Mathematics College

## Answers

**Answer 1**

ANSWER

The** future value** of the investment is **$2704.3515**

STEP-BY-STEP EXPLANATION:

Given information

**The present value = $2700**

**Annual simple interest rate = 2.25%**

**number of compounded period = 8 months**

*Let the future value be F.V*

To find the future value, we need to apply the below formula

[tex]F\mathrm{}V\text{ = }P.V(1+r)^n[/tex]

Where

• FV = future value

,

• PV = Present value

,

• r = interest rate

,

• n = compounding period

The next thing is to convert 8 months to a year

let x be the number of years

Recall that,

**12 months is equivalent to 1 year**

**8 months is equivalent to x years**

Mathematically,

[tex]\begin{gathered} 12\text{ = 1} \\ 8\text{ = x} \\ \text{Cross multiply} \\ 12\cdot\text{ x = 8} \\ 12x\text{ = 8} \\ \text{Divide both sides 12} \\ \frac{12x}{12}\text{ = }\frac{8}{12} \\ x\text{ = 06667 year} \end{gathered}[/tex]

Using the above formula, we can now find the future value of the investment

[tex]\begin{gathered} F\mathrm{}V=P.V(1+r)^n \\ F\mathrm{}V\text{ = 2700( 1 + }\frac{2.25}{100})^{0.667} \\ F\mathrm{}V=2700(1+0.0225)^{0.667} \\ F\mathrm{}V=2700(1.0225)^{0.067} \\ F\mathrm{}V\text{ = }2700\text{ x 1.014}945 \\ F\mathrm{}V\text{ = \$2704.3515} \end{gathered}[/tex]

## Related Questions

Solve all parts of the problem. Show all steps thoroughly

### Answers

**Given**

h(t)=30.5t+8.7

**Find**

Meaning of slope

Meaning of y-intercept

**Explanation**

(a)

Slope = 30.5

It means the average speed of the hot air balloon is 30.5 ft/min

(b)

y-intercept = 8.7

It means the initial height of the balloon is 8.7 ft

**Final Answer**

(a) 30.5

(b) 8.7

betermine the angles in the Mangle,912290x - 28

### Answers

To solve fo x, equate all the angles to 180 degree

That is;

x + x - 5 + x - 28 = 180 (sum of angle in a triangle)

3x -33 = 180

Add 33 to both-side

3x =213

Divide both-side by 3

x = 71

The angles are;

x = **71°**

x - 5 = 71 - 5 =**66°**

x - 28 = 71 - 28 =**43°**

A hole must be excavated for a swimming pool in the shape shown in the figure. Whatvolume of depth must be removed in order to create this hole?10 m30 m1 m4 m

### Answers

**The Solution:**

Given:

We are asked to find the volume.

Observe that the base surface that can give a uniform cross-section is a **trapezoid.**

So, **the formula for the volume is:**

[tex]Volume=\frac{1}{2}(a+b)h\times H[/tex]

In this case:

[tex]\begin{gathered} a=1m \\ \\ b=4m \\ \\ h=height\text{ of the trapezoid}=? \\ \\ H=10m \end{gathered}[/tex]

Find h:

[tex]\begin{gathered} h^2+3^2=30^2 \\ \\ h^2=900-9 \\ \\ h^2=891 \\ \\ h=\sqrt{891}=29.8496m \end{gathered}[/tex]

Substitute:

[tex]Volume=\frac{1}{2}(1+4)29.85\times10=5\times29.85\times5=746.241m^3[/tex]

Therefore, **the correct answer is 746.241 cubic meters.**

There are 13 balls numbered 1 through 13 placed in a bucket. What is the probability of reaching into the bucket and randomly drawing two balls numbered 12 and 2without replacement, in that order? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

### Answers

**Explanation **

We are given the following:

• 13 balls numbered 1 through 13 placed in a bucket.

We are required to determine the probability of randomly drawing two balls numbered 12 and 2 without replacement, in that order.

**This is achieved thus:**

The probability of randomly selecting a ball numbered 12 from the bucket is:

[tex]Pr.(12)=\frac{1}{13}[/tex]

The probability of randomly selecting 2 from the bucket after the first selection is:

[tex]Pr.(2)=\frac{1}{12}[/tex]

Therefore, the probability of randomly selecting two balls numbered 12 and 2 is:

[tex]\begin{gathered} Pr.=\frac{1}{13}\times\frac{1}{12} \\ Pr.=\frac{1}{156} \end{gathered}[/tex]

**Hence, the answer is:**

[tex]\frac{1}{156}[/tex]

can you please set the answer up like the question its easier for me to understand

### Answers

We have to prove that:

[tex]\angle VWX\cong\angle YZX[/tex]

And we are given that:

[tex]\begin{gathered} \bar{WV}\parallel\bar{YZ} \\ X\text{ is the midpoint of }\bar{VY} \end{gathered}[/tex]

**Statement 1: **

[tex]\bar{WV}\parallel\bar{YZ}[/tex]

*Reason: *Given

**Statement 2:**

[tex]\text{There are lines that passes through WV and YZ}[/tex]

*Reason: *Postulate of existence of lines

**Statement 3:**

[tex]\text{The line WZ is tranversal to WV and YZ}[/tex]

*Reason: *Information given on the graph.

**Statement 4: **

[tex]\angle VWX\cong\angle YZX[/tex]

*Reason: *Alternate interior angles are congruent.

The Sanchez Family pays $1,975 per month to rent a four-bedroom house. They are planning to buy a house and make monthly payments of $2,590. If the cost of movingwas $545, find their additional cost for housing the first year.$6,850$7,925$7,380$8,175None of these choices are correct.

### Answers

Determine the additional cost of housing for a month.

[tex]2590-1975=615[/tex]

Determine the additional cost of housing for a year.

[tex]12\cdot615=7380[/tex]

The moving charge is 545

Let E be the event that a corn crop has an infestation of earworms, and let B be the event that a corn crop has an investigation of corn borers.

### Answers

We will see how to determine independent probabilities of two events with the help of set notations.

We will define two events that can occur independently as follows:

[tex]\begin{gathered} \text{Event ( E ) = Corn crop infected by earth worms} \\ \text{Event ( B ) = Corn crop infected by corn borers} \end{gathered}[/tex]

The probability of occurrence of each event is defined by the prefix " p " preceeding each event notation as follows:

[tex]\begin{gathered} p\text{ ( E ) = 0.18} \\ p\text{ ( B ) = 0.11} \\ \text{p ( E \& B ) = 0.06} \end{gathered}[/tex]

We can express the two events ( E and B ) as two sets. We will Venn diagram to express the events as follows:

We have expressed the two events E and B as circles which are intersecting. The region of intersection is the common between both events ( E & B ).

The required probability is defined as an instance when the corn crop is subjected to either earth worm or corn borers or both!

If we consider Venn diagram above we can see the required region constitutes of region defined by event ( E ) and event ( B ). We can sum up the regions defined by each event!

However, if we consider region E and B as stand alone we see that the common region is added twice in the algebraic sum of induvidual region E and B. We will discount the intersection region once to prevent over-counting. Therefore,

[tex]p\text{ ( E U B ) = p ( E ) + p ( B ) - p ( E \& B )}[/tex]

The above rule is the also denoted as the rule of independent events ( probabilities ).

We will use the above rule to determine the required probability p ( E U B ) as follows:

[tex]\begin{gathered} p\text{ ( E U B ) = 0.18 + 0.11 - 0.06} \\ p\text{ ( E U B ) = 0.23} \end{gathered}[/tex]

Therefore, the required probability is:

[tex]0.23\ldots\text{ Option D}[/tex]

-5x+7=52how would i answer this

### Answers

Answer:

**x = - 9**

Explanation:

The given equation is

- 5x + 7 = 52

We want to solve for x

Subtracting 7 from both sides, it becomes

- 5x + 7 - 7 = 52 - 7

- 5x = 45

Dividing both sides of the equation by - 5, we have

- 5x/- 5 = 45/- 5

**x = - 9**

Hello! I need some help with this homework question posted below. Q19

### Answers

Answer:

(-∞, -4] U [1, ∞)

Explanation:

The **given function** is:

[tex]f(x)=2(x-1)(x+4)^3[/tex]

Since f(x) ≥ 0, we are going to find the range of values of x for which f(x) ≥ 0

**By carefully observing the graph shown:**

f(x) ≥ 0 for values of x less than or equal to -4, and also for values of x greater than or equal to 1.

This can be written **mathematically** as:

x ≤ -4 or x ≥ 1

This can be written in **interval notation** as:

(-∞, -4] U [1, ∞)

Bismark Tractor put a markup of 26% on cost on a part for which it paid $350. Find the markup

### Answers

From the question

Percentage markup = 26%

Selling price(SP) = $350

To find the Markup

The formula below will be used

[tex]\text{ \%Markup }=\frac{SP-CP}{CP}-100\text{\%}[/tex]

Since Cost price(CP) is not given

Hence, substitute given values to find CP

[tex]26=\frac{350-CP}{CP}\times100[/tex]

Solve for CP

Cross multiply

[tex]26CP=100(350-CP)[/tex]

Expand the bracket

[tex]26CP=35000-100CP[/tex]

Collect like terms

[tex]\begin{gathered} 26CP+100CP=35000 \\ 126CP=35000 \end{gathered}[/tex]

Divide both sides by 126

[tex]\begin{gathered} \frac{126CP}{126}=\frac{35000}{126} \\ CP=\text{ \$}277.78 \end{gathered}[/tex]

Hence the cost price is $277.78

To find Markup the formula below will be used

[tex]\text{Markup }=SP-CP[/tex]

Hence,

[tex]\begin{gathered} \text{Markup }=\text{ \$}350-\text{ \$}277.78 \\ \text{Markup }=\text{ \$}72.22 \end{gathered}[/tex]

**Therefore, the markup is $72.22**

The first term of a geometric sequence is 6. The common ratio is 2. Find the7th term of the sequence using the explicit formula.

### Answers

The geometric sequence is given by:

[tex]a_n=a\cdot r^{n-1}[/tex]

where:

a = first term of the sequence

r = common ratio

so:

[tex]\begin{gathered} n=7 \\ a_7=6\cdot2^{7-1} \\ a_7=6\cdot2^6 \\ a_7=6\cdot64 \\ a_7=384 \end{gathered}[/tex]

What is the place value of9 in 8.00231497?

### Answers

**ANSWER**

Ten-millionths

**EXPLANATION**

We want to find the place value of 9 in 8.00231497.

The number 9 is placed 7 places beyond the decimal point. This implies that its value is 7 orders of 10 less than 8 and its **place value is ten-millionths.**

That is the answer.

Find the area a of the sector of a circle radius 50 centimeters formed by central angle1/10 radian

### Answers

Given:

Radius of the circle = 50 cm

Central angle = 1/10 rad

Let's find the area of the sector.

To find the area of the sector, apply the formula:

[tex]Area=\frac{1}{2}\times r^2\theta[/tex]

Where:

r is the radius = 50 cm

θ is the central angle in radians = 1/10 radian

Hence, we have:

[tex]\begin{gathered} \text{Area}=\frac{1}{2}\times50^2\times\frac{1}{10} \\ \\ \text{Area}=\frac{1}{2}\times2500\times\frac{1}{10} \\ \end{gathered}[/tex]

Solving further:

[tex]Area=\frac{1\times2500\times1}{2\times10}=\frac{2500}{20}=125\operatorname{cm}^2[/tex]

**Therefore, the area of the sector of the circle is ****125 square centimeters.**

**ANSWER:**

**125 cm²**

The length of a rectangle is five times its width. If the perimeter of the rectangle is 120 ft, find its area.

### Answers

Solution

The length of a rectangle is five times its width.

Let the length be represented by L

Let the width be represented by W

The length of the rectangle is five times the width i.e

[tex]L=5W[/tex]

To find the perimeter, P, of a rectangle, the formula is

[tex]P=2(L+W)[/tex]

Given that the perimeter, P, of the rectangle is 120ft,

Subsitute for length and width into the formula above

[tex]\begin{gathered} P=2(L+W) \\ 120=2(5W+W) \\ 120=2(6W) \\ 120=12W \\ \text{Divide both sides by 12} \\ \frac{12W}{12}=\frac{120}{12} \\ W=10ft \end{gathered}[/tex]

Recall that, the length of the rectangle is

[tex]\begin{gathered} L=5W \\ L=5(10) \\ L=50ft \\ W=10ft \end{gathered}[/tex]

To find the area, A, of a rectangle, the formula is

[tex]A=LW[/tex]

Substitute the values of the length amd width into the formula above

[tex]\begin{gathered} A=(50)(10)=500ft^2 \\ A=500ft^2 \end{gathered}[/tex]

**Hence, the area of the rectangle is 500ft²**

In ∆QRS, the measure of

### Answers

Notice that the given triagle is a right triangle. Remember the definition of the **cosine** of an angle on a right triangle.

[tex]\cos (\theta)=\frac{\text{Side adjacent to }\theta}{\text{ Hypotenuse}}[/tex]

Plugging in the information of the diagram:

[tex]\cos (\angle SQR)=\frac{SQ}{QR}[/tex]

Substitute the given values of each segment:

[tex]\cos (29)=\frac{5}{x}[/tex]

Isolate *x* and use a calculator to find a decimal expression for *x:*

[tex]\begin{gathered} x=\frac{5}{\cos (29)} \\ \Rightarrow x=5.716770339\ldots \\ \Rightarrow x\approx5.7 \end{gathered}[/tex]

**Therefore, the length of the side QR, to the nearest tenth of a foot is:**

[tex]5.7[/tex]

The two polygons are similar. Write a proportion and solve for x. I just need help with 11 and 13

### Answers

11)

Given data:

The given pair of traingles.

The expression for the ratio of the coorresponding sides is,

[tex]\begin{gathered} \frac{5}{x}=\frac{2}{1} \\ 5=2x \\ x=2.5 \end{gathered}[/tex]

Thus, **the value of x is 2.5.**

13)

Given data:

The given pair of rectangles.

The expression for the ratio of the corresponding sides is,

[tex]\begin{gathered} \frac{3}{x}=\frac{4}{6} \\ 18=4x \\ x=\frac{18}{4} \\ =4.5 \end{gathered}[/tex]

Thus, **the value of x is 4.5.**

I can help solve this question it's not very hard

### Answers

Hello!

First, let's **graph all these functions** in the graph below:

• green,: first function

,

• blue,: second function

,

• red,: third function

As we can see, the first and the second grow almost the same (lines are very near), while the **third grows faster**.

is d=65t proportional or non proportional?

### Answers

A proportional relationship can be said to be a relationship between two variables with equivalent ratios. Here the two variables vary directly with each other.

Thus, using the equation:

**y = kx**

where k is the constant

Here, we have:

d = 65t

where 65 is the constant of proportionality

We can say d varies directly as t

Therefore **d = 65t** is proportional.

**ANSWER:**

**Proportional**

7. Determine whether y varies directly with x. If so, find the constant of variation and write the equation.42-41-24X-2

### Answers

We have to find two points from the graph to find the slope of the line equation:

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-2}{0-(-4)}=-\frac{2}{4}=-\frac{1}{2}[/tex]

We took the points (-4, 2) and (0, 0)

x1 = -4

y1 = 2

x2 = 0

y2 = 0

Then, using the point-slope form of the line equation, we have, for point (0, 0):

[tex]y-0=-\frac{1}{2}(x-0)\Rightarrow y=-\frac{1}{2}x[/tex]

Then,** the constant of variation is k = -1/2 and y = (-1/2)x.**

if you can't read it it says : rewrite the expression (1/2)(x - y) -4 using the distributive property

### Answers

The given expression is

(1/2)(x - y) -4

When applying the ditributive property, we multiply each term inside the bracket by the term outside the bracket. Thus, we have

1/2 * x - 1/2 * y - 4

= x/2 - y/2 - 4

Thus, the correct option is C

I am learning this in class but I don’t understand it please help

### Answers

**Answer:**

**The quotient is**; (the whole number)

[tex]6[/tex]

and **the remainder** is;(numerator of the fraction)

[tex]5[/tex]

**Each day they will hike:**

[tex]6\frac{5}{12}[/tex]

**Explanation:**

From the question, it was given that they have to hike a total of 77 miles in 12 days.

total distance = 77 miles

Total time = 12 days

To get the distance they will hike per day, we will divide the total distance by the total time.

[tex]\begin{gathered} r=\frac{77}{12}=\frac{72+5}{12} \\ r=\frac{72}{12}+\frac{5}{12} \\ r=6+\frac{5}{12} \\ r=6\frac{5}{12} \end{gathered}[/tex]

Therefore, **The quotient is**; (the whole number)

[tex]6[/tex]

and **the remainder** is;(numerator of the fraction)

[tex]5[/tex]

suppose 160 geology students measure the mass of an ore sample. due to the human error and limitations in the reliability of the balance not all the readings are equal the result are found to closely approximate a normal curve with the mean 85 g and the standard deviation 1 g . use the symmetry of the normal curve and the empirical rule

### Answers

In a group of samples find the deviation

there are 160 students

mean is the sum of samples/ number of samples

standard deviation is a number defined by

Deviation = √ sum of squares = 1

Then find number of students with readings more than 85g

looking at the curve. 80 students are measuring more than 85g, and substracting deviation standard= 1 . The result more precise is 80-1= 79 students

Dominique paints faces at a carnival. Her goal is to earn $100. She spends $16 on supplies and charges $3 per face. How many faces will she need to paint to meet her $100 goal.

### Answers

**38 faces**

**Explanation:**

Amount to be earned = $100

Amount spent on supplies = $16

This is an expenses on the business

Amount charged per face = $3

**Let x represent the number of faces to be painted**

The total calculation:

[tex]\begin{gathered} 100=\text{ 3x -16} \\ 100+16\text{ = 3x} \\ 116\text{ = 3x} \\ \text{Divide through by 3} \\ x\text{ =}\frac{116}{3} \\ x\text{ = 38.67} \\ Since\text{ number of faces can't be decimal or fraction,} \\ we\text{ will approxi}mate\text{ to 39 faces} \end{gathered}[/tex]

**Note:** $16 was subtracted because it was an expense and to make a profit of $100, it snould not include expenses.

**Therefore, the number of faces she needs to paint to meet her $100 goal is 38 faces.**

MAT 115 StatisticsWhich of the following probabilities for the sample points A, B, and C could be true if A, B, and C are the only sample points in an experiment?Explain why each of the other 3 answers are wrong.1) P(A) = 5/10, P(B) = 2/10, P(C) = 1/102) P(A) = 0, P(B) = 1/2, P(C) = 1/23) P(A) = 1/5, P(B) = 1/6, P(C) = 1/34) P(A) = -1/10, P(B) = 1/2, P(C) = 6/10

### Answers

The addition of the 3 probabilities must be equal to 1.

1) P(A) + P(B) + P(C) = 5/10 + 2/10 + 1/10 = 4/5 ≠ 1

2) P(A) + P(B) + P(C) = 0 + 1/2 + 1/2 = 1

3) P(A) + P(B) + P(C) = 1/5+ 1/6 + 1/3 = 7/10 ≠ 1

4) a probability can't be negative

Then, **the correct option is option 2**

PQ is tangent to •C at P. If PQ = 5 and CQ = 6, find CP and m

### Answers

**Answer****:**

[tex]\begin{gathered} CP=\sqrt{11} \\ m\operatorname{\angle}C=56.44 \end{gathered}[/tex]

**Explanation****:**

**Step 1. **The information that we have is that

• PQ=5

,

• CQ=6,

and that PQ is tangent to circle C.

Since PQ is a tangent line, it forms a 90° angle with the circumference, and the triangle is a right triangle.

We need to find CP and the measure of angle C (m

**Step 2. **To find CP we use the **Pythagorean theorem:**

In this case:

[tex](CQ)^2=(CP)^2+(PQ)^2[/tex]

Substituting the known values:

[tex]6^2=(CP)^2+5^2[/tex]

Solving for CP:

[tex]\begin{gathered} 6^2-5^2=(CP)^2 \\ 36-25=(CP)^2 \\ 11=(CP)^2 \\ \sqrt{11}=CP \end{gathered}[/tex]

**The value of CP is:**

[tex]\boxed{CP=\sqrt{11}}[/tex]

**Step 3. **To find the measure of angle C, we use the trigonometric function sine:

[tex]sinC=\frac{opposite\text{ side}}{hypotenuse}[/tex]

The opposite side to angle C is 5 and the hypotenuse is 6:

[tex]sinC=\frac{5}{6}[/tex]

Solving for C:

[tex]C=sin^{-1}(\frac{5}{6})[/tex]

Solving the operations:

[tex]\begin{gathered} C=s\imaginaryI n^{-1}(0.83333) \\ C=56.44 \\ \downarrow \\ \boxed{m\operatorname{\angle}C=56.44} \end{gathered}[/tex]

**Answer****:**

[tex]\begin{gathered} CP=\sqrt{11} \\ m\operatorname{\angle}C=56.44 \end{gathered}[/tex]

What is the inverse of the following conditional? If Tracy is not going to Quinn's candy shop then she is not going to buy sour straws.

### Answers

In order to find the inverse of this conditional, we need to negate both the first and second statement.

So we have:

First statement: "Tracy is not going to Quinn's candy shop"

Second statement: "she is not going to buy sour straws"

Negating these, we have:

First statement: "Tracy is going to Quinn's candy shop"

Second statement: "she is going to buy sour straws"

So the inverse will be:

**"If Tracy is going to Quinn's candy shop then she is going to buy sour straws."**

A coin is tossed and a six sided die numbered 1 through 6 is rolled. Find the probability of tossing a head and then rolling a number greater then 4. Round to three decimal places

### Answers

[tex]\begin{gathered} \text{The sample space for a coin is 2} \\ S=(H,T) \\ \text{Thus, probability of tossing a head is:} \\ Pr(H)=\frac{1}{2} \end{gathered}[/tex][tex]\begin{gathered} \text{The sample space for a die is 6} \\ S=(1,2,3,4,5,6) \\ \text{Thus, the probability of rolling a number greater than 4 is:} \\ Pr(>4)=\frac{2}{6}=\frac{1}{3} \end{gathered}[/tex]

Hence, the probability of tossing a head and then rolling a number greater that 4 is:

[tex]\begin{gathered} \frac{1}{2}\times\frac{1}{3} \\ \Rightarrow\frac{1}{6} \\ \Rightarrow0.167 \end{gathered}[/tex]

Solve the system of equationsy=-2x-3 y=2x^2+4x-1Round to the nearest hundredth

### Answers

**Given:**

[tex]y=-2x-3[/tex][tex]y=2x^2+4x-1[/tex]

**Requires:**

We need to solve the given system of equations.

**Explanation:**

Consider equation.

[tex]y=2x^2+4x-1[/tex][tex]Substitute\text{ }y=-2x-3\text{ in the equation to find the value of x.}[/tex][tex]-2x-3=2x^2+4x-1[/tex]

Add 2x+3 to both sides of the equation.

[tex]-2x-3+2x+3=2x^2+4x-1+2x+3[/tex][tex]0=2x^2+6x+2[/tex][tex]2x^2+6x+2=0[/tex]

Divide both sides of the equation by 2.

[tex]\frac{2x^2}{2}+\frac{6x}{2}+\frac{2}{2}=\frac{0}{2}[/tex][tex]x^2+3x+1=0[/tex]

Which is of the form

[tex]ax^2+bx+c=0[/tex]

where a=1, b=3, and c =1.

Consider the quadratic formula.

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Substitute a=1, b=3, and c =1 in the equaiton.

[tex]x=\frac{-3\pm\sqrt{3^2-4(1)(1)}}{2(1)}[/tex][tex]x=\frac{-3\pm\sqrt{9-4}}{2}[/tex][tex]x=\frac{-3\pm\sqrt{5}}{2}[/tex][tex]x=\frac{-3\pm\sqrt{5}}{2}[/tex]

M&M candy contain 50 pics, some are yellow and rest are green there are 9 yellow pieces for every green piece, how many yellow pieces are there??

### Answers

We need to create a table as follows:

Yellow pieces Green pieces Yellow/Green

5 50 - 5 = 45 5/45 = 0.11

10 50 - 10 = 40 10/40 = 0.225

15 50 - 15 = 35 15/35 = 0.4286

25 50 - 25 = 25 25/25 = 1

35 50 - 35 = 15 35/15 = 2.333

45 50 - 45 = 5 45/5 = 9

We define the number of yellow pieces, then we calculate the number of green pieces taking into account that the sum of yellow and green is 50.

Finally, we found the relation between yellow and green pieces. The answer is going to be the row where the division between the yellow and green pieces is 9. Because that division tells us how many Yellow pieces are for every green piece.

**Answer: 45 yellow pieces**

at the end of the holiday season in January, the sales at a department store are expected to fall. It was initially estimated that for the x day of January, The sales will be s(x). The financial analysis at the store correct other projection and are not expecting the total sales for the X day of January to be t(x)T(1)=

### Answers

[tex]\begin{gathered} T(x)=\frac{13}{5}+\frac{32}{5(3x+1)^2} \\ T(1)=\text{ }\frac{13}{5}+\text{ }\frac{32}{5(3(1)+1)^2} \\ T(1)=\frac{13}{5}+\frac{32}{5(4)^2} \\ T(1)=\frac{13}{5}+\frac{32}{5(16)} \\ T(1)=\frac{13}{5}+\frac{2}{5} \\ T(1)=\frac{15}{5}=3 \\ \end{gathered}[/tex][tex]\begin{gathered} T^{\prime}(x)=\frac{\text{ 13}}{5}+\frac{32}{5(3x+1)} \\ T^{\prime}(x)=\text{ }\frac{dt(x)}{dx}(\frac{13}{5})+\frac{dt(x)}{dx}(\frac{32}{5(3x+1)} \\ T^{\prime}(x)=0+(\text{ -32\rparen\lparen}\frac{\frac{dt(x)}{dx}5(3x+1)^2}{\frac{dt(x)}{dx}(5(3x+1)^2)^2} \\ T^{\prime}(x)=0\text{ - 32\lparen}\frac{5(\frac{dt(x)}{dx}(3x+1)^2)}{(5(3x+1)^2)^2} \\ T^{\prime}(x)=0\text{ -32\lparen}\frac{5(\frac{dt}{dx}(g)^2)(\frac{dt}{dx}(3x+1)}{(5(3x+1)^2)^2} \\ T^{\prime}(x)=0\text{ -32\lparen}\frac{5(2g)(3)}{(5(3x+1)^2)^2} \\ T^{\prime}(x)=0\text{ - 32\lparen}^\frac{5(2)(3x+1)(3)}{(5(3x+1)^2)^2} \\ T^{\prime}(x)=0\text{ -32\lparen}\frac{5\text{ x \lparen}2)(3x+1)(3)}{25(3x+1)^4} \\ T^{\prime}(x)=0\text{ - 32\lparen}\frac{2(3)}{5(3x+1)^3}) \\ T^{\prime}(x)=0\text{ - 32\lparen}\frac{6}{5(3x+1)^3}) \\ T^{\prime}(x)=\text{ - }\frac{192}{5(3x+1)^3} \\ T^{\prime}(1)=\text{ - }\frac{192}{5(3(1)+1)^3} \\ T^{\prime}(1)=\text{ - }\frac{192}{5(4)^3} \\ T^{\prime}(1)=\text{ - }\frac{192}{320} \\ T^{\prime}(1)=\frac{\text{ - 3}}{5} \end{gathered}[/tex]