Mathematics College

## Answers

**Answer 1**

Given the expression:

[tex]\frac{x-3}{2x+3}[/tex]

We need to find the value of the expression when x = 7

So, we will substitute with x = 7 into the expression as follows:

[tex]\frac{7-3}{2\cdot7+3}=\frac{7-3}{14+3}=\frac{4}{17}[/tex]

so, the answer will be 4/17

## Related Questions

please show me how to solve this triangle, thank you!

### Answers

**Statement Problem: **Solve for the missing sides of the triangle;

**Solution:**

The sum of angles in a triangle is **180degrees.** Thus,

[tex]\begin{gathered} \angle A+\angle B+\angle C=180^o \\ \angle B=180^o-\angle A-\angle C \\ \angle B=180^o-42^o-96^o \\ \angle B=42^o \end{gathered}[/tex]

Since measure angle A and measure angle B are equal. Thus, the triangle is isosceles and the two sides are equal.

[tex]a=b[/tex]

We would apply sine rule to find the missing side **a.**

[tex]\begin{gathered} \frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c} \\ \frac{\sin A}{a}=\frac{\sin C}{c} \end{gathered}[/tex][tex]\begin{gathered} \frac{\sin42^o}{a}=\frac{\sin96^o}{12} \\ a=\frac{12\sin42^o}{\sin96^o} \\ a=8.07 \\ a\approx8.1 \end{gathered}[/tex]

Thus,

[tex]a=b=8.1[/tex]

**CORRECT ANSWERS:**

[tex]\begin{gathered} a=8.1 \\ b=8.1 \\ m\angle B=42^o \end{gathered}[/tex]

Nathan and some friends are going to the movies. At the theater, they sell a bag of popcorn for $6 and a drink for $4. How much would it cost if they bought 5 bags of popcorn and 7 drinks? How much would it cost if they bought pp bags of popcorn and dd drinks?Total cost, 5 bags of popcorn, and 7 drinks: Total cost, p bags of popcorn and d drinks:

### Answers

a) Since the cost of a bag of popcorn is $6 and the cost of a drink is $4,

[tex]\begin{gathered} T=6\cdot5+7\cdot4 \\ \Rightarrow T=30+28=58 \\ \Rightarrow T=58 \end{gathered}[/tex]

**Therefore, the answer to the first question is $58.**

b) Substitute 5 for p and 7 for d in the expression above; therefore,

[tex]T=6p+4d[/tex]

**The total cost is given by the equation T=6p+4d, where T is in dollars, p is the number of bags of popcorn and d is the number of drinks.**

Hello! I need some help with this homework question, please? The question is posted in the image below. Q4

### Answers

a) f(0) = -1

b) f(1) = 1

c) f(4) = 7

d) f(5) = 121

**Explanation:**

. Since for every value between -2 (excluded) and 4 (included)

~ 0 , 1 and 4

You have to use the first equation

=> f(0) = 2 * 0 - 1 = -1

=> f(1) = 2 * 1 - 1 = 1

=> f(4) = 2 * 4 - 1 = 7

. For values between 4 (exclude) and 5(included)

~ 5

You have to use the second equation

=> f(5) = 5^3 - 4 = 121

I need help answering this if you can show your work to the be good

### Answers

Let:

x = Number of sodas purchased

y = Number of hamburgers purchased

The food truck charges $3 for sodas, so the total cost for sodas will be:

3*x=3x

also, it charges $8 for each hamburger, hence, the total cost for hamburgers will be:

8*y = 8y

Since Jack wants to spend no more than $30, the total cost must be less or equal than $30:

[tex]\begin{gathered} \text{Total cost }\leq\text{ 30} \\ \text{Total cost = total cost for sodas+total cost for hamburgers} \\ 3x+8y\le30 \end{gathered}[/tex]

Cylinder A has radius r, height h, and a volume of 10 pi cubic units. Cylinder B hastwice the radius and twice the height.hATBWhat is the volume of cylinder B?I2r2h

### Answers

Volume of a cylinder:

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

For cylinder A:

[tex]10\pi cm^3=h*r^2*\pi[/tex]

For cylinder B:

[tex]V_B=2h*(2r)^2*\pi[/tex]

Simplify the equation for volumen of cylinder B:

[tex]\begin{gathered} V_B=2h*4r^2*\pi \\ V_B=8*(h*r^2*\pi) \end{gathered}[/tex]

in the equation for the volume of cylinder A you have the value of h*r^2*π:

[tex]\begin{gathered} V_B=8*(10\pi cm^3) \\ V_B=80\pi cm^3 \end{gathered}[/tex]Then, the volume of cylinder B is 80π cubic centimeters.

how is the metric system important to a pharmacy Technician?

### Answers

The metric system is a system of decimals in which all the measurements are taken as multiples or divisions based on a factor of 10. We have to convert between different units of measurements while working in a pharmacy. Metric system helps to make fast and easy conversions of units of measurements. Therefore, metric system is important to a pharmacy technician.

Ben has a collection of 15 coins and quarters and dimes there's seven quarters in the collection. describe ratio that compares the coins that compare the whole coin collection part of it then write the ratio and at least two different ways

### Answers

Since the collection contains quarters and dimes, we are going to compare the whole collection to the quarters (7),

We can represent a ratio, like:

15:7 or 15/7

Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of the equation. (3, 7); y=3x+7

### Answers

The** linear equation parallel **to y= 3x + 7 is:

y = 3x - 2

**How to find the linear equation?**

A general **linear equation** is of the form:

y = m*x + b

Where m is the slope and b is the y-intercept.

Two lines are **parallel **only if the lines have the same slope and different y-intercepts.

So a line **parallel **to y = 3x + 7 will be of the form:

y = 3x + c

To find the value of c we use the point (3, 7) which must belong to the line, replacing the values in the** linear equation:**

7 = 3*3 + c

7 = 9 + c

7 - 9 = c

-2 = c

The** linear equation** is y = 3x - 2

Learn more about** linear equations:**

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Estimate the time it would take you to drive 278 miles at38 miles per hour. Round to the nearest hour

### Answers

Speed formula:

[tex]s=\frac{d}{t}[/tex]

d is the distance

t is the time

As you need to find a time having the distance and speed, solve the equation above for t:

[tex]\begin{gathered} t\cdot s=d \\ t=\frac{d}{s} \end{gathered}[/tex]

Use the given data to find the time:

[tex]\begin{gathered} t=\frac{278mi}{38mi/h} \\ \\ t=7.31h \\ \\ t=7h \end{gathered}[/tex]Then, it would take you 7 hours to drive 278 mi at 38mi/h

mrs Middleton makes a solution to Clean her windows she uses 2:1 ratio for every two cups of water she uses one cup of vinagar if ms middleton uses a gallon of water how mant cups of vinagara. 12 cups b. 2 quartz c. 2 pints d. 1 gallon

### Answers

To answer this question we have to find (among the options) the amount that represents half the amount of water used.

Since the ratio of water to vinegar is 2:1, half of the amount of water will be used of vinegar.

In this case we have to find the answer that represents half a gallon.

That answer is 2 quarts. 2 guarts are 0.5 gallons, it means they are half the amount of water used.

It means that the answer is b. 2 quarts.

Write in terms of confunction of a complementary angle:tan 26°

### Answers

ANSWER

*The cofunction of tan 36 degrees is ***cot 54 degrees**

**STEP-BY-STEP EXPLANATION**

Given information

[tex]\text{tan 26}\degree[/tex]

Co function of tan can be written below as

[tex]\begin{gathered} \tan \text{ }(A)\text{ = cot (B)} \\ \text{if, A + B = 90} \end{gathered}[/tex][tex]\begin{gathered} \text{tan 36 = cot (90 - 36)} \\ \tan \text{ 36 = cot 54} \end{gathered}[/tex]

Therefore,

**tan 36 = 0.7265**

**cot 54 = 0.7265**

Hence, the cofunction of tan 36 is cot 54

The endpoints CD are given. Find the coordinates of the midpoint m. 24. C (-4, 7) and D(0,-3)

### Answers

To find the coordinates of the midpoint

We will use the formula;

[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\text{ }\frac{y_1+y_2}{2})[/tex]

x₁ = -4 y₁=7 x₂ = 0 y₂=-3

substituting into the formula

Xm = x₁+x₂ /2

=-4+0 /2

=-2

Ym= y₁+ y₂ /2

=7-3 /2

=4/2

=2

The coordinates of the midpoint m are (-2, 2)

If Danica has $1200 to invest at 8% per year compounded monthly, how long will it be before he has $2400? If the compounding is continuous,how long will it be? (Round your answers to three decimal places.)

### Answers

**ANSWER**

**EXPLANATION**

a) To find the time it will take before he has $2400, we have to apply the formula for monthly compounded amount:

[tex]undefined[/tex]

give the coordinates of the image of each point under a reflection across to given line.(0,8); y=x

### Answers

**Answer:**

(8, 0)

**Explanation: **

Whenever a point (x,y) is reflected across the line **y=x, **the transformation rule is given below:

[tex](x,y)\to(y,x)[/tex]

That is, the x-coordinate and y-coordinate change places.

Therefore, the image of the point (0,8) when reflected across the line y=x is:

[tex](8,0)[/tex]

**The correct answer is (8,0).**

Refer to attached image.

213 and 131 are incorrect.

### Answers

**Answer:**

P(X<16) = 0.64P(X>12) = 0.64

**Step-by-step explanation:**

Given a **graph of a probability density function**, you want the probabilities ...

**P(X < 16)****P(X > 12)**

Probability from PDF

The probability of a given range of values of X is the area under the density curve for those values of x.

P(X < 16)

The triangular area to the left of X=16 has a base of 16 and a height of 0.08. Its area is given by the area formula for a triangle:

A = 1/2bh

A = 1/2(16)(0.08) = 0.64

**The probability is P(X<16) = 0.64**.

P(X > 12)

The area to the right of X=12 is a trapezoid with parallel "bases" of 0.06 and 0.10. The "height" of the trapezoid is 20-12 = 8. The area is given by the formula ...

A = 1/2(b1 +b2)h

A = 1/2(0.06 +0.10)(8) = 0.64

**The probability is P(X>12) = 0.64**.

Convert the fraction to a decimal. Round the quotient to hundredths when necessary70 over 45

### Answers

**Given:**

[tex]\frac{70}{45}[/tex]

**Required: **

We need to convert the given fraction to a decimal.

**Explanation:**

Divide the number 70 by 45.

[tex]\frac{70}{45}=1.555...[/tex]

Round off to the nearest hundredth.

[tex]\frac{70}{45}=1.56[/tex]

**Final answer:**

[tex]\frac{70}{45}=1.56[/tex]

**Given:**

[tex]\frac{70}{45}[/tex]

**Required: **

We need to convert the given fraction to a decimal.

**Explanation:**

Divide the number 70 by 45.

[tex]\frac{70}{45}=1.555...[/tex]

Round off to the nearest hundredth.

[tex]\frac{70}{45}=1.56[/tex]

**Final answer:**

[tex]\frac{70}{45}=1.56[/tex]

what are the equations of the asysyoptes of the rational function

### Answers

To find the asymptotes, we have to solve the following.

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

We have to find two numbers whose product is 3 and whose sum is 4. Those numbers are 3 and 1.

[tex](x-3)(x-1)=0[/tex]

So, the solutions are x = 3 and x = 1.

Hence, the asymptotes x = 1 and y = 1/2.

**The graph below shows the function.**

Graph transformation of the following line given the transformation: g(x)= -f(x) -2

### Answers

Transformation of a Function

We are given the function:

[tex]y=f(x)=\frac{2}{3}x+8[/tex]

And it's required to find another function g(x) according to the transformation:

g(x) = -f(x) - 2

First, we calculate the negative of f(x):

[tex]-f(x)=-(\frac{2}{3}x+8)=-\frac{2}{3}x-8[/tex]

And now we subtract 2 to find g(x):

[tex]g(x)=-\frac{2}{3}x-8-2=-\frac{2}{3}x-10[/tex]

The equation above is in the slope-intercept form where the slope is m=-2/3 and the y-intercept = -10

Answer:

[tex]g(x)=-\frac{2}{3}x-10[/tex]

7/11% of a quantity is equal to what fraction of a quantity

### Answers

7/11% can be written as:

[tex]\begin{gathered} \frac{\frac{7}{11}}{100}=\frac{7}{11}\times\frac{1}{100} \\ \frac{\frac{7}{11}}{100}=\frac{7}{1100} \end{gathered}[/tex]

So 7/11% of a quantity is equal to 7/1100 fraction of a quantity

**Answer:41/10,000**

**7/17% = 0.41% = 0.0041**

**41/10,000**

**Step-by-step explanation:**

Trent earns scores of 60, 90, and 72 on three chapter tests for a certain class. His homework grade is 68 and his grade for a class project is 64. The overall average for the course is computed as follows: the average of the three chapter tests makes up 50% of the course grade; homework accounts for 10% of the grade; the project accounts for 20%; and the final exam accounts for 20%. What scores can Trent earn on the final exam to pass the course if he needs a "C" or better? A "C" or better requires an overall score of 70 or better, and 100 is the highest score that can be earned on the final exam. Assume that only whole-number scores are given. To obtain a "C" or better, Trent needs to score between and Inclusive.

### Answers

A: 90% - 100%

B: 80% - 89%

C: 70% - 79%

D: 60% - 69%

F: 0% - 59%

Using the data provided:

[tex]0.5(\frac{60+90+72}{3})+0.1(68)+0.2(64)+0.2(x)\ge70[/tex]

Where:

x = Score of the final exam in order to get at least a C.

Solve for x:

[tex]\begin{gathered} 37+6.8+12.8+0.2x\ge70 \\ 56.6+0.2x\ge70 \\ 0.2x\ge70-56.6 \\ 0.2x\ge13.4 \\ x\ge\frac{13.4}{0.2} \\ x\ge67 \end{gathered}[/tex]

**He needs to score between 67 and 100**

HELP PLEASE!!!!!!!!!!! ILL MARK BRAINLIEST

### Answers

[tex]-1\frac{3}{4}[/tex] is located at a point 1 on the **number line. **

1.1125 is located at point 6 on the **number line. **

14 / 8 is located at point 8 on the **number line. **

-0.875 is located at point 3 on the **number line. **

What are the locations of the numbers?

The numbers are made up of mixed fractions, improper fractions, decimals, positive numbers and negative numbers.

A **mixed number **is a number that has a whole number, a numerator and a denominator. The numerator that has a smaller value than the denominator. and a proper fraction. . An example of a **mixed number **is 1 1/4. An** improper fraction** is a fraction in which the numerator is bigger than the denominator. An example of an i**mproper fraction** is 14/8.

A **negative number **is a number that is smaller in value than 0. **Negative numbers **would be to the left of zero on **number line.** An example of a **negative number **is -1.4. A **positive number **is a number that is greater in value than 0**. Positive number**s are located to the right of 0 on the **number line**. An example of a **positive number **is 4.2.

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[tex]-1\frac{3}{4}[/tex] is located at a point 1 on the **number line. **

1.1125 is located at point 6 on the **number line. **

14 / 8 is located at point 8 on the **number line. **

-0.875 is located at point 3 on the **number line. **

What are the locations of the numbers?

The numbers are made up of mixed fractions, improper fractions, decimals, positive numbers and negative numbers.

A **mixed number **is a number that has a whole number, a numerator and a denominator. The numerator that has a smaller value than the denominator. and a proper fraction. . An example of a **mixed number **is 1 1/4. An** improper fraction** is a fraction in which the numerator is bigger than the denominator. An example of an i**mproper fraction** is 14/8.

A **negative number **is a number that is smaller in value than 0. **Negative numbers **would be to the left of zero on **number line.** An example of a **negative number **is -1.4. A **positive number **is a number that is greater in value than 0**. Positive number**s are located to the right of 0 on the **number line**. An example of a **positive number **is 4.2.

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In a right triangle, the side opposite angle β has a length of 16.4 cm. The hypotenuse of the triangle has a length of 25.1 cm. What is the approximate value of sin(β)?

### Answers

**Given**

Length of hypotenuse= 25.1 cm

length of BC = 16.4 cm

**Find**

Value of

[tex]sin\beta[/tex]

**Explanation**

As , we know

[tex]sin\beta=\frac{opposite}{hypotenuse}[/tex]

now, put values

[tex]sin\beta=\frac{16.4}{25.1}=0.653[/tex]

**Final Answer**

Value of

[tex]sin\beta=0.653\text{ approx}[/tex]

I need help with math. I have a big exam coming up but I do t understand this lesson at all. Can I have help answering all the questions?

### Answers

**Step 1**

**Given;**

[tex]\begin{gathered} Head\text{ represent male} \\ Tail\text{ represent female} \end{gathered}[/tex]

The total number of puppies is 4 represented by 4 coins.

**Step 2**

Find the experimental probability that exactly 3 of the puppies will be female

[tex]\begin{gathered} From\text{ table we find that THTT, TTHT, HTTT and HTTT are the only outcomes that } \\ \text{show exactly 3 females} \\ Remember\text{ tail\lparen t\rparen is for female puppies} \end{gathered}[/tex]

Therefore, the total number of samples/coin tosses=20

The formula for probability is;

[tex]Pr\left(event\right)=\frac{Numberofrequiredevent}{Total\text{ number of events}}[/tex]

Total number of events =the total number of samples/coin tosses=20

Number of required events= outcomes with 3 T's from the tab;e=4

Hence.

[tex]=\frac{4}{20}=0.2=0.2\times100=20\text{\%}[/tex]

**Answer;**

[tex]\frac{4}{20}=0.20=20\text{\%}[/tex]

1(c). What is a better deal? Explain. Deal 1: 2 mediums 14'' (round) pizza for $14 total Deal 2: 1 large 20'' (round) pizza for $13 total

### Answers

To get the better deal of the two, we need to find the cost per area of pizza for each deal and compare.

**Deal 1: 2 medium 14'' (round) pizza for $14 total **

The area of a circle is calculated as

[tex]A=\pi r^2[/tex]

where r is the radius.

The area of the pizza is calculated to be:

[tex]\begin{gathered} r=14 \\ \therefore \\ A_1=\pi\times14^2=196\pi \end{gathered}[/tex]

Hence, the total area for the two pizzas will be:

[tex]\Rightarrow196\pi\times2=392\pi[/tex]

The cost per square inch of pizza is, therefore, calculated to be:

[tex]\Rightarrow\frac{14}{392\pi}=0.011[/tex]

The pizza costs $0.011 per square inch.

**Deal 2: 1 large 20'' (round) pizza for $13 total**

The area of the pizza is calculated to be:

[tex]\begin{gathered} r=20 \\ \therefore \\ A_2=\pi\times20^2=400\pi \end{gathered}[/tex]

Hence, the cost per square inch of pizza is calculated to be:

[tex]\Rightarrow\frac{13}{400\pi}=0.010[/tex]

The pizza costs $0.010 per square inch.

**CONCLUSION:**

The better deal will be the deal with the lesser cost per square inch. As can be seen from the calculation, both deals are about the same price per square inch if approximated. However, without approximation, Deal 2 has a slightly lesser cost per square inch.

**Therefore, ****DEAL 2 IS THE BETTER DEA****L.**

What is lim (2x² - x + 3)/(3x² + 5) as x approaches + ∞?

### Answers

Given:

lim (2x² - x + 3)/(3x² + 5)

We are to

DATA ANALYSIS AND STATISTICS Outcomes and event probability A number cube is rolled three times. An outcome is represented by a string of the sort OEE (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll). The 8 outcomes are listed in the table below. Note that each outcome has the same probability. For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event. Event A: An odd number on each of the last two rolls Event B: An even number on the last roll Event C: An even number on the last roll or the second roll (or both) Explanation Check 000 0 0 OOE EEE O Outcomes OEO 0 0 EOO EEO EOE OEE 0 0 Probability 0 0 0 00 음 0/5 X Nikida V Españe

### Answers

**Event A:**

The event A occurs when an odd number is rolled in the second roll **and **in the third roll. We can see in the table that the outcomes that correspond with this event are:

OOO

EOO

Now to calculate the probability, we need to divide the number of favorable outcomes by the number of total outcomes. There are 8 possible outcomes, and the favorable outcomes for event A are 2. Thus:

[tex]P(A)=\frac{2}{8}=\frac{1}{4}[/tex]

**Event B:**

In event B we want the last roll to be even. Then, the outcomes corresponding to this event are:

OOE

EEE

EOE

OEE

The number of favorable outcomes is 4, the total outcome is 4:

[tex]P(B)=\frac{4}{8}=\frac{1}{2}[/tex]

**Event C:**

Here, we are looking for outcomes with an even number in the second or last roll (or both). Thus the outcomes that satisfy this are:

OOE

EEE

OEO

EEO

EOE

OEE

The number of favorable outcomes is 6, and the number of total outcomes is 8:

[tex]P(C)=\frac{6}{8}=\frac{3}{4}[/tex]

An accountant finds that the gross income, in thousands of dollars, of a small business can be modeled by the polynomial −0.3t 2 + 8t + 198, where t is the number of years after 2010. The yearly expenses of the business, in thousands of dollars, can be modeled by the polynomial −0.2t 2 + 2t + 131.a. Find a polynomial that predicts the net profit of the business after t years. b. Assuming that the models continue to hold, how much net profit can the business expect to make in the year 2016?I know that the equation is -0.1t^2+6t+67, but i don't know how to find part b.

### Answers

**ANSWER:**

**STEP-BY-STEP EXPLANATION:**

a.

We know that the net profit is equal to the incomes minus the expenses, therefore, the final equation would be:

[tex]\begin{gathered} \text{profit = income - expense} \\ \text{replacing} \\ p=-0.3t^2+8t+198-(-0.2t^2+2t+131) \\ p=-0.3t^2+8t+198+0.2t^2-2t-131 \\ p=-0.1t^2+6t+67 \end{gathered}[/tex]

b. t is the number of the years after 2010. Therefore, for the year 2016, x is equal to 6 (2016 - 2010), we replace:

[tex]undefined[/tex]

Can you please help me out with a question

### Answers

AS shown in the figure:

The measure of arc RT = 27

The measure of arc FN = 105

The measure of angle FUN will be as follows:

[tex]m\angle\text{FUN}=\frac{1}{2}(105+27)=\frac{1}{2}\cdot132=66[/tex]

So, the answer is **option C. 66**

the answer is C. yw!

decide whether circumference or area would be needed to calculate the total number of equally sized tiles on a circular floor and explain your reasoning

### Answers

The total number of equally-sized tiles on a circular floor.

Here, we are covering the region or the total space occupied by all the tiles on the floor.

Hence, the area is calculated.

<

Z2

Find the midpoint m of z₁ = (9+7i) and Z₂ = (-7+7₂).

Express your answer in rectangular form.

m=

Re

### Answers

The **midpoint** m of z₁ = (9+7i) and Z₂ = (-7+7i) is** 1 + 7i** .

Given **complex numbers**:

[tex]z_{1}[/tex] = (9 + 7i) and [tex]z_{2}[/tex] = (-7 + 7i)

compare these numbers with a1+ib1 and a2+ib2, we get

a1 = 9, a2 = -7 , b1 = 7 and b2 = 7.

Mid point of complex numbers = a1 + a2 /2 + (b1 + b2 /2)i

= (9 + (-7)/2 + (7 + 7 /2)i

= 2/2 + 14/2 i

Mid point m = 1 + 7i

Therefore the midpoint m of z₁ = (9+7i) and Z₂ = (-7+7i) is** 1 + 7i**

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