Each car is traveling at a constant speed. Find the number of miles each car travels in 1 hour at the given rate. 97 1/2 miles in 3/2 hours

Answer:

------------------------------------

100 dozen add 20% is:

Answer:

50%

Step-by-step explanation:

(new-old)/old × 100

(600 - 400)/400 × 100

(200)/400 × 100

0.5 × 100

50%

The percent error of the measurement is -1.2%, to the nearest tenth of a percent.

To calculate the percent error, we need to use the following formula:

Percent Error = (Actual Value - Measured Value) / Actual Value x 100

In this example, the actual value is 8.6 inches and the measured value is 8.7 inches. Plugging these values into the formula, we get:

Percent Error = (8.6 - 8.7) / 8.6 x 100

Simplifying, this gives us:

Percent Error = -0.1 / 8.6 x 100

Finally, we can calculate the percent error to the nearest tenth of a percent:

Percent Error = -1.2%

Therefore, we can conclude that the percent error of the measurement is -1.2%, to the nearest tenth of a percent.

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The square feet of the garden that could contain flowers, given the side lengths of the stepping stone and the garden, is C. 16 ft².

To find the portion of the garden that could contain flowers, first find the total area of the entire garden ;

= Length of garden x Width

= 4 x 6

= 24 ft ²

The stepping stones will not contain flowers so their area should be deducted from the area of the garden :

= 24 - ( 2 x ( 2 x 2 ))

= 24 - ( 2 x 4 )

= 24 - 8

= 16 ft²

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Answer: 4 pie chart

Step-by-step explanation:

Each pie chart  [tex]\pi[/tex] wil have 4 parts to it  depending on  how the shape of the pie  is

The charge for the t-shirt earlier than the cut price of 25 percent is $20.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, the 25% discount, the price of a t-shirt was 15$.

Since, After 25% discount price of t-shirt = 15

Thus

Original price of t-shirt = 15 * 100/75

Original price of t-shirt = 20

Therefore, the price before the discount of 25 percent is $20.

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The domain of (f/g)(x) in interval notation is [-3, 6].

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

From the graph,

f(x) has x values from x = -1 to x = 6

g(x) has x values from x = -3 to x = 5

The function f(x) is f(x) = mx + c

Find two coordinates from the graph of f(x).

= (-1, 3) and (6, 4)

m = (4 - 3) / (6 + 1) = 1/7

Now,

3 = (1/7) x -1 + c

3 = -1/7 + c
c = 3 + 1/7

c = 22/7

f(x) = (1/7)x + 22/7  _____(1)

The function g(x) is f(x) = mx + c

Find two coordinates from the graph of g(x).

= (-3, 2) and (5, 4)

m = (4 - 2) / (5 +3) = 2/8 = 1/4

Now,

2 = 1/4 x (-3) + c

2 = -3/4 + c
c = 2 + 3/4

c = 11/4

g(x) = (1/4)x + 11/4  _______(2)

Now,

From (1) and (2)

(f/g)(x)

= f(x)/g(x)

= ((1/7)x + 22/7) / ((1/4)x + 11/4)

The domain of f(x) and g(x) will include the domain of both f(x) and g(x).

So,

x = -1 to x = 6 and x = -3 to x = 5

This can be written as,

[-3, 6]

Thus,

The domain of (f/g)(x) is [-3, 6].

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∑ (-1)ⁿ xⁿ/n   is convergent for  x ∈ (−1,1].

Given the series ∑ (-1)ⁿ xⁿ/n

we can use the ratio test by evaluating:

n/(n+1) |x|

So we get two cases,

i) x = 1

∑ (-1)ⁿ xⁿ/n  = (-1)ⁿ/n which is the alternate harmonic series and is convergent.

ii) ∑ (-1)ⁿ xⁿ/n = ∑ (-1)ⁿ  (-1)ⁿ/n = ∑ 1/n which is the harmonic series and is divergent.

In conclusion the series is convergent for x ∈ ( -1, 1].

A power series' radius of convergence is equal to the diameter of the biggest disk at the series' convergence point. A non-negative real number or are both possible. When it is positive, the power series converges to the Taylor series of the analytical function absolutely and evenly on compact sets inside the open disk with radius equal to the radius of convergence.

The radius of convergence is the shortest or smallest of all the estimated distances from the center of the disk of convergence to each individual singularity of a function in the event of multiple singularities (singularities are those values of the argument for which the function is not defined).

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For given parametric curve the equations of both tangents at point where it crosses itself are: y = ± (√15x + 2√15)

The graph of parametric curve x = cos t + 2 cos 2t, y = sin t + 2 sin 2t (t ∈ [0, 2π]) is as shown below.

From the graph we can observe that, the curve crosses itself at (-2, 0).

Let x = -2

cos t + 2 cos 2t = -2,

and y = 0

sin t + 2 sin 2t = 0

sin t + 2 (2 sin(t) cos(t)) = 0

sin t + 4 sin t cos t = 0

sin t(1 + 4 cos t) = 0

sin(t) = 0   OR   1 + 4 cos(t) = 0

sin(t) = 0   OR   cos(t) = -1/4

From sin(t) = 0

⇒ t = 0 or t = π,

but for these values of t, cos t + 2 cos 2t = -2 is not true.

This means, the point (-2, 0) must corresponds to cos(t) = -1/4

[tex]\Rightarrow t=cos^{-1}(\frac{1}{4} )[/tex]

When cos(t) = -1/4,

sin(t) = [tex]\frac{\sqrt{15} }{4}[/tex]                ..............(by identity sin²(t) + cos²(t) = 1)

And

[tex]sin(2t) = 2sin(t)cos (t)\\sin(2t) = 2\times \frac{\sqrt{15} }{4} \times (\frac{-1}{4} )\\\\sin(2t) = -\frac{\sqrt{15} }{8}[/tex]

[tex]\\\\cos(2t)=2cos^2{t} - 1\\\\cos(2t)=2(\frac{-1}{4} )^2 - 1\\\\cos(2t)=\frac{1}{8}-1\\\\ cos(2t)=\frac{-7}{8}[/tex]

Now we find derivative of given parametric equations with respect to t.

for x = cos t + 2 cos 2t,

dx/dt = -sin(t) -4 sin(2t)

y = sin t + 2 sin 2t

dy/dt = cos(t) + 4 cos(2t)

Consider dy/dx

[tex]= \frac{\frac{dy}{dt} }{\frac{dx}{dt} }\\\\= \frac{cos(t) + 4 cos(2t) }{-sin(t) -4 sin(2t)}\\\\=\frac{\frac{-1}{4}+4~\frac{-7}{8} }{-\frac{\sqrt{15} }{4}-4~\frac{\sqrt{15} }{8} }\\\\=-\sqrt{15}[/tex]

This means, slope m = -√15

We have the point (−2,0)

Using equation of line y=mx+b the y-intercept would be,

0 = -√15 (−2) + b

b = -2√15

So, the equation for this tangent line :

y = -√15x - 2√15

And the equation of other tangent would be,

y = √15x + 2√15

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Answer:

  (x/9)² +(y/3)² = 1 . . . P = (x, y)

Step-by-step explanation:

You want the equation of the locus of a point P that is 3 cm from the x-axis end of a 12 cm rod whose ends are on the x- and y-axes.

Let the x- and y-intercepts of the rod ends be represented by 'a' and 'b', respectively. The fixed length of the rod tells us ...

  a² +b² = 12²

according to the Pythagorean theorem.

The location of point P is 3/12 = 1/4 of the way from the x-intercept to the y-intercept. Its coordinates in terms of 'a' and 'b' are ...

  P = 3/4(a, 0) +1/4(0, b) = (3a/4, b/4)

If we define the point P as having coordinates (x, y), then we have ...

  3a/4 = x   ⇒   a = 4/3x

  b/4 = y   ⇒   b = 4y

Using these values in the above relation between 'a' and 'b', we have ...

  (4/3x)² +(4y)² = 12²

We can divide by 12² to get the following equation of the ellipse that is the locus of P.

  (x/9)² +(y/3)² = 1 . . . . . . useful domain/range: 0≤x≤9; 0≤y≤3.

The ordered pairs which correctly lists all of the x-intercepts of the graphed function include the following: C. (1, 0), (2, 0), and (–3, 0).

In Mathematics, the x-intercept can be defined as the point at which the graph of a particular function crosses the x-coordinate (x-axis) and the value of "y" is equal to zero (0).

By critically observing the given graphed function (see attachment), the x-intercept is given by the following ordered pairs:

This ultimately implies that, this function would cross the x-coordinate (x-axis) at points (1, 0), (2, 0), and (-3, 0).

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The Third Angles Theorem states that if two angles of a triangle are equal, then the third angle must also be equal to the other two.

This theorem can also be stated as "the measure of the third angle of a triangle is equal to the sum of the measures of the two known angles." This theorem can help solve for missing angles in a triangle and can also be used to determine if the given triangle is right-angled, obtuse-angled, or acute-angled. Additionally, this theorem is related to the Triangle Inequality Theorem which states that the sum of any two sides of a triangle must be greater than the third side.

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Answer:

See below

Step-by-step explanation:

[tex]f(x)=|x-2|\\f'(x)=\frac{x-2}{|x-2|}\\f'(2)=\frac{2-2}{|2-2|}=\frac{0}{0}[/tex]

So, the function is not differentiable at x=2.

We can find the discount by taking the product between the price of the couch and the decimal form of the percentage, the discount on the couch is equal to $258.75

We know that for a couch whose price is $1,725, we apply a discount of the 15%.

Then we just need to find the 15% of $1,725, to do so, we need tu multiply the number by the decimal form of that percentage.

To get the decimal form, you need to take the quotient between the percentage and 100%, you will get:

15%/100% = 0.15

Then the discount is:

0.15*$1,725 = $258.75

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Numbers greater than 500 can be obtained using the digits 2345 is 30.

A number is an arithmetic value used for representing the quantity and used in making calculations. A written symbol like “3” which represents a number is known as a numeral. A number system is a writing system for denoting numbers using digits or symbols in a logical manner.

The following numbers can be formed using the given numbers that are greater than 500:

523, 532, 542, 543, 524, 534, 2345, 2435, 2354, 2453, 2543, 2534, 3245, 3254, 3425, 3452, 3542, 3524, 4235, 4253, 4325, 4352, 4523, 4532, 5234, 5243, 5432, 5423, 5342 and 5324.

Thus, Numbers greater than 500 can be obtained using the digits 2345 is 30.

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There are numbers greater than 500 can be obtained using the digits 2345 is 30

The combination method is defined as the way of selecting objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.

Here we have to find the numbers that are greater than 500 can be obtained using the digits 2345.

By using the given digits, we have created the following number that are greater that 500 as listed as follows:

=> 523, 532, 542, 543, 524, 534, 2345, 2435, 2354, 2453, 2543, 2534, 3245, 3254, 3425, 3452, 3542, 3524, 4235, 4253, 4325, 4352, 4523, 4532, 5234, 5243, 5432, 5423, 5342 and 5324.

Therefore, the total resulting number is 30.

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[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{3(ab^2)^2}{6a^3b^{-3}}\implies \cfrac{3}{6}\cdot \cfrac{(ab^2)^2}{a^3b^{-3}}\implies \cfrac{1}{2}\cdot \cfrac{(a^2b^4)}{a^3b^{-3}}\implies \cfrac{1}{2}\cdot \cfrac{b^4 b^3}{a^{-2}a^3} \\\\\\ \cfrac{1}{2}\cdot \cfrac{b^{4+3}}{a^{-2+3}}\implies \cfrac{1}{2}\cdot\cfrac{b^7}{a^1}\implies \cfrac{b^7}{2a}[/tex]

The integral, ∫ [ (9ˣ - eˣ )/3ˣ ] dx evaluate value is 3ˣ/ ln(3) - eˣ/3ˣ(1 - ln 3). So, the correct answer is option (c).

Integration is defined as the process of finding the area of the region under the curve. This is done by drawing as many small rectangles covering up the area and summing up all their areas. If d/dx(F(x) = f(x), then ∫ f(x) dx = F(x) + C, where C is integration constant and indefinite integrals. We have an integral, say , I = ∫ [ (9ˣ - eˣ )/3ˣ ] dx

and we have to determine its value.

I = ∫ [ (9ˣ - eˣ )/3ˣ ] dx

=> I = ∫ [ (9ˣ/3ˣ - eˣ/3ˣ ] dx

=> I = ∫ [ (3²ˣ/3ˣ - eˣ/3ˣ ] dx

=> I = ∫ [ (3²ˣ/3ˣ - eˣ/3ˣ ] dx

=> I = ∫ [ (3ˣ - eˣ/3ˣ ] dx

=> I = ∫ 3ˣ dx - ∫ eˣ3⁻ˣ dx

=> I = 3ˣ/ ln(3) - eˣ/3ˣ(1 - ln 3) + C

( since, ∫aˣ dx = aˣ/ln a)

where C --> integration constant

So, the required value is 3ˣ/ln(3)-eˣ/3ˣ(1 - ln 3).

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Complete question:

Find integral ∫ [ (9ˣ - eˣ )/3ˣ ] dx .

a) 3ˣ - eˣ/(1 - ln 3) + C

b) 9ˣ/2ln3 - eˣ/(3ˣ ln 3) + C

c) 3ˣ/ln3 - eˣ/3ˣ(1 - ln 3) + C

d) 3ˣ/ln3 - eˣ/3ˣ + C

The solution to the system of equations for this problem is given as follows:

a. (1, -1, -4).

The system of equations for this problem is defined as follows:

The augmented matrix for the system is given as follows:

[tex]\left[\begin{array}{cccc}2&1&1&-3\\3&-5&3&-4\\5&-1&2&-2\end{array}\right][/tex]

To place in row-echelon form, first only the first row of the first column may have a diagonal different of zero, hence the transformation is given as follows:

Hence the matrix is given as follows:

[tex]\left[\begin{array}{cccc}2&1&1&-3\\0&-13&3&1\\0&-7&-1&11\end{array}\right][/tex]

Now the element at the third row and second column must be of zero, hence the transformation is of:

R3 = 13R3 - 7R2

Thus the matrix is of:

[tex]\left[\begin{array}{cccc}2&1&1&-3\\0&-13&3&1\\0&0&-34&136\end{array}\right][/tex]

Thus the solution for z is given as follows:

-34z = 136

34z = -136

z = -136/34

z = -4.

The solution for y is given as follows:

-13y + 3z = 1.

13y = 3z - 1

13y = -13

y = -1.

The solution for x is given as follows:

2x + y + z = -3.

2x = -3 - y - z

2x = -3 + 1 + 4

2x = 2

x = 1.

Meaning that option a is correct.

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For the distance of 5 miles covered in 4 hours, we can write the unit rate as {r] = 1.25 miles/hour.

The rate at which one value changes with respect to per unit change in the other value is called the unit rate. Mathematically -

{ r } = y/x                                                          .... Eq { 1 }

Given is the distance of 5 miles covered in 4 hours.

We can write the unit rate as -

{r} = 5/4

{r} = 1.25 miles/hour

Therefore, for the distance of 5 miles covered in 4 hours, we can write the unit rate as {r] = 1.25 miles/hour.

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Geometric series is convergent if the |r|<1 where r is the common ratio.

Let Sn=∑ni=0(−3/4)i then

Sn=(−3/4)n+1−1(−3/4)−1

Now take n→∞ then

Sn→0−1(−3/4)−1=4/7

because |−3/4|<1 and so (−3/4)n→0. Now note that your sum is

lim ∑i=1n+1(−3)i−14i=lim 14∑i=1n+1(−3)i−14i−1=1/4.lim Sn=1/7.

Geometric series: A geometric series is the result of adding together geometric sequences indefinitely. Depending on the sequence given to us, such infinite sums can either be finite or infinite. A series is considered to be convergent if the partial sums gravitate to a certain value, also known as a limit. In contrast, a divergent series is one whose partial sums do not reach a limit. Divergent series frequently reach, reach, or avoid a particular number.

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The quantity of the surullitos left over is 7.

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 a chef makes 750 surulfitos and donates half of them to a soup kitchen. The rest are divided equally among 16 plates.

The leftover surulfitos are,

E =  750 / ( 2 x 16 )

E = 375 / 16

E = 23⁷/₁₆

The remainder is 7 so the leftover surullitos are 7.

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The wavelength of the given speed and frequency would be = 0.062m

Speed is defined as the distance a wave travels in a given amount of time, such that it is measured in meters per second.

The frequency of a wave is defined as the number of cycles that can be completed in a given time. This is measured in Hertz (Hz).

The wavelength is defined as the distance if a wave which can be measured in meters.

The formula for wave speed = v = fλ

Where v = Speed = 5.410x10⁴

f = 872khz = 872000hz

λ = ?

make λ the subject of formula;

λ = 5.410x10⁴/872000

λ = 54100/872000

λ = 0.062m

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When Zoey logged the grade level and instrument of every middle school student, she discovered that 28% of the eighth graders at the School of Rock play the guitar.

In mathematics, a ratio or number expressed as a fraction of 100 is called a percentage. Also occasionally used are the acronyms "pct.," "pct," and "pc." However, the percentage symbol "%" is widely used to represent it. The % quantity is dimensionally empty. Basically, percentages are fractions when the denominator is 100. A percent symbol (%) should be placed next to a number to indicate that it is a percentage. For instance, you score a 75% on a test if you properly answer 75 out of 100 questions (75/100). When calculating percentages, multiply the result by 100 after dividing the amount by the total. By multiplying (value/total) by 100%, the percentage is determined.

given

from the table

number of 8th grader = 64

8th grader playing guitar = 18

% of 8th grader playing grader = 18/64*100

= 0.28125*100

= 28.125%

When Zoey logged the grade level and instrument of every middle school student, she discovered that 28% of the eighth graders at the School of Rock play the guitar.

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The number of coins of nickels and dimes will be 16 and 2, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Jacob has $1 worth of nickels and dimes. He has a total of 18 nickels and dimes altogether.

Let 'x' be the number of nickels and 'y' be the number of dimes. Then the equations are given as,

x + y = 18                          ....1

0.05x + 0.10y = 1             ....2

From equations 1 and 2, then we have

0.05(18 - y) + 0.10y = 1

0.90 - 0.05y + 0.10y = 1

0.05y = 0.10

y = 2

Then the value of the variable 'x' is given as,

x + 2 = 18

x = 16

The number of coins of nickels and dimes will be 16 and 2, respectively.

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312%, 312' 4', 13, 9, 4.2 x 10-2. This is a decending order.

What is meant by decending?

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The cot(θ) is positive in the first and the third quadrants and negative in the second and the fourth quadrants

From the question, we have the following parameters that can be used in our computation:

Function: cot(θ)

Mathematically, this can be represented as

cot(θ) = 1/tan(θ)

This is the same for the cotangent function

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Answer:

i think it's true am a 6 grader i really try

Step-by-step explanation:

Answer:

y=mx+c

Step-by-step explanation:

Waiter is given $10.52 and total bill including tax and tip = $67.33

Tip is the amount of money given by the customer himself so as to express the gratitude towards the hospitality from a particular service sector.

before tax paying cost for food = $52.60

sales tax rate is 8%

so, the amount of tax = $52.60 × 8/100 = $ 4.21

If 20% tip is given by customer, then the amount of tip =$52.60 × 20/100

amount of tip = $10.52

Waiter is given $ 10.52.

total bill including tax and tip = $52.60 + $4.21 + $10.52

                                               = $67.33

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