i inserted a picture of the question, i can give you the answer to the previous question if it helps. C(t) = -0.30(t-12)^2 + 40

The inequalities which represent relationships between the number of doubles (x) and amount of gospels (y) are x + y ≤ 11,7x + 4y ≥ 56 and y ≥ 3.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given,

No more than 11

x + y ≤ 11

Total earning ≥ $56

7x + 4y ≥ 56

At least 3 gospels

y ≥ 3

Hence "The inequalities which represent relationships between the number of doubles (x) and amount of gospels (y) are x + y ≤ 11,7x + 4y ≥ 56 and y ≥ 3".

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By continuity of polynomial function, y = 50 - 3.5x is a continuous function.

What is a continuous function?

A function is said to be continuous if the graph of the function has no breakage or no discontinuity at any point

y = 50 - 3.5x is a polynomial function.

All polynomial functions are continuous function.

y = 50 - 3.5x is a continuous function.

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Answer:

[tex]3x - 6 = 9[/tex]

We need to subtract both expressions, then simplify it and make only one expression:

First, subtract both expressions:

Then:

Now, simplify like terms:

Therefore, the result expression is -11x+15y.

Answer:

-2/5

Step-by-step Explanation:

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

[tex]m = \frac{10 - ( - 2)}{ - 11 - 19} [/tex]

[tex]m = \frac{12}{ - 30} [/tex]

[tex]m = - \frac{2}{5} [/tex]

In this case you have a linear equation of the form:

y=mx+b

To graph a line we only need to specify two points of the line and then join them.

b the intercept is zero in this case, and the slope of your line is -1/2. Since the intercept is zero, this means that the line crosses the origin, so the point (0,0) is included in the line, to find other poin of the line we just have to replace a value of x and calculate the value of y, for example let's take x equals 2.

Now, we know that the line crosses the points (0,0) and (2,-1), let's graph them.

the The area of the triangle is 35.1

We can get the height of the triangle using Pythagorean theorem

a^2+b^2=c^2

the height is 7.8

the area of the triangle is 1/2 * base * height

1/2 * 9 *7.8 = 35.1

From the graph of miles driven and pricing, it can be observed that for 200 miles option A price is $100 and option B price is $70.

So option A cost more than option B.

Determine the difference between $100 and $70 to obtain how much option A cost more than option B.

So option A cost $30 more than option B.

From the graph, it can be observed that lines of option A and option B intersect each other at (50,40). So option A and option B cost same for 50 miles.

The value of x for the rhombus sides will be equal to 7 units.

A rhombus is a quadrilateral with four equal-length sides. The term equilateral quadrilateral refers to the fact that all of its sides are the same length. A quadrilateral is a four-sided polygon with four edges and four corners in geometry.

Given that there is a rhombus ABCD, and the sides are AB = 2x - 3, BC = 5y + 1, CD = 11, and AD = 20 - z.

The value of x will be calculated by equating the sides AB and CD

AB = CD

2x - 3 = 11

2x = 11 + 3

2x = 14

x = 7

Therefore, the value of x for the rhombus sides will be equal to 7 units.

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We solve as follows:

The 95% confidence interval for the standard deviation of the height of students at UH is given by; CI = (1.81, 4.03)

How to find the confidence interval for standard deviation?

The formula for the confidence interval for the standard deviation is given by the formula;

CI = √[(n - 1)s²/(χ²ₙ ₋ ₁, α/2)], √[(n - 1)s²/(χ²ₙ ₋ ₁, (1 - α)/2)]

We are given;

Sample size; n = 19

D F = n - 1 = 19 - 1 = 18

Standard Deviation; s = 3.2

Confidence Level; CL = 95% = 0.95

Significance level; α = 1 - 0.95 = 0.05

Thus, using Chi-square distribution table online we have;

χ²₁₃, ₀.₀₂₅  = 24.736

(χ²₁₃, ₀.₉₇₅) = 5.01

Now, the 95% confidence interval for the standard deviation of the height of students at UH is given by :-

CI = √[(18 * 3.2²/(24.736)], √[(18 * 3.2²/(5.01)]

CI = (1.81, 4.03)

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We are given the initial function to be

Page 5

Question 4

We are told to use the function above to estimate how long it will take for the amount in the body to be 175mg.

This simply translates to making A= 175 in the equation so that we will obtain

So we will make t the subject of the formula

To do so, we can follow the steps below

Step 1: Divide both sides by 550

Next, we will take the natural logarithm to both sides

Next, we will divide both sides by -0.316

Thus, the value of t = 3.6256 hours.

The sequence first term is a = 2112 and last term is b = 33.

The formula for the geometric mean is,

Determine the geometric mean of 2112 and 33.

So geometric sequence is 264.

Answer: 264

Answer:

16.57

Step-by-step explanation:

19.17 - 2.6 = 16.57

Answer:

0.11

Explanation:

First, find the total of the color frequency:

The Frequency with which it lands on Green = 5

Therefore, the probability that the next spin will land on the green:

The required probability is 0.11 (to the nearest hundredth).

The range of the jogger's heart rate is defined by the interval from the minimum value to the maximum value, where we can have values in the y-axis.

Looking at the graph, the minimum heart rate is 60 bpm, and the maximum is 110 bpm, and we can have any value inside this interval.

So the range is:

Okay, here we have this:

Considering that when two parallel lines are intersected by a transversal, corresponding angles have the same measure. In this case

To solve for the value of x in the length of a rectangle:

Area of a rectangle = length x width , If the area of a rectangle is less than 108 thus the value is greater than 108cm²

Hence the correct answer for the value of x > 4

The value of x is less than 4

What is an Area?

An object's Area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

According to the question,

Length = (2x+1) cm

Width = 12 cm

To solve , the Area of the rectangle = length x width i.e.

less than 108 cm^2

length x width = (2x+1) x 12 cm

Area < 108 cm^2

So,

(2x+1) x 12  < 108

2x+1 < 108/12

2x+1 < 9

2x < 8

x < 4

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Answer: 2(x-2)=6

Step-by-step explanation: when they say twice, so you make is times 2, then it said the difference of a number which would be a variable, or x, and 2, is 6, so one part is =6, next is the variable -2, so you can use x-2, then in order to multiply everything, you need to make parenthesis. So, it would be x-2=6, but you forgot the parathesis, so 2(x-2)=6

Answer:

BC=OB-OA

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

BC= -1-3/2--3

-4/5=BC

Apply the compound interest formula:

• A= P (1 + r/n)^nt

Where:

A = future value

P = Principal investment = $10,000

r = interest rate in decimal form = 7.5 /100 = 0.075

n= number of compounding periods per unit t = 1 (anually)

t= years = 20

Replacing:

A = 10,000 ( 1+ 0.075 )^20

The rate of change at point A on the graph below for the y-axis in relation to the x-axis is -0.5.

The term "rate of change" (ROC) describes the rate at which something changes over time.

Thus, it is not the number of individual changes themselves but rather the acceleration or deceleration of changes (i.e., the rate).

The rate of change is a tool used in finance to comprehend price returns and spot trend momentum.

Other instances of changing rates are as follows: 40 more rats are added to the colony every week.

So, the rate of change is:

The point is given at 1.5 with respect to the y-axis.

And we can clearly see that it has been decreased to 1 with respect to the y-axis.

So, the rate of change:

1.0 - 1.5 - = -0.5

Therefore, the rate of change at point A on the graph below for the y-axis in relation to the x-axis is -0.5.

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Michael mows 1/3 of the yard, and the remaining is for Mel,

Note that 1 whole yard is 1

So the remaining is 1 - 1/3 = 2/3

Mel can mow 3/4 of the entire yard in 1 hour :

So in 1 whole yard, Mel can mow it for :

Mel's rate in mowing 1 yard is 4/3 hrs

Since Mel will mow 2/3 of the yard, multiply it by her rate will be :

8/9 or 0.89 hour

Note that multiplication can be expressed as division,

The number of hours Mel can finish mowing the yard is :

Since the answer is same, 8/9 hour is correct.

To summarize the answers :

1. 8/9 hr or 0.89 hr

2. 2/3, as explained above.

3. The division problem is :

4. 8/9 hr or 0.89 hr

Let's solve for x by factoring this quadratic equation.

We first need to determine which two numbers multiply to -28 (c) but add to 3 (b).

The two numbers that multiply to -28 and add to 3 are 7 and -4.

Therefore, we can factor this equation like so:

Now, we can set this equation to 0 and solve for x.

If we look at each factor individually, we can determine the values of x:

Subtract 7 from both sides of the equation.

Now, let's look at the other factor:

Add 3 to both sides of the equation.

The solution of x^2 + 3x - 28 is x = -7, x = 4.

The value of x for functions f(x)=(1+2x)/x and g(x)=2+x is 1 or -1

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given,

f(x)=(1+2x)/x

g(x)=2+x

f(x)=g(x)

Plug in values of f(x) and g(x)

(1+2x)/x=2+x

1+2x=x(2+x)

Apply distributive property on RHS

1+2x=2x+x²

1+2x-2x=x²

x²=1

x=±1

The value of x is 1 or -1.

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The equation of the linear function in slope intercept form is  y = 2x -6

The equation of a line in slope intercept form can be represented as follows:

y = mx + b

where

Therefore, let's find the slope of the linear function using (0, -6)(1, -4).

m = -4 + 6 / 1 - 0

m = 2 / 1

m = 2

Therefore, the y-intercept of the linear function can be calculated using (0, -6) and the lope.

y = 2x + b

-6 = 2(0) + b

b = -6

Therefore, the equation of the line is y = 2x -6

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As given by the question

There are given that the expression

Now,

The value of the given expression is:

Hence, the correct option is C.

Answer: t=2*±√(35)=±11.8322

Step-by-step explanation: STEP

1

:

           t2

Simplify   ——

           20

Equation at the end of step

1

:

  t2          

 (—— +  8) -  15  = 0

  20          

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  20  as the denominator :

        8     8 • 20

   8 =  —  =  ——————

        1       20  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

t2 + 8 • 20     t2 + 160

———————————  =  ————————

    20             20  

Equation at the end of step

2

:

 (t2 + 160)    

 —————————— -  15  = 0

     20        

STEP

3

:

Rewriting the whole as an Equivalent Fraction :

3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  20  as the denominator :

         15     15 • 20

   15 =  ——  =  ———————

         1        20  

Polynomial Roots Calculator :

3.2    Find roots (zeroes) of :       F(t) = t2 + 160

Polynomial Roots Calculator is a set of methods aimed at finding values of  t  for which   F(t)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  t  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  160.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,4 ,5 ,8 ,10 ,16 ,20 ,32 ,40 , etc

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        161.00    

     -2       1        -2.00        164.00    

     -4       1        -4.00        176.00    

     -5       1        -5.00        185.00    

     -8       1        -8.00        224.00    

Note - For tidiness, printing of 15 checks which found no root was suppressed

Polynomial Roots Calculator found no rational roots

Adding fractions that have a common denominator :

3.3       Adding up the two equivalent fractions

(t2+160) - (15 • 20)     t2 - 140

————————————————————  =  ————————

         20                 20  

Trying to factor as a Difference of Squares:

3.4      Factoring:  t2 - 140

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 140 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Equation at the end of step

3

:

 t2 - 140

 ————————  = 0

    20  

STEP

4

:

When a fraction equals zero :

4.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 t2-140

 —————— • 20 = 0 • 20

   20  

Now, on the left hand side, the  20  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  t2-140  = 0

Solving a Single Variable Equation:

4.2      Solve  :    t2-140 = 0

Add  140  to both sides of the equation :

                     t2 = 140

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  

                     t  =  ± √ 140  

Can  √ 140 be simplified ?

Yes!   The prime factorization of  140   is

  2•2•5•7

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 140   =  √ 2•2•5•7   =

               ±  2 • √ 35

The equation has two real solutions  

These solutions are  t = 2 • ± √35 = ± 11.8322  

The area of a rectangle is the product of its length and breadth. The maximum area enclosed by the fence is 36800 square meter  and the dimensions of the enclosed area are 115 meter and 320 meter. The width is given as 115 meter.

A rectangle is a type of parallelogram that has equal diagonals.

All the interior angles of a rectangle are equal to the right angle.

The diagonals of a rectangle do not bisect each other.

The dimensions of the given rectangle is (650 - 2x) and x.

Then, the area of the given rectangle is A(x)  = x(650 - 2x)

In order to find the maximum area enclosed take the derivative of A(x) and equate it to zero as follows,

(660 - 2x) - 2x = 0

=> 4x = 660

=> x = 660 / 4

=> x = 115

Now, the maximum area is the value of A(x) at x = 115 as below,

= 115 × (650 - 2×115)

= 115 × 320

= 36800

The dimensions for the maximum area are 115 and (650 - 2 × 115) = 320.

Hence, the largest area enclosed is 36800 square meter and the dimensions of the enclosed area are 115 meter and 320 meter. The width labeled in the figure is given as 115 meter.

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The general vertex-equation of a parabola has the following form:

Where:

• a is a multiplicative factor,

• (h, k) are the coordinates of the vertex of the parabola.

In this exercise we have the following equation:

Vertex of the parabola

To find the vertex of the parabola, we will complete squares to take the equation f(x) to the general form as in the equation above.

i. We factorize the equation of f(x) in the following way:

ii. Now, we rewrite the term inside the parenthesis as:

iii. Now, we see that the term in parenthesis can be rewritten as a square:

iv. Finally, we rewrite the term inside and outside the parenthesis as:

In the last step, we rewrite the term inside the parenthesis to have the same shape as in the general expression.

Comparing the equation that we have obtained and the general one, we see that the coordinates of the vertex are:

Second point

We find a second point by evaluating the function f(x) in x = 1, we get:

The coordinates of the second point are (1, -15).

Graph

We have the following points of the parabola:

Using these points and taking into account that the axis of symmetry is x = -1 (because the x-coordinate of the vertex is -1), we get the following graph:

Coordinates of the vertex: (-1, -27)

Coordinates of the second point: (1, -15)