10(x + 4) = (2x-1) + 4​

Answer:

16

Step-by-step explanation:

3^x +1 = f(X)

2x-4 = g(x)

find f(2)-g(-1)

we substitute in function f(X) by value (2), and in function g(X) by value (-1)

1. 3^x +1 becomes 3^2+1 =9+1=10

2. 2(-1)-4= -2-4=-6

then f(2)-g(-1)

= 10-(-6) =10+6=16

Answer:

50.32

Step-by-step explanation:

In calculating the factor A variation, there are two degrees of freedom. In determining the variation of factor B, there are two degrees of freedom.

A two-factor factorial design is an experiment that collects data for all potential values of the two factors of the study. The design is a balanced two-factor factorial design if equivalent sample sizes are used for every of the possible factor combinations.

Suppose we have two components, A and B, each of which has a high number of levels of interest. We will select a random level of component A and a random level of factor B, and n observations will be taken for each experimental combination.

From the data given:

a.

In calculating the factor A variation, there are two degrees of freedom.

In determining the variation of factor B, there are two degrees of freedom.

b.

Finding the degree of freedom using the interaction variation, there are four degrees of freedom.

c.

In finding the random variable, there are 9(4-1) = 27 degrees of freedom.

d.

In calculating the total variable, there are 9*4-1 =35 degrees of freedom.

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By using the figure below, the value of line segment PT is equal to 54 units.

In Mathematics, the midpoint of a line segment with two endpoints can be calculated by adding each point on a line segment together and then divide by two (2).

Since T is the midpoint of PQ, we have the following:

Line segment PT = Line segment TQ

7x + 5 = 9x - 9

9x - 7x = 9 + 5

2x = 14

x = 14/2

x = 7.

Now, we can determine the value of PT:

PT = 7x + 5

PT = 7(7) + 5

PT = 54 units.

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Complete Question:

Use the figure to the right to find the value of PT. T is the midpoint of PQ PT=7x+9 and TQ=9x-5

Answer:

386.75

Step-by-step explanation:

added in the picture

The cost of joining the gym for 6 months is 386.75.

Given,

The function G(m) = 49.5m + 89.75 represents the cost of joining the gym in addition to the one-time membership fee.

The cost, G, is measured in dollars for m months.

We need to find the value of G(6).​

Here,

The one-time membership = 89.75.

Now,

Putting m = 6 months in:

G(m) = 49.5m + 89.75

G(6) = 49.5 x 6 + 89.75

       = 297 + 89.75

       = 386.75

Thus the cost of joining the gym for 6 months is G(6) = 386.75.

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Answer:

LCM of 4 and 5 is 20.

a/b = 3/4 = 15/20

b/c = 5/6 = 20/24

a:b:c = 15:20:24

Answer:

616.2442

area to the nearest whole number=616

Step-by-step explanation:

using formula 1/2absinx

where a =44,b=29 ,x=105

1/2x44x29xsin105

44x29=1276

1276÷2=638

638 x sin 105

the sin of 105 is 0.9659

if u are using a four figure table where u can't find 105 under sin of angle

u simply subtract 105 from 180=75

638 x 0.9659 =616.2442

approx.616

The grοwth rate (r) represented as a percentage is 4%, which is οptiοn (c).

A percentage is a number οr ratiο expressed as a fractiοn οf 100. It is οften denοted using the percent sign, "%", althοugh the abbreviatiοns "pct.", "pct" and sοmetimes "pc" are alsο used. A percentage is a dimensiοnless number; it has nο unit οf measurement.

The given pοpulatiοn grοwth mοdel is:

P = 6191(1.04)¹

Here, P represents the pοpulatiοn after οne year, 6191 represents the initial pοpulatiοn, and 1.04 is the grοwth factοr.

The grοwth factοr is calculated as:

grοwth factοr = 1 + grοwth rate

where the grοwth rate is a decimal representatiοn οf the percentage increase in pοpulatiοn.

Sο, in this case, we can calculate the grοwth rate as:

grοwth rate = grοwth factοr - 1 = 1.04 - 1 = 0.04

Tο cοnvert this tο a percentage, we multiply by 100:

grοwth rate as a percentage = 0.04 * 100% = 4%

Therefοre, the grοwth rate (r) represented as a percentage is 4%, which is an οptiοn (c).

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Answer:

31.55

Step-by-step explanation:

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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Answer:

$1984.80

Step-by-step explanation:

165.40 times 12 equals 1984.80

Answer:

He pays $1984.80 on his loan in one year.

Step-by-step explanation:

If he pays 165.40 per month, and there are 12 months in one year, then we must multiply the values together.

165.4*12 = 1984.8

He pays $1984.80 on his loan in one year.

Answer:

yes.

Step-by-step explanation:

r these just free points?

Answer: -1 Is the answer.

Answer: DESMOS

Step-by-step explanation:

Your OHVA teacher reminded you in class to use DESMOS to see the graph and then sketch it on your test...

Dilation involves changing the size of the polygon

The best rule of dilation is \((x,y) \to \frac 72(x,y)\)

The coordinates of vertices Q and Q' are given as;

Q = (6,2)

Q' = (21, 7)

The scale factor of dilation is then calculated as:

\(k = \frac {Q'}{Q}\)

So, we have:

\(k = \frac {(21,7)}{(6,2)}\)

Factorize

\(k = \frac {7/2(6,2)}{(6,2)}\)

Divide

\(k = \frac {7}2\)

So, the transformation rule is:

\((x,y) \to \frac 72(x,y)\)

Hence, the best rule of dilation is \((x,y) \to \frac 72(x,y)\)

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Answer:

The correct answer is:

D. Action: Divide both sides by 4.

E. Property: Division property of equality.

Thus, the perimeter of the shown triangle using the distance formula is found as  13.45 units.

A path that encircles a region is referred to as a perimeter. Adding the lengths of every one of the sides together is the simplest formula for calculating the perimeter. The word circumference, that only encompasses a circle's perimeter, is used to describe the distance around a circle.

Given that:

Perimeter = sum of all sides

Perimeter = AB + BC + CA

Estimate each distance using the distance formula:

d = √(x2 - x1)² + (y2 - y1)²

AB = √(1 - 5)² + (5 - 3)²

AB = √(-4)² + (-2)²

AB = √(16 + 4)

AB = √20

BC = √(3 - 1)² + (0 - 5)²

BC = √(2)² + (-5)²

BC = √(4 + 25)

BC = √29

CA = √(5 - 3)² + (3 - 0)²

CA = √(2)² + (3)²

CA =  √(4 + 9)

CA = √13

Perimeter = AB + BC + CA

Perimeter = √20 + √29 + √13

Perimeter = 4.47 + 5.38 + 3.60

Perimeter = 13.45 units.

Thus, the perimeter of the shown triangle using the distance formula is found as  13.45 units.

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Translating shape A by the vector \((^1_4)\) means translating 1 unit right and 4 unit up to get A'(4, 7), B'(7, 7), C'(7, 5) and D'(4, 5)

Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.

Let us assume that the vertices of shape A is at A(3, 3), B(6, 3), C(6, 1) and D(3, 1)

Translating shape A by the vector \((^1_4)\) means translating 1 unit right and 4 unit up to get A'(4, 7), B'(7, 7), C'(7, 5) and D'(4, 5)

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9514 1404 393

Answer:

Step-by-step explanation:

If you divide the first equation by 2, you get ...

  4x -3y = 6

If C=4, the second equation would be identical to this, giving a dependent system of equations with an infinite number of solutions.

If you want a system of equations with one solution, the value of C must be anything except 4. (That system will have the solution (x, y) = (0, -2).)

The equation of the line passing through the points: (3,-10.5) and (1,-7.5) is \(3x+2y+12=0.\)      

Every point on a line fulfills the equation of that line, which means that every point on the line represents every other point on the line.

The equation of a line passing through two-points \((x_{1} ,y_{1} )\) and \((y_{1} ,y_{2} )\) is given by the formula,

                  \(y-y_1= \frac{y_2-y_1}{x_2-x_1}(x-x_1)\)

So, the equation of the line passing through the points (3,-10.5) and (1,-7.5) will be-

⇒\(y-(-10.5)=\frac{-7.5-(-10.5)}{1-3} *(x-3)\)

⇒\(y+10.5=\frac{-7.5+10.5}{-2} *(x-3)\)

⇒\(y+10.5=\frac{3}{-2} *(x-3)\)

⇒\(y+10.5=\frac{-3x}{2} +\frac{9}{2}\)

⇒\((y+10.5)*2=-3x+9\)

⇒\(2y+21=-3x+9\)

⇒\(2y+3x+21-9=0\)

⇒\(3x+2y+12=0\)

Hence, the equation of the line passing through the points (3,-10.5) and (1,-7.5) is  \(3x+2y+12 =0\).

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Answer:150?

Step-by-step explanation:

Answer:

1.D

2.B

Step-by-step explanation:

1. The x intercept is the value of x when y is zero. We know that the x intercept is 0.5 so we must find a value of k that will make our rational function equal zero when x=0.5

\(y = \frac{k}{x + 1} - 2\)

Substitute x=0.5 and y=0.

\(0 = \frac{k}{0.5 + 1} - 2\)

\(0= \frac{k}{1.5} - 2\)

\(2 = \frac{k}{1.5} \)

\(3 = k\)

D is the Answer.

2. We need to consider the function

\( \frac{2x}{1 - {x}^{2} } \)

Since the numerator is a linear term, it will have one zero to the equation using fundamental Theorem of Algebra so C is wrong.

This is a rational function because we are dividing two polynomials by each other and q(x) or the denominator isnt zero. So D is wrong.

The denominator is a quadratic term so it will have two vertical asymptote according to the fundamental Theorem of Algebra So A is Wrong.

B is Right, the equation isnt defined at x=0 because when we plug 0 into the denominator, it doesn't equate to zero.

The given options, the only value greater than 1 is 1.003. Therefore 0.886, which is less than 1 and makes the inequality true.

The given number sentence is 5.3 × > 5.3, where we need to find the scaling factor that makes the inequality true. To do this, we can divide both sides of the inequality by 5.3. This gives us:

5.3 × x > 5.3 ÷ 5.3 × k

We need to find the value of k that makes the inequality true. Simplifying the right-hand side of the equation, we get:

5.3 ÷ 5.3 × k = k × 1 = k

Substituting this into our equation, we get:

5.3 × x > k

We know that 5.3 × 1 = 5.3, which means that k must be greater than 1 to satisfy the inequality. Among the given options, the only value greater than 1 is 1.003. However, this value would make the inequality too large, so it is not the correct answer.

The correct answer is therefore 0.886, which is less than 1 and makes the inequality true.

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6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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Based on the information given, the price of the zero coupon bond is $692.04.

To calculate the price of a zero coupon bond, we need to use the following formula:

\(\sf P =\dfrac{F}{1+r\div n}^{(nt)\)

Where:

Also, the annual interest rate is 7.50%, which is the market interest rate, and the compounding is semiannual, which means n = 2. Finally, the time to maturity is 5 years.

Plugging in the values into the formula, we get:

\(\sf P = \dfrac{1000}{(1+0.075\div2)^{(2\times5)}}\)

\(\sf P = \dfrac{1000}{(1.0375)^{10}}\)

\(\sf P = \dfrac{1000}{1.4450}\)

\(\sf P = \$692.04 \ \ (rounded \ to \ the \ nearest \ cent)\)

Therefore, the price of the zero coupon bond is $692.04.

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Solution :

The formula for the linearization of a function \($f(x)$\) at a point \($x$\) = a is given as

\($L(x)=f(a)+(x-a)f'(a)$\)

Assuming the time is t and the distance travelled is \($f(t)$\), that makes the speed as \($f'(t)$\).

So substituting them in the linearization formula,

A. At t = 7 minutes

   f(7) = 2.5 km

    f'(7) = 0.5 kpm

  ∴ \($L_7(t)=f(7)+(t-7)f'(7)$\)

             \($=2.5+(t-7)0.5$\)

              \($=2.5+0.5t-3.5$\)

              \($=0.5t-1$\)

B. At t = 18 minutes

      f(18) = 14.8 km

    f'(18) = 0.8 kpm

  ∴ \($L_{18}(t)=f(18)+(t-18)f'(18)$\)

               \($=14.8+(t-18)0.8$\)

              \($=14.8+0.8t-14.4$\)

              \($=0.8t-0.4$\)

C. Substituting the value of t as 14 in both the linearization to determine the position at 14 minutes, we get

\($L_7(14)=0.5(14)-1.0$\)

          = 7 - 1

          = 6 km

\($L_{18}(14)=0.8(14)+0.4$\)

            = 11.2 + 0.4

            = 11.6 km

D. According to the linearization at 7, the distance travelled between the 7 minutes and 14 minutes is = 6 km - 2.5 km

                                           = 3.5 km

And between the 14 minutes and 18 minutes is = 14.8 km - 6 km

                                                                              = 8.8 km

This is an average speed of 0.5 kpm in the first interval and an average speed of 2.2 kpm.

Now, according to the linearization of 18, the distance travelled between the 7 minutes and the 14 minutes is = 11.6 km - 2.5 km

                                                           = 9.1 km

And between 14 minutes and 18 minutes is = 14.8 km - 11.6 km

                                                                       = 3.2 km

This gives an average speed of 1.3 kpm in the first interval and 0.8 kpm in the second interval.

Therefore, the second approximation is the better one since the average speed are closer to the actual readings in the second linearization.  

First, let's do the easy part! Multiplying 50 by 3 will give us how far the bus would travel in 3 hours. 50 x 3 = 150.

Now let's do the quarter. 50 / 4 = 12.5. Simply add these two together now!

The bus will travel 162.5 miles!

Hope this helps :)

Complete Question

Of a company's personnel, 7 work in design, 14 in manufacturing, 4 in testing, 5 in sales, 2 in accounting and 3 in marketing. A committee of 6 people is to be formed to meet with upper management.Lucy works in the design department and her husband Ricky works in marketing. In how many ways can the committee be formed if they cannot both be on the committee together

Answer:

The value is \(F = 1582240 \ ways\)

Step-by-step explanation:

Generally the total number of personnel in the company is mathematically evaluated as

          \(N = 7 + 14 + 4 + 5 + 2 + 3\)

=>       \(N =35\)

The number of personnel that are to make up the committee is n =  6

  Generally the number of ways of selecting the 6 person committee from the  total number of personnel in the company is mathematically represented as

         \(n = ^{35}C_{6}\)

=>       \(n = 1.62316 * 1 0^6\)

Here C stands for combination hence we are going to be making use of the combination function in our calculators  

Generally the number of ways of selecting 6 person committee from the  total number of personnel without including  Lucy and  the husband Ricky is

        \(k = ^{35 - 2} C_{6-2}\)

=>     \(k = ^{33} C_{4}\)

=>     \(k = 40920\)

Generally the number of way of selecting the committee in such a way that Lucy and the husband are not on the committee together is mathematically evaluated as

        \(F = 1.62316 * 1 0^6 - 40920\)

=>    \(F = 1582240 \ ways\)