HELP! Recursive and explicit growth problem

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The shaded area under the standard normal curve is 2.58%.

According to z-score table,

Area for < 2.23 = 0.9871

Area for >2.23 = 1 - 0.9871

                        = 0.0129

Area for < 2.23 = 0.0129

Total area = 0.0129 + 0.0129

                 = 0.0258

Area percent = 0.0258*100

                      = 2.58%

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The rate at which the surface area is changing when r = 6cm is 96[tex]cm^{2}[/tex]/min.

The surface area of a sphere with radius r is given by4π[tex]r^{2}[/tex]

Given;

S = surface area at time t,  and r = radius at time t

radius of a spherical ball is increasing at a rate of 2 cm/min

radius: 6cm

Area of a sphere is A = 4π[tex]r^{2}[/tex]

Step 1: Differentiate area of a spherical ball

A = 4π[tex]r^{2}[/tex]

[tex]\frac{dA}{dt}[/tex] =[tex]\frac{d}{dt}[/tex](4π[tex]r^{2}[/tex])

=4π [tex]\frac{d}{dt}[/tex]([tex]r^{2}[/tex])

=4π2r [tex]\frac{dr}{dt}[/tex]

[tex]\frac{dA}{dt}[/tex] = 8πr

since we have that dr/dt = 2 cm/min. Thus, the radius of the ball is 6cm, we have;

[tex]\frac{dA}{dt}[/tex]= 8π(6)(2) =96π

So, the rate at which the surface area is changing when r = 6cm is 96[tex]cm^{2}[/tex]/min.

Note that measuring area unit is cm2/min

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Step-by-step explanation:

4t - 7 + 83 = 180

4t + 76 = 180

4t = 104

t = 26

If we start with the parent quadratic function, then the transformation is:

g(x) =  (x - 17)^2 + 4

The definitions of translations are:

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N).

If N is positive, the shift is to the left.If N is negative, the shift is to the right.

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N.

If N is positive, the shift is upwards.If N is negative, the shift is downwards.

Then if the parent function is:

f(x) = x^2

The translation of 17 units to the right and 4 units up is:

g(x) = f(x - 17) + 4 = (x - 17)^2 + 4

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The observation of the graphing speed versus time is given below.

The rate at which the speed is changing is known as acceleration.

From the graph, the line segment OA and DE have linear acceleration which increases the velocity.

Similarly, from the graph, the line segment BC and EF have linear deacceleration which decreases the velocity.

From the graph, line segment AB has constant acceleration which increases the velocity.

And from the graph, the line segment CD has zero acceleration which makes the velocity to be constant.

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Total Water Used by a standard flush in a week i.e. 7 days is 22.4 gallons.

What is Multiplication?

In mathematics, multiplying implies adding equal groups. The number of items in the group grows as we multiply.

Solution:

Given that,

The standard toilet uses 1.6 gallons of water per flush

Also, it is flushed twice a day

To Find, Total water used in a week i.e. 7 days

Since, flush uses 1.6 gallons water per flush

Total water used in a day is 2*1.6 = 3.2 gallons

This implies,

Total water used in 7 days = 7 * 3.2 = 22.4 gallons

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The differentiation of the given function is 12[tex]x^3[/tex](5[tex]x^2[/tex] +2).

In the given question we have to differentiate the given function with respect to x.

The given function is f(x) = [tex]2x^4(5x^2+3)[/tex]

Before differentiating the function we first simplify the given expression.

To simplify the expression we multiply the 2x^4 to each term under the bracket.

Now the function;

f(x) = [tex]2x^4\cdot5x^2+3\cdot2x^4[/tex]

As we know that if the base is same en power get added.

f(x) = [tex]10x^{4+2}+6x^4[/tex]

f(x) = [tex]10x^{6}+6x^4[/tex]

Now differentiating the function with respect to x.

f'(x) = d/dx([tex]10x^{6}+6x^4[/tex])

f'(x) = 10d/dx([tex]x^6[/tex]) + 6d/dx([tex]x^4[/tex])

As we know that d/dx of x^n =nx^(n-1). So

f'(x) = 10∙6 [tex]x^5[/tex] + 6∙4 [tex]x^3[/tex]

f'(x) = 60[tex]x^5[/tex]+24[tex]x^3[/tex]

Now taking 12x^3 common

f'(x) = 12[tex]x^3[/tex](5[tex]x^2[/tex] +2)

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Answer:

y=-2x-2

Step-by-step explanation:

If the endpoints of the line segment are (7,4) and (-9,-4), that means that the slope will be:

[tex]\frac{-4-4}{-9-7}[/tex] = [tex]\frac{-8}{-16}[/tex]=[tex]\frac{1}{2}[/tex]. For the perpendicular bisector to be perpendicular to the line, it must have a perpendicular slope, which will be the negative reciprocal of [tex]\frac{1}{2}[/tex], which is -[tex]2[/tex]. The perpendicular bisector must also go through the midpoint of the segment, which is (-1, 0) because -1 is the average of 7 and -9 and 0 is the average of 4 and -4.

Now we find the equation!

y=mx+b. Plug in -[tex]2[/tex]     as the "m", or slope:

y=-[tex]2[/tex]x+b

Now, plug in the point (-1, 0):

0=-[tex]2[/tex]*-1+b

0=[tex]2[/tex]+b

b=-[tex]2[/tex]

So, we have m=-[tex]2[/tex] and b=-[tex]2[/tex] and we can form our equation!

y=-[tex]2[/tex]x-[tex]2[/tex]

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The Xavier is not getting better mileage with his new car .

In the question ,

it is given that

distance travelled by Xavier's new car in 25 gallons = 528 miles

the mileage can be calculated using the formula = (distance travelled)/( gallons of fuel used) .

So , mileage of the new car = 528/25 = 21.12 miles per gallon ,

the milage of Xavier's former car = 20.28 miles per gallon .

From the above data , we can see that the mileage of former car is greater than new car .

Therefore , The Xavier is not getting better mileage with his new car .

The given question is incomplete , the complete question is

Xavier's new car uses 25 gallons for 528 miles , His former car was able to travel 20.28 miles per gallon. Is Xavier getting better gas mileage in his new car?

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Answer:

Step-by-step explanation:

The answer is [14, 42].

The number 14 is even.

7 x 2 = 14

An even number, 42.

7 x 6 = 42

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The number of Students going on the trip is 375.

In the question,

It is given that:

There are 125 students in Grade 3.

There are 125 students in Grade 4.

There are 125 students in Grade 5.

So, Total number of students going on trip = Number of students in Grade 3 + Number of students in Grade 4 + Number of students in Grade 5

= 125 + 125 + 125 = 375.

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The 2.51 × 10⁻⁵ Watts/cm² sound intensity of the sound from the rocket engine has a decibel level of 114 dB

A decibel is a unit to measure the relative loudness of sound or to express the ratio electrical or acoustic power.

The intensity of the sound of the rocket engine = 2.51 × 10⁻⁵ Watts/cm²

Converting the unit of the sound intensity to Watts/m² gives;

1 cm² = 0.0001 m²

10,000 cm² = 1 m²

2.51 × 10⁻⁵ Watts/cm² = 10000 × 2.51 × 10⁻⁵ Watts/m² = 0.251 Watts/m²

The equation for the decibel from the power of sound is presented as follows;

[tex]\beta\ (dB)=10\cdot log_{10}\left(\dfrac{I}{I_0} \right)[/tex]

Where;

I₀ = 10⁻¹² W/m²

Which gives;

[tex]\beta\ (dB)=10\cdot log_{10}\left(\dfrac{0.251 }{10^{-12}} \right) = 113.9967373215 \approx 114[/tex]

The number of decibels for the power of the sound given to the nearest decibel by the rocket engine is 114 decibels

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The number of months required to pay off the loan will be 15.

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 student requests a loan for $1178.80. The monthly payment of the loan is $42.10. So far, the student has paid $547.30.

The number of the months will be calculated as,

N = ( 1178.8 - 547.30) / 42.10

N = 631.5 / 42.10

N = 15

Therefore, the number of months required to pay off the loan will be 15.

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Using the given exponential function, it is found that:

a) The number of mosquitoes in the container after 5 days is of: 346.

b) The number of days until the container reaches the maximum capacity is of: 10 days.

The exponential function that models this problem is presented as follows:

P(t) = 24(4)^(0.385t).

Hence, after five days, the number of mosquitoes is of:

P(5) = 24(4)^(0.385 x 5) = 346 mosquitoes.

The number of days that it takes for the container to reach it's maximum capacity of 5000 is obtained solving the exponential function with logarithms as follows:

[tex]5000 = 24(4)^{0.385t}[/tex]

[tex](4)^{0.385t} = \frac{5000}{24}[/tex]

[tex](4)^{0.385t} = 208.3[/tex]

[tex]\log{(4)^{0.385t}} = \log{208.3}[/tex]

Applying the power property of logarithms, we have that:

[tex]0.385t\log{4} = \log{208.3}[/tex]

[tex]t = \frac{\log{208.3}}{0.385\log{4}}[/tex]

t = 10 days.

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The frequency distribution based on the information given is illustrated below.

What is the frequency distribution of table?

A frequency distribution table is the chart that summarizes all the data under two columns - variables/categories, and their frequency.

It should be noted that the distribution table has two or three columns and the first column lists all the outcomes as individual values or in the form of class intervals, depending upon the size of the data set.

Given the above information the frequency distribution table is:

Cost of living[tex]\begin{table}[]\begin{tabular}{ll}Cost of living & Number of States \\85.0 - 94.9 & 9 \\95.0 - 104.9 & 5 \\105.0 - 114.9 & 0 \\115.0 - 124.9 & 2 \\125.0 - 134.9 & 2 \\135.0 - 144.9 & 1 \\145.0 = 154.9 & 1 \end{tabular}\end{table}[/tex]   Number of states

85.0 - 94.9             9

95.0 - 104.9         5

105.0 - 114.9         0

115.0 - 124.9         2

125.0 - 134.9         2

135.0 - 144.9         1

145.0 - 154.9         1

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Answer:

yes yes ...................

Answer:

C: 108 cubic inches

Step-by-step explanation:

This problem is simply asking us to calculate volume, and in a rectangular shape can be calculate as: length * width * height

Since we know that the base is 4 inches by 9 inches, we already have the length and width.

We're also given that the depth, which in this case is our height, as 3 inches.

So we multiply these three numbers: [tex]4 \text{ in} * 9 \text{ in} * 3\text{ in} = 108\text{ in}^3[/tex]

So our answer is 108 cubic inches

In the equation 2[(4m * 3.5) / 400] = 171.5, the value of m is 2450

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.

In the equation given;

2[(4m * 3.5) / 400] = 171.5

To solve for m, we have to expand the bracket and make m the subject of formula.

2[(4m * 3.5) / 400] = 171.5

2[14m/400] = 171.5

28m / 400 = 171.5

28m = 400 * 171.5

28m = 68600

m = 68600 / 28

m = 2450

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Earned income is said to be $35,000, Base tax amount at that level is $4386, The amount over $31850 is  $3150, Line 3 is multiplied by 25% is $787.50, The sum of lines 2 and 4 is $5173.50 and This amount divided by 12 is $431.13.

Two or more expressions with an Equal sign is called as Equation.

Given,

The given Federal Income Tax Table Single: Over But not over The tax is $0 $7,825 10% of the amount over $0 $7,825 $31,850 $788 + 15% of the amount over $7,825 $31,850 $77,100 $4,386 + 25% of the amount over $31,850 $77,100 $160,850 $15,699 + 28% of the amount over $77,100 $160,850 $349,700 $39,149 + 33% of the amount over $160,850 $349,700 And Over $101,469 + 35% of the amount over $349,700

Earned income is said to be $35,000.

Base tax amount at that level is $4386.

The amount over $31850 is $35000-31850 = $3150

Line 3 is multiplied by 25%: $3150×0.25 = $787.50

The sum of lines 2 and 4 is $4386 +787.50 = $5173.50

This amount divided by 12 is ... $5173.50/12 ≈ $431.13

Hence, Earned income is said to be $35,000, Base tax amount at that level is $4386, The amount over $31850 is  $3150, Line 3 is multiplied by 25% is $787.50, The sum of lines 2 and 4 is $5173.50 and This amount divided by 12 is $431.13.

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Answer:

a) about 190 acres

b) around 240 acres

c) exponential decay because the amount of land available is decreasing at an increasingly rapid rate over time.

The answer is option (a)

Hope this answer helps you

The distance (in ft) that the car will travel in the first 10 seconds is 16.8 feet.

Speed describes how accelerated something or somebody is moving. If you know the distance traveled and the time it took, you can calculate the average speed of an object.

The speed formula is speed = distance/time.

We have been given certain vehicles that can accelerate from a standing start to a speed of v(t) = −0.24t² + 12t feet per second after t seconds (for 0 ≤ t < 30).

Then the distance that it will travel from its starting point in the first t seconds is;

[tex]\int\limits^{30}_b {v(t) } \, dx \\\\\\\int\limits^{30}_b {-0.24t^2 + 12t } \, dt \\\\\\\int\limits^{30}_b {-0.48t + 12} \, dt \\\\-0.48(30) + 12\\\\14.4 + 12 = 26.4[/tex]

At zero it will be 12 feet.

b. the distance (in ft) that the car will travel in the first 10 seconds.

-0.48(10) + 12 = 16.8 feet.

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The correct option regarding whether the linear functions are parallel is given as follows:

C. The slope of f(x) is of 2 and of g(x) is of 5. Since they are different, the lines are not parallel.

First, we start with the definition of a linear function, in slope-intercept format, which is given as follows:

y = mx + b.

In which the coefficients are given as follows:

If two linear functions are parallel, they have the same slope.

The slope is given by the change in y when x is increased by one, hence the slopes of the functions are given as follows:

Due to the different slopes, the two lines are not parallel, hence option C is correct.

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The solution is

a) The ascending order is 32 % < 2 1/2 < √9 < π

b) The ascending order is -4 < -3.4 < -3 < -2 1/2 < π

c) The ascending order is -5/8 < 0 < 250% < 3.4

What is Ascending Order?

When numbers are arranged in ascending order, they are done so from least to largest. We must first compare the numbers before we may arrange them in any order. Compare first, then order. Numbers arranged in ascending order: Determine how many digits each number has.

Given data ,

A)

32 % , π , 2 1/2 , √9

32 % = 32 / 100

        = 0.32

π = 3.14

2 1/2 = 2.5

√9 = 3

So , arranging the numbers in ascending order we get ,

0.32 < 2.5 < 3 < 3.14

Hence , the ascending order is 32 % < 2 1/2 < √9 < π

B)

-3.4 , -4 , -3 , -2 1/2 , π  

Hence , the ascending order is -4 < -3.4 < -3 < -2 1/2 < π

C)    

250 % , 3.4 , -5/8 , 0

250 % = 2.5

-5/8 = -0.625

So , arranging the numbers in ascending order we get

-0.625 < 0 < 2.5 < 3.4

Hence , the ascending order is -5/8 < 0 < 250% < 3.4

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Answer:

k=44

Step-by-step explanation:

1 + 2 + 3 + 4......+ k = 990

Arithmetic sequence  with  d = 1    a1 = 1

1   +   1+ 1    +   1 +2 ...... 1+ (k-1) = 990    

ak = a1 + (k-1)     <====formula for sequence

Sum of a sequence formula =   Sk = k ( a1+ak)/2

990 = k ( 1 + (1 + k-1) /2

1980 = k^2 + k

 k^2 + k - 1980 = 0       Use quadratic formula   a = 1   b = 1   c = - 1980

       to find k = 44