = 3 - 1.418
x = 1.582 hours.
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The surface area of the figure shown is 192 cm².
What is the value of x?
8 cm
6 cm
10 cm
X cm
The value of x = 6cm.
What is surface area?
The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object refers to the space occupied by its outer surface.
From the given figure,
Surface area(A) = [tex]192cm^{2}[/tex]
Height = 8cm
a base side = 6 cm
b base side = 10 cm
c base side = x cm
Therefore, TSA= 2B +Px = [tex]2 \times\frac{1}{2} \times8\times6 +(6+10+8)x[/tex]
=48+24x
Thus, 60+24x=192
[tex]x=\frac{192-48}{24}[/tex]
x= 6cm
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label the vertices then use the pythagorean theorem to find x
Answer:
5cm. 8cm
Step-by-step explanation:
Label all the vertices then use Pythagorean theorem
c² = a² + b²
review the video to determine whether each statement about the following equation is true or false. dndt
The statemet 2, the variable K represent carrying capacity and the variable N represent population size, is correct.
In the given question we have to review the video to determine whether each statement about the following equation is true or false.
The given equation is:
[tex]\frac{dN}{dt}=rN(\frac{K-N}{K})[/tex]
The given equation is used to find the annual growth of population.
In which, dN/dt = the annual increase for the population,
r = the annual growth rate,
N = the population size, and
K = the carrying capacity.
So the statemet two, the variable K represent carrying capacity and the variable N represent population size, is correct.
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the string of a kite is 100 meters long and it makes an angle of 60° with the horizontal line.find the height of the kite assuming that there is no slack in the string (â3=1.73)
The height of the kite assuming that there is no slack in the string is 86.6 m.
We have given that,
the string of a kite is 100 meters long and it makes an angle of 60°.
and we have to find the height of the kite.
So therefore we know the formula for right angled triangle,
i.e. sinθ = Opposite side/ Hypotenuse
Here θ = 60°
Opposite side = height of the kite = h (say)
Hypotenuse = length of string = 100 m
⇒ sin60° = [tex]\frac{h}{100}[/tex]
h = 100sin60°
= 100 × [tex]\frac{\sqrt{3} }{2}[/tex]
= 50 × 1.732
h = 86.6 m
Hence the height of the kite is 86.6 m.
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Solve it please I need this asap!
The angles ∠BCD and ∠BAD are opposite interior angles of a parallelogram. in which the alternate interior angles ∠BAC and ∠ACD and ∠BCA and ∠DAC are congruent, from which by angle addition property, ∠BCD ≅ ∠BAD
What are alternate interior angles?Alternate interior angles are angles formed by the transversal to two parallel lines on the inside of the parallel lines, and on opposite sides of the transversal.
The two column-method used to prove that ∠BCA is congruent to ∠DAC can be presented as follows;
Step [tex]{}[/tex] Statement Reason
1. [tex]\overline{BC}[/tex]║ [tex]\overline{AD}[/tex], [tex]\overline{AB}[/tex]║[tex]\overline{CD}[/tex] [tex]{}[/tex] Given
2. [tex]{}[/tex] ∠BCA ≅ ∠DAC ║ lines cut by a trans. form ≅ int. ∠s
3. [tex]{}[/tex] [tex]\overline{AC}[/tex]║[tex]\overline{CA}[/tex] [tex]{}[/tex] Reflexive Property
4. ∠BAC ≅ ∠ACD [tex]{}[/tex] Alternate interion angles
5. ∠BCA = ∠DAC[tex]{}[/tex] Definition of congruency
[tex]{}[/tex] ∠BAC = ∠ACD
6. ∠BCD = ∠BCA + ∠ACD[tex]{}[/tex] Angle addition property
∠BAD = ∠BAC + ∠DAC
7. ∠BCD = ∠BCA + ∠ACD [tex]{}[/tex] Substitution property
8. [tex]{}[/tex] ∠BCD = ∠BAD [tex]{}[/tex] Substitution property
9. ∠BCD ≅ ∠BAD [tex]{}[/tex] Definition of congruency
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Unless specified, all approximating rectangles are assumed to have the same width. Evaluate the upper and lower sums for f(x) = 1 + cos cos($) -ISXS*, with n = 3, 4, and 6. Illustrate each case with a sketch similar to the figure shown below. (Round your answers to two decimal places.) n = 3: upper sum ll lower sum n = 4: upper sum II lower sum n = 6: upper sum IO lower sum
In this Trigonometric Functions F(x) = 1 + cos(1/X): n=3 (12.01, 8.10), n=4 (11.65,8.50), and n=6 (11.24, 9.12), with their upper and lower value
What is Trigonometric Functions?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
F(x) = 1 + cos(1/X)
for n=3
Upper sum = 12.01
Lower sum = 8.10
Δx = (b-a)/n = 2π / 3
for n=4
Upper sum = 11.65
Lower sum = 8.50
Δx = (b-a)/n = π / 2
for n=6
Upper sum = 11.24
Lower sum = 9.12
Δx = (b-a)/n = π / 3
Hence, n=3 (12.01, 8.10), n=4 (11.65,8.50), and n=6 (11.24, 9.12), with their upper and lower value.
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Find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit. Assume that revenue, Upper R left parenthesis x right parenthesis, andcost, Upper C left parenthesis x right parenthesis, of producing x units are in dollars. R(x)=3x, C(x)=0.05x^2+0.04x+10
To maximize the profit 29.6 units must be produced.
What is the maxima or minima?
The maxima and minima of a function collectively referred to as extrema in mathematical analysis, are the highest and lowest values of the function, either on the whole domain or within a specific range.
We have given,
The revenue function is,
R(x)=3x
Cost function,
C(x)=0.05x^2+0.04x+10,
Where
x = number of units produced.
Thus, profit = revenue - cost
P(x) = 3x - (0.05x^2+0.04x+10)
= -0.05x^2 + 2.96x - 10
Differentiating with respect to x,
P'(x) = -0.1x + 2.96
Again differentiating with respect to x,
P''(x) = -0.1
For maxima or minima,
P'(x) = 0,
0 = -0.1x + 2.96
-0.1x = -2.96
x = 2.96/0.1
For x = 29.6,
P''(x) = negative,
Hence, to maximize the profit 29.6 units must be produced.
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There are 6 circles and 10 squares. What is the simplest ratio of circles to total shapes?.
The simplest expression of the ratio of circles to squares is 5:3.
Describe ratio.
A relationship between two quantities is called a ratio, and it is expressed as one quantity divided by the other.
There are 6 circles and 10 squares.
These steps can be used to determine the ratio of two quantities:
Finding the quantities of both scenarios for which we are calculating the ratio is the first step. There are 10 squares and 6 circles in this instance.
It should be expressed as a fraction, a/b. Thus, we represent it as 10/6.
If you can, make the fraction even simpler. The ultimate ratio will be shown by the simple fraction.
In this case, 10/6 can be reduced to 5/3.
As a result, the simplest expression of the ratio of circles to squares is 5:3.
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help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!
a. [tex]123.1(1.069)^3 \approx 150.4[/tex]
b. [tex]123.1(1.069)^{20} \approx 467.5[/tex]
Solve and Graph.
[tex]\tt |4x+1|\:\le 6[/tex]
The value of x from the inequality equation | 4x + 1 | ≤ 6 , is
-7/4 ≤ x ≤ 5/4
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the equation be A
The value of the equation A is | 4x + 1 | ≤ 6 be equation (1)
From the modulus function rule , we know
If , | x | ≤ a , then -a ≤ x ≤ a
So , on simplifying the equation , we get
-6 ≤ 4x + 1 ≤ 6
Now , the two values are
4x + 1 ≥ -6 be equation (2)
4x + 1 ≤ 6 be equation (3)
From equation (2) , 4x + 1 ≥ -6
Subtracting 1 on both sides , we get
4x ≥ -7
Divide by 4 , we get
x ≥ -7/4
And , From equation (3) , 4x + 1 ≤ 6
Subtracting 1 on both sides , we get
4x ≤ 5
Divide by 4 on both sides , we get
x ≤ 5/4
Therefore , the solution is -7/4 ≤ x ≤ 5/4 and the graph is given below
Hence , The value of x from the inequality equation | 4x + 1 | ≤ 6 , is
-7/4 ≤ x ≤ 5/4
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Which expression is equivalent to13k+7+5(k+6)?
Answer:
18k +37
Step-by-step explanation:
13k + 7 + 5(k + 6)
13k + 7 + 5k + 30
13k + 5k + 7 + 30
18k +37
Each hamburger patty is 1/8 pound. Drag the correct equation to each amount to show how many 1/8 pound hamburger patties can be made.
Answer:
3 pounds:
3 ÷ [tex]\frac{1}{8}[/tex] = 24
7 pounds:
7÷[tex]\frac{1}{8}[/tex] = 56
Step-by-step explanation:
3÷[tex]\frac{1}{8}[/tex] = [tex]\frac{3}{1}[/tex] x [tex]\frac{8}{1}[/tex] = [tex]\frac{24}{1}[/tex] = 24
If it takes 1/8 of a pound to make 1 hamburger. Then it would take 1 pound to make 8 hamburgers.
3 x 8 = 24
7x8 = 56
When would you calculate an expected value? a. When your data points occur on different datesb. When your data points have various probabilities of occurringc. When you need to know the exact outcome of a future, unknown eventd. When you only have one data point
We calculate an expected value when the given data points have various probabilities of occurrence .
The expected value , applies best when we are performing the test or experiment many times. For example, EV applies well to gambling situations to describe expected results for thousands of gamblers per day, repeated day after day after day. However, the EV does not very accurately predict one particular outcome on one specific test.
For example, when drawing a playing card from a standard deck, on one specific draw, the likelihood of drawing a 2 is equal to the likelihood of drawing a 6 or 7 or 8 or any other numbered card.Over many many draws, the theoretical value to expect is 6.538. Obviously, there is no “6.538” card in the deck. But if you were gambling, you would expect to draw a card higher than 6 more often than not.To learn more about expected value
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