If f(x)f(x) is an exponential function where f(4)=21f(4)=21 and f(4.5)=47f(4.5)=47, then find the value of f(7.5)f(7.5), to the nearest hundredth.

Answer:

  (c)  25/4

Step-by-step explanation:

A perfect square trinomial is obtained by "completing the square." The constant in a perfect square trinomial is the square of half the x-coefficient.

A "perfect square trinomial" is the square of a binomial.

  (x +a)² = x² +2ax +a²

Of note here is that the constant (a²) is the square of half of the x-term coefficient:

  ((2a)/2)² = a²

The given expression (x² +5x) has an x-term coefficient of 5. The square of half that is ...

  (5/2)² = 25/4

The constant that must be added to make x² +5x into a perfect square trinomial is 25/4.

  (x² +5x) +25/4 = x² +5x +25/4 = (x +5/2)²

Answer:

(2, 60°)

Step-by-step explanation:

A point in polar form (a,b) is represented by a radius and an angle (r, ϴ). To convert, use the formula r² = a² + b² to get r, and  [tex]tan^{-1}[/tex](b/a) = ϴ

[tex]r = \sqrt{1^{2} + \sqrt{3} ^{2} }[/tex]

[tex]r = \sqrt{1+3}[/tex]

[tex]r = \sqrt{4}[/tex]

= 2

[tex]tan^{-1}[/tex]([tex]\sqrt{3}[/tex]/1) = ϴ

= 60°

The average speed can be shown as (A + B)/50 miles per minute, where the distance between town A and his home is A miles, and that from his home to town b is B miles, and the total time is 50 minutes.

The average speed of any object is given as the ratio of the total distance traveled by the body, to the total time taken.

Average Speed = Total Distance/Total Time.

In the question, we are informed that the person drove from town a to his home and then to town b, with the total journey time as 50 minutes.

We are asked to find the average speed of the person.

We assume the distance from town a to his home to be A miles.

We assume the distance from his home to town b to be B miles.

Thus, the total distance traveled = A + B miles.

The total time taken by the person is given to be 50 minutes.

We know that the average speed of any object is given as the ratio of the total distance traveled by the body, to the total time taken.

Thus, the average speed of the person can be shown as:

Average Speed = (A + B)/50 miles per minute.

Thus, the average speed can be shown as (A + B)/50 miles per minute, where the distance between town A and his home is A miles, and that from his home to town b is B miles, and the total time is 50 minutes.

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Answer:

x = 20 units

Step-by-step explanation:

See attached.

Answer:

[tex]x = 94[/tex]

Step-by-step explanation:

To find the value of [tex]x[/tex], we have to first find the lengths of the sides of the squares and add them.

The formula for area of a square is as follows:

[tex]{area = (length \space\ of \space\ side)^2}[/tex]

This means the length of a side of a square can be found by:

[tex]\boxed {length \space\ of \space\ side = \sqrt{area}}[/tex]

Now we can find the lengths of sides of each of the squares:
• Length of side of larger square = [tex]\sqrt{8100}[/tex]

                                                       = 90

• Length of side of smaller square = [tex]\sqrt{16}[/tex]

                                                          = 4

Next we can just add the lengths of the sides to get the value of [tex]x[/tex] :

[tex]x = 90 + 4[/tex]

⇒ [tex]x \bf = 94[/tex]

Answer:

[tex]a=22, b=11\sqrt{3}[/tex]

Step-by-step explanation:

Given a 30-60-90 triangle, the shortest side is always opposite of the smallest angle, in this case 11 is opposite the 30° angle. The largest side of a 30-60-90 triangle will always be twice the smallest, giving [tex]a[/tex] a measure of [tex]22[/tex]. To get the side across the 60° angle we multiply the smallest side by the square root of 3. Meaning [tex]b=11\sqrt{3}[/tex]

The correct option regarding whether the requirements for a hypothesis test are satisfied is:

D. The conditions are satisfied. The samples are random, and each sample has at least 5 successes and 5 failures.

There are two conditions:

These two conditions are satisfied for this problem, hence, researching this problem on the internet, option D is correct.

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Answer:

[tex]y-1=5(x-8)[/tex]

Step-by-step explanation:

Well first let's find the derivative in using the power rule

h'(t) = (-4.9)t + 157

h'(t) = -9.8t + 157

we can see from the image above that the maximum height is 1452.602 so that is the answer to the second question.

h'(1452.602) = -9.8(1452.602) + 157

h' = 14,078.500

Answer:

42

Step-by-step explanation:

-14 1/9 is about -14.

-2 9/10 is about -3.

Multiplying these, we get (-14)(-3)=42.

Answer:

x = 8

Step-by-step explanation:

[tex]2logx=log64\\logx^2=log64[/tex]

now that both sides has log, you can remove them and leave it as:

[tex]x^{2} =64\\[/tex]

take the square root of both sides:

[tex]x = [8, -8]\\x = 8[/tex]

logarithmic equations can't have negative solutions, plus -8 isn't an option

i hope this helped!

The 680 tons of fuel needed to cover the next 1790 miles distance.

According to the statement

We have given that the ship covered a 1651 miles distance at 20 knots by a 580 tons of fuel oil.

And distance remaining to next port is 1790 miles and speed increases to 25 knots.

And we have to find that how much fuel used to reach that port.

So, Distance covered = 1651 mile

fuel used = 580 tons

distance covered with 1 tons fuel = 1651/580

distance covered with 1 tons fuel = 2.85 mile at a speed of 20 knots.

so, The fuel consumption for 1790 mile is = 1790/2.85

The fuel consumption for 1790 mile is = 628 tons of fuel needed.

So, The 680 tons of fuel needed to cover the next 1790 miles distance.

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The height of the cylinder is (a) 8.75 meters

The given parameters are:

Volume = 315[tex]\pi[/tex]

Radius, r = 6

The volume of a cylinder is:

[tex]V = \pi r^2 h[/tex]

So, we have:

[tex]315\pi = \pi * 6^2 * h[/tex]

Divide both sides by 36[tex]\pi[/tex]

h = 8.75

Hence, the height of the cylinder is (a) 8.75 meters

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Answer:

base = 12 cm , altitude = 16 cm

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] ba ( b is the base and a the altitude )

here a = b + 4 , then

[tex]\frac{1}{2}[/tex] b(b + 4) = 96 ( multiply both sides by 2 to clear the fraction )

b(b + 4) = 192

b² + 4b = 192 ( subtract 192 from both sides )

b² + 4b - 192 = 0 ← in standard quadratic form

(b + 16)(b - 12) = 0 ← in factored form

equate each factor to zero and solve for b

b + 16 = 0 ⇒ b = - 16

b - 12 = 0 ⇒ b = 12

however, b > 0 then b = 12

so base = 12 cm and altitude = b + 4 = 12 + 4 = 16 cm

Answer:

base = 12 cm

Altitude = 16 cm

Step-by-step explanation:

        [tex]\sf \boxed{Area \ of \ triangle = \dfrac{1}{2}*base*height}[/tex]

base = x cm

altitude or height = (x + 4) cm

[tex]\sf \dfrac{1}{2}*x*(x+4) = 96\\\\[/tex]

x * (x + 4) = 96*2

x*x + x*4 = 192

x² + 4x   = 192

x² + 4x - 192 = 0

Sum = 4

Product = -192

Factors =  (-12) , 16

When we add (-12) & 16, we get 4. When we multiply (-12) & 16, we get (-192).

Rewrite the middle term using the factors.

x² + 16x - 12x - 192 = 0

x(x + 16) -12(x + 16) = 0

(x + 16)(x - 12) = 0

x - 12 = 0     or x + 16 = 0

x = 12             or x = -16

Ignore x = -16 as measurements won't be in negative value.

x = 12

Base = 12 cm

Altitude = 12 + 4 = 16 cm

Answer:

4.8

Step-by-step explanation:

60 percent of 8 is 4.8

I hope this helps!

Answer:

Step-by-step explanation:

here is a solution and verify

[tex]\large\displaystyle\text{$\begin{gathered}\sf \left(\frac{4x}{y}\right)^{2} \end{gathered}$}[/tex]

To raise 4x/y to a power, raise the numerator and denominator to the power, and then divide.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{(4x)^{2} }{y^{2} } \end{gathered}$}[/tex]

Expand (4x)².

[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{4^{2} x^{2} }{y^{2} } \end{gathered}$}[/tex]

Calculates 4 to the power of 2 and gets 16.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \frac{16x^{2} }{y^{2} } \end{gathered}$} }[/tex]

The 98% confidence interval for the average amount spent by 10 to 11-year-olds on a trip to the mall is 23.36 ± 2.933.

The confidence interval for a given level of percentage is given by

C. I = μ ± Z(σ/√n)

Where,

μ - mean, σ - standard deviation, n - sample size, and z - critical value.

The critical value is calculated by

step 1: 100% - (the confidence level)

step 2: Converting the step 1 result into decimal value

step 3: dividing the step 2 result by 2

This is indicated by α/2. So, from the normal distribution table, the z-value at α/2 is said to be the required critical value and denoted by Z_(α/2) or Z.

It is given that,

A survey of several 10 to 11-year-olds recorded the following amounts spent on a trip to the mall: $18.31,$25.09,$26.96,$26.54,$21.84,$21.46

Sample size n = 6

Step 1: Finding the mean for the given amounts of the survey:

Mean μ = (18.31 + 25.09 + 26.96 + 26.54 + 21.84 + 21.46)/6

             = 23.36

Step 2: Finding the standard deviation:

Standard deviation σ = √summation(x - mean)²/n

On calculating, we get σ = 3.09

Step 3: Finding the critical value:

It is given that the confidence level is 98%

So, (100% - 98%) = 2%

Converting into decimal gives 0.02

So, α/2 = 0.02/2 = 0.01

Thus, at 0.01, the critical value Z = 2.326

Step 4: Constructing the confidence interval:

C.I = 23.36 ± (2.326) × (3.09/√6)

    = 23.36 ± (2.326 × 1.261)

    = 23.36 ± 2.933

So, the lower bound = 23.36 - 2.933 = 20.427

the upper bound = 23.36 + 2.933 =26.293

Therefore, the 98% confidence interval lies from 20.427 to 26.293.

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The value of w(u(4)) is 73.

u( x ) = - 2*x + 2

w( x ) = 2*x^2 + 1

w( u( x ) ) = w( - 2*x + 2  )

⇒ w( u( x ) ) = 2*( - 2*x + 2  )^2 + 1

⇒ w( u( x ) ) = 2*[ 2^2 + ( 2*x )^2 - 2*2*( 2*x ) ] + 1

⇒ w( u( x ) ) = 2*[ 4 + 4*x^2 - 8*x ] + 1

⇒ w( u( x ) ) = 8 + 8*x^2 - 16*x + 1

⇒ w( u( x ) ) = 8*x^2 - 16*x + 9

⇒ w( u( 4 ) ) = 8*4^2 - 16*4 + 9

⇒ w( u( 4 ) ) = 8*16 - 16*4 + 9

⇒ w( u( 4 ) ) = 128 - 64 + 9

⇒ w( u( 4 ) ) = 73

In mathematics, a feature from a set X to a fixed Y assigns to each detail of X exactly one detail of Y. The set X is called the domain of the function and the set Y is referred to as the codomain of the function. features were firstly the idealization of how various quantity relies upon any other quantity.

These elementary functions include

A function is defined as a relation between a set of inputs having one output each. In simple phrases, a function is a courting among inputs wherein every entry is associated with exactly one output. every function has a site and codomain or range. A characteristic is normally denoted through f(x) in which x is the input.

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Lines a and b are parallel based on the Converse of Same-Side Interior Angles Theorem,

The Converse of Same-Side Interior Angles Theorem states that, if the sum of two interior angles on same side of a transversal equals 180 degrees, then the lines they lie on are parallel to each other.

Since  M<7 + m<11 = 180, lines a and b are parallel based on the Converse of Same-Side Interior Angles Theorem,

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The ratio of its width to its length is; 5 :9.

The ratio of its length to its perimeter is; 9: 28.

1). From the task content, the land measures 4.5 km long and 2.5 km wide. Hence, the ratios is; 2.5: 4.5.

Therefore, we have; 5: 9 by expression as whole number ratios.

2) Since the perimeter of the rectangle is; 2(2.5+4.5) = 14.

The ratio of length to perimeter expressed simply is therefore; 9: 28.

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The standard equation for the circle is (x - 1 ) ^2 + (y + 3)^2 = 2 ^2

A circle is a closed curve that is drawn from a fixed point called the center in which all points on the curve are the same distance from the center of the center. The equation of a circle with center (h, k) and radius r is given by:

(x-h)^2 + (y-k)^2 = r^2

This is the standard form of the equation. So if we know the coordinates of the center of the circle and also its radius, we can easily find its equation.

Consider any point P(x, y) on the circle. Let "a" be the radius of the circle which is equal to OP.

We know that the distance between the point (x, y) and the origin (0,0) can be found using the distance formula which is equal to -

√[x^2+y^2]= a

Therefore the equation of a circle with center as origin is,

x^2+y^2= a^2

Where "a" is the radius of the circle.

An alternative method

Let's derive another way. Assume that (x,y) is a point on the circle and the center of the circle is at the origin (0,0). Now, if we draw a perpendicular from the point (x,y) to the x-axis, we get a right triangle, where the radius of the circle is the hypotenuse. The base of the triangle is the distance along the x-axis and the height is the distance along the y-axis. Applying the Pythagorean theorem here, we therefore obtain:

x^2+y^2 = radius^2

We need to find the standard equation for the circle with center (1,-3) that passes through the point (2,2)

Standard equation for circle is

(x-h)^2 + (y-k)^2 = r^2................(1)

Here h = 1 , k = -3 and r = 2

put this value of h, k and r in equation (1), we get

(x - 1 ) ^2 + (y + 3)^2 = 2^2

Hence the standard equation of the circle is

(x - 1 ) ^2 + (y + 3)^2 = 2 ^2

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Answer:

Step-by-step explanation:

Solution :  

hello :

note :

Use the point-slope formula.

y - y_1 = m(x - x_1)   when : x_1= -1      y_1= 5  

     m= the slope is : (YC - YA)/(XC -XA)

(-1-2)/(0-3) = -3/-3 =1

( parallel to AC means same slope)

an equation in the point-slope form is : y -5 = 1(x+1)

y=x+6

The expressions that represent the slope of a tangent to the curve [tex]y = \frac{1}{x+1}[/tex] are [tex]m = \lim_{h \to 0}\frac{\frac{1}{x + h + 1} - \frac{1}{x + 1} }{h}[/tex] and [tex]m = -\frac{1}{(x + 1)^{2}}[/tex], respectively.

The slope at any point of the function can be found by definition of derivative following algebraic handling:

[tex]m = \lim_{h \to 0}\frac{\frac{1}{x + h + 1} - \frac{1}{x + 1} }{h}[/tex]

[tex]m = \lim_{h \to 0} \frac{\frac{x+1 - x - h - 1}{(x + h + 1)\cdot (x + 1)} }{h}[/tex]

[tex]m = -\lim_{h\to 0} \frac{1}{(x + h + 1)\cdot (x + 1)}[/tex]

[tex]m = -\frac{1}{(x + 1)^{2}}[/tex]

Thus, the expressions that represent the slope of a tangent to the curve [tex]y = \frac{1}{x+1}[/tex] are [tex]m = \lim_{h \to 0}\frac{\frac{1}{x + h + 1} - \frac{1}{x + 1} }{h}[/tex] and [tex]m = -\frac{1}{(x + 1)^{2}}[/tex], respectively.

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The slope intercept equation can be represented as follows:

y = 9 / 7 x + 1

y = 11 / 4 x - 8

y = 11 / 8 x + 6

The slope intercept equation can be represented as follows:

y = mx + b

where

Therefore,

The slope intercept equation can be represented as follows:

9x - 7y = - 7

7y = 9x + 7

y = 9 / 7 x + 1

11x - 4y = 32

4y = 11x - 32

y = 11 / 4 x - 8

11x - 8y = -48

8y = 11x + 48

y = 11 / 8 x + 6

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The radius of the cylinder exists 1.93mm.

Let V be the volume of the cylinder exists 200 mm³

r be the radius

h be the height exists 17

Volume of cylinder, V = π r²h

200 = π r² (17)

200 = 53.40707 r²

200 =  53.41 r²

simplifying the above equation, we get

r² = 200/53.41

r² = 3.74461 = 3.74

r² = 3.74

r = 1.933907961 = 1.93

Therefore, r = 19.3

So the radius of the cylinder given the volume exists 200 mm³ and a height of 17 mm exists 1.93 mm.

Therefore, the radius of the cylinder exists 1.93mm.

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Answer:

Step-by-step explanation:

sin(28) = 2184 / x

x= 2184/ sin(28) = 2184 / 0.4694 = 4652.75

4652.75 / 12  =  387.7 ft

ANSWER: 387.7ft

In the given case, The length of the zipline needed is approximately 96.7 feet.

To find the length of the zipline needed, we can use trigonometry. Let's start by drawing a sketch to visualize the problem. | | zipline | | | | | | | | | | John | Building 28°

John's location, with the angle of elevation labeled as 28°. John is 182 feet away from the base of the building, and he is 71.5 inches tall.

To find the length of the zipline, we can use the tangent function.

The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

In this case, the opposite side is John's height, and the adjacent side is the distance between John and the building. Using the tangent function, we have: tan(28°) = opposite / adjacent

We want to find the length of the zipline, which is the hypotenuse of the right triangle formed by John, the building, and the zipline. Let's call this length "x".

Therefore, we can rewrite the equation as: tan(28°) = 71.5 inches / 182 feet To solve for x, we need to convert the units so that they match.

Let's convert inches to feet: 71.5 inches = 71.5 inches * (1 foot / 12 inches) ≈ 5.96 feet (rounded to the nearest hundredth)

Now, let's solve for x: tan(28°) = 5.96 feet / 182 feet

To isolate x, we can multiply both sides by 182 feet: x ≈ tan(28°) * 182 feet Using a calculator, we find that tan(28°) ≈ 0.5317.

Multiplying this by 182 feet, we get: x ≈ 0.5317 * 182 feet ≈ 96.7 feet (rounded to the nearest tenth) .

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Her answer should look like y = x + 2, x ≤ 2

The complete question is added as an attachment

From the attached graph, we have the following points

(x, y) = (2, 4) and (0, 2)

See that the difference between the y and x values is 2 where y > x

So, we have

y - x = 2

Add x to both sides

y = x + 2

The highest value of x in the graph is 2.

So, we have

x ≤ 2

Hence, her answer should look like y = x + 2, x ≤ 2

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Answer:

6b-4b=a+3a

2b=4a

4a=2b

a=2b/4

a=b/2