Mathematics College

## Answers

**Answer 1**

**Given:**

The range of spray is 12 feet and rotation angle is 200 degree.

**Required:**

How many square feet of grass is watered by the sprinkler.

**Explanation:**

Here

radius r = 12 ft

angle of rotation = 200 degree

We have a formula to find the sector area

[tex]A=\frac{\pi r^2\emptyset}{360}[/tex]

now put the value

[tex]A=\frac{3.14*12^2*200}{360}[/tex][tex]A=\frac{3.14*144*20}{36}[/tex][tex]A=\frac{3.14*144*10}{18}[/tex][tex]A=\frac{3.14*144*5}{9}[/tex][tex]A=3.14*16*5[/tex][tex]A=251\text{ ft}^2[/tex]

**Final Answer:**

251 square feet of grass is watered by the

## Related Questions

Draw the image of the given figure according to the mapping rule. Describe the mapping in simple terms such as "Right 3, reflect over x-axis". Then name the type of mapping. (x,y)>(x+4,-y)

### Answers

Given:

(x, y) ------> (x + 4, -y)

Getting the coordinates:

B (-1, 4)

C (1, 6)

D (0, 2)

Applying the given rule:

(x, y) ------> (x + 4, -y)

B (-1, 4) -----> (-1 + 4, -4) = B' (3, -4)

C (1, 6) -----> (1 + 4, -6) = C' ( 5, -6)

D (0, 2) -----> (0 + 4, -2) = D' (4, -2)

x + 4 should be "Right 4, reflect over x-axis"

x + 4 indicates a shift 4 units to the right.

Then the -y indicates a reflection over the x - axis.

The type of mapping is just like matching one figure to another.

. Mandy wants to buy a variety of beverages for her birthday party. Shewants to make sure she has enough to drink for all her friends, so shedecides to buy 10 liters of beverages. If she buys at least onecontainer of each beverage, what combination of beverages can shebuy to equal exactly 10 liters?

### Answers

Solution

Logical reasoning:

The quantity of Beverages present at the store ;

Soda = 2000ml = 2L

Apple Juice = 2.5L

Fruit Punch = 1.5L

Lemonade = 2L

We have to buy exactly 10 liters but it should be at least one container of each beverage.

Soda + Apple juice + Fruit Punch + Lemonade = 8L

So we need 2 L more.

The only way of doing this is by either having 2 container of soda or 2 container of lemonade.

Therefore

**The combination of beverages she can purchased; **

**Soda = 2 container**

**Apple juice = 1 container**

**Fruit punch= 1 container**

**Lemonade = 1 container**

a family is 500 feet above the ground in the basket of a hot-air balloon in ascending at the consistent rate shown.Adele hello and someone accidentally dropped a penny out of the balloon write a model for height h,p of the penny t seconds after the penny dropped

### Answers

**Answer:**

**A model for height h of the penny t seconds after the penny dropped is;**

[tex]h=500+10t-16t^2[/tex]

**Explanation:**

Given that the penny was dropped from a hot-air balloon that moves at a constant rate of;

[tex]u_0=10ft\text{/s}[/tex]

*Note that the penny will also have the same initial rate.*

At the point when the penny was dropped they are already at height;

[tex]h_0=500ft[/tex]

The gravitational pull on the penny (acceleration due to gravity);

[tex]a=-32ft/s^2[/tex]

The height of the penny at time seconds after it was dropped can be modelled using the equation of motion;

[tex]h=h_0+u_0t+\frac{1}{2}at^2_{}_{}^{}[/tex]

Where;

[tex]\begin{gathered} h_0=initial\text{ height} \\ u_0t=height\text{ covered by initial velocity} \\ \frac{1}{2}at^2=height\text{ covered by gravitational pull} \end{gathered}[/tex]

Substituting the given values we have;

[tex]\begin{gathered} h=h_0+u_0t+\frac{1}{2}at^2_{} \\ h=500+10t+\frac{1}{2}(-32)t^2 \\ h=500+10t-\frac{32}{2}t^2 \\ h=500+10t-16t^2 \end{gathered}[/tex]

Therefore, **a model for height h of the penny t seconds after the penny dropped is;**

[tex]h=500+10t-16t^2[/tex]

Which point is located on the x-axis? O-5.1) 5) (10) O(2.2)

### Answers

Which point is located on the x-axis?

All points of the form (0, y) lie on the x-axis

(x, y)

for example

(0, 5)

(0, -1 )

(0,0 )

6. As a salesperson, you are paid $57.32 once a week plus $3.25 per sale. This week you want your pay to be at least $195. Write an inequality for the number of sales you need to make and graph the solutions. Solve and graph the solutions.

### Answers

We know that

• There is a one-time payment of $57.32.

,

• There is a weekly payment of $3.25 per sale.

,

• The minimum payment you want to get is $195.

Based on the given information, we can form the following inequality

[tex]57.32+3.25w\ge195[/tex]

Then, we solve for w (sales)

[tex]\begin{gathered} 3.25w\ge195-57.32 \\ 3.25w\ge137.68 \\ w\ge\frac{137.68}{3.25} \\ w\ge42.36 \end{gathered}[/tex]

So, you need to make at least 43 sales. Observe that we can't take 42 sales as an answer because that way there wouldn't be enough money to reach the payments.

1

Select the correct answer from each drop-down menu.

E

Points A, B, and form a triangle. Complete the statements to prove that the sum of the interior angles of ABC is 180°.

Statement

Reason

Points A, B, and C form a triangle.

given

Let DE be a line passing through Band parallel to AC. definition of parallel lines

23 25 and 21 - 24

m21 = m 24 and mZ3 = m 25

m24+ m2 2 + m 25 = 180°

angle addition and definition of a straight line

substitution

m21 + m22+ m23 = 180°

### Answers

**SOLUTION **

**Statement **

[tex]\angle3\cong\angle5\text{ and }\angle1\cong\angle4[/tex]

**Reason **

Alternate interior angles

**Statement **

[tex]m\angle1=\angle4\text{ and }\angle3=\angle5[/tex]

**Reason **

Alternate interior angles are congruent

Using the table below, what is the rate of change? Don’t forget to include your units.

### Answers

The rate of change can be determined as,

[tex]\begin{gathered} \text{Rate of change=}\frac{Difference\text{ in cost}}{\text{difference in the number of tickets}} \\ =\frac{192-120}{40-25} \\ =\frac{72}{15} \\ =4.80 \end{gathered}[/tex]

**Thus, the rate of change is $4.80/ticket.**

**Thus, option (D) is the correct answer.**

Cylindrical water tank 10ft diameter 7ft height what is the volume?use the value 3.14 for pi round to the nearest whole number

### Answers

The volume of a cylinder can be calculated by the product of the area of its base and its height.

[tex]V=A_b\cdot h[/tex]

We already have the height, bu t we need to calculate the area of the base.

The base is a circunference with diameter 10 ft. The radius of the circunference is half the diameter, so:

[tex]r=\frac{10}{2}=5[/tex]

The area of a circunference can be calculate using its radius:

[tex]\begin{gathered} A_b=\pi r^2 \\ A_b=\pi5^2 \\ A_b=25\pi \end{gathered}[/tex]

So, the volume is:

[tex]\begin{gathered} V=A_b\cdot h \\ V=25\pi\cdot7 \\ V=175\pi \end{gathered}[/tex]

Noiw, using the value of 3.14 to pi, we have:

[tex]\begin{gathered} V=175\pi \\ V=175\cdot3.14 \\ V=549.5 \end{gathered}[/tex]

So,

find the measure of the numbered angles in rhombus DEFG

### Answers

In a rhombus, the diagonals are perpendicular, which means all four triangles created are right triangles. Also, the diagonals bisects the angles, making all four triangles congruent.

Therefore we can write the following relations:

<1 = <2

<5 = <6

<1 + <6 = 90°

<5 + 27° = 90°

<4 = 27°.

First, let's calculate the angle <5:

[tex]\begin{gathered} <5+27°=90°\\ \\ <5=90-27\\ \\ <5=63° \end{gathered}[/tex]

From this value, we also have that <6 = 63°. Then, we can find that <1 = 27°, and then <2 = 27°.

<3 is an angle created in the intersection point of the diagonals, therefore <3 = 90°.

So the answer is:

**<1 = 27°, <2 = 27°, <3 = 90°, <4 = 27°, <5 = 63°, <6 = 63°.**

General MathematicsProblem:Gene bought a living room suite for ₱85,000. He agreed to pay in 5 months at 12% simple interest rate. How much will he pay for the furniture?

### Answers

**Answer:**

[tex]\text{Total}=89,284[/tex]

**Step-by-step explanation:**

Simple interest is represented as:

[tex]\begin{gathered} I=Prt \\ where, \\ I=\text{ interest } \\ P=\text{ principal} \\ r=\text{ interest rate } \\ t=\text{ time (years)} \end{gathered}[/tex]

Then, the interest for a living room suite of 85,000 at a 12% simple interest.

[tex]\begin{gathered} I=85000\cdot0.12\cdot\text{0}.42 \\ I=4,284 \end{gathered}[/tex]

Hence, he will pay for the furniture at the original price plus interest:

[tex]\begin{gathered} \text{Total}=\text{ 85,000+4,284} \\ \text{Total}=89,284 \end{gathered}[/tex]

A farmer is building a fence to enclose a rectangular area consisting of two separate regions. The four walls and one additional vertical segment (to separate the regions) are made up of fencing, as shown below.A rectangular area consisting of two separated regions.A rectangular area consisting of two separated regions.If the farmer has 246 feet of fencing, what are the dimensions of the region which enclose the maximal area?

### Answers

Let the width be x and the length be y as shown in the figure.

The perimeter of the fence is 246 feet so it follows:

[tex]\begin{gathered} 3x+2y=246 \\ y=\frac{246-3x}{2} \end{gathered}[/tex]

The area of the fence is given by:

[tex]\begin{gathered} A=xy \\ A=x(\frac{246-3x}{2}) \\ A=123x-\frac{3}{2}x^2 \end{gathered}[/tex]

Differentiate w. r. t. x to get:

[tex]\frac{dA}{dx}=123-3x[/tex]

For maxima and minima calculation, the derivative is zero so it follows:

[tex]\begin{gathered} 123-3x=0 \\ 3x=123 \\ x=\frac{123}{3}=41 \end{gathered}[/tex]

So the width is 41 feet and the length y is given by:

[tex]y=\frac{246-3(41)}{2}=\frac{123}{2}=61.5[/tex]

**So the width is 41 feet and length is 61.5 feet, the area covered is 2521`.5 sq feet.**

solue for &

X(3 + X) = 3x + x²

### Answers

we have

[tex]g(x)=x^2-3x-10[/tex][tex]g\mleft(x+3\mright)=x^2+bx-c[/tex]

Solve for b and c

step 1

Find out g(x+3)

[tex]g(x+3)=(x+3)^2-3(x+3)-10[/tex]

simplify

[tex]g(x+3)=x^2+6x+9^{}-3x-3-10[/tex]

combine like terms

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

equate with the given expression

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

b=3

c=4

3x=bx -------> b=3

-4=-c ------> c=4

Use the given information to solve the right triangle ABC for all missing partsa = 36 ft, B = 64 degreesA= ° (Type an integer or a decimal.)b≈(Do not round until the final answer. Then round to the nearest whole number as needed.)c≈(Do not round until the final answer. Then round to the nearest whole number as needed.

### Answers

**Answer:**

**Explanation:**

Given the right triangle with side length, a = 36ft and angle measure of B = 64 degrees.

X2+8 divided by 6 equals X

### Answers

The given equation is

[tex]\frac{x^2+8}{6}=x[/tex]

First multiply both sides of the equation by 6

[tex]undefined[/tex]

If city council wanted to determine how per capita income might be a predictor of crime rate, what statistical method would be most appropriate.Continuous probability distributionRegression analysisConfidence intervalHypothesis test

### Answers

The city council wants to determine how does the income level affect the crime rate.

You have to determine which statistical method is best to do so, let's analyze the given options.

- Continuous probability distribution: this is a probability distribution for a random variable X that can take any number. It will give you an idea of the shape of the distribution in the case that you are studying a continuous variable but you won't know if the variable in study is being affected by another variable or variables.

Besides, the given variables "per capita income" and "crime rate" are discrete variables, so *this statistical method does not apply for the given situation.*

- Regression analysis: this analysis is a statistical method that allows you to analyse the relationship between a dependent variable (or response variable) and one or more independent variables (predictor variables)

*This statistical method applies for the given situation.*

-Confidence interval: The confidence interval is a way to estimate the range of values of a population parameter of a population of interest.

*This statistical method does not apply.*

-Hypothesis test: This method allows you to determine whether or not there is enough statistical evidence to assess the plaussability of a statistical hypothesis for a population of interest. This is, if the information of a sample taken allows you to draw conclusions regarding a population of interest.

*This statistical method may apply but is not the best one to use.*

The most appropiate method to apply to determine if the per capita income is a predictor of the crime rate is the **regression analysis.**

The preimage was (-5, -4) and after the rotation, the image was (4, 5). What many degrees counterclockwise did the point rotate? a. none of the aboveb. 180 c. 90 d. 270

### Answers

In determining the degrees counterclockwise did the point rotate from (-5,-4) to (4,5), let's first identify how the point changes from (-5,-4) to (4,5).

We get,

[tex]\text{ (-5, -4) }\rightarrow\text{ (4, 5) : A(x, y) }\rightarrow\text{ A'(-y, -x)}[/tex]

In transformation using rotation, the common rotations are the following,

[tex]\text{ }90^{\circ}\text{ }counterclockwise\text{ }\rightarrow\text{ A(x,y) = A'(}-y,x)[/tex][tex]270^{\circ}counterclockwise\rightarrow A(x,y)=A^{\prime}(y,-x)^{}[/tex][tex]undefined[/tex]

solve the simultaneous equation x + y equals to 15x + y equals to 3

### Answers

We want to solve the simultaneous equations:

x + y = 15

x + y = 3

what set of numbers does -5.2 belong to integers integers & rationalcountingrational

### Answers

rational because you can express as a fraction

[tex]-5.2=-\frac{52}{10}=-\frac{26}{5}[/tex]

can you guys help me with this Geo question please ?

### Answers

[tex]\begin{gathered} since\text{ AB bisect }\angle CAD \\ AC=AD \\ 2x-12=x+9 \\ 2x-x=9+12 \\ x=21 \end{gathered}[/tex]

**A. 21**

Determine if each of the following situations is Discrete Or Continuous The time it takes for a car battery to die Discrete or Continuous:Why?:

### Answers

hello

a discrete data is a set of data belonging to distinct and separate values.

a continuous data is a set of data in which the values belonging to the set can take any value within a finite or infinite interval.

the answer to this question should be continuous because the set of values (break values) ranges in velocity.

continuous data usually requires a measuring device

Do number 8 please.Assuming that the formula is valid for previous times, what was the car worth one year ago?

### Answers

Since the value in dollars **x** years from now is given by:

[tex]12,000(\frac{9}{10})^x^{}[/tex]

And the moment **"right now"** can be represented as **x=0**, then replace **0** for **x** in the expression and evaluate it. Since every number elevated to the 0th power is equal to 1, then:

[tex]12,000(\frac{9}{10})^0=12,000(1)=12,000[/tex]

**Therefore, the car is worth $12,000 right now.**

To find the value of the car one year ago, notice that the time "one year ago" can be represented with **x=-1**. Then, replace **x=-1** into the formula:

[tex]12,000(\frac{9}{10})^{-1}=12,000(\frac{10}{9})=13,333.33\ldots[/tex]

**Therefore, the car was worth approximately $13,333.33 one year ago.**

Find the digits in the ones place, in the hundredths place, and in the ten thousandths place for the following number 293.0584

### Answers

Given the place value below

[tex]293.0584[/tex]

Definition of tenths, hundredths. and thousandths

Ones

The one place refers to the number position to the immediate left of the decimal.

Hundredths

The position of the second digit to the right of the decimal point.

Ten-Thousandths

The position of the third digit to the right of the decimal point.

**Therefore,**

**3 is the digit in the one place.**

**0 is the digit in the **

find the coordinates of the midpoint of a segment with the given endpoints show your work

### Answers

7.

(-3,5) (7,-1)

The midpoint is the midway between two points.

In this case, we have 2 coordinate points (x,y)

point 1 = (-3,5)

point2 = (7,-1)

To find the midpoints we have to add each coordinate and divide by 2.

(-3,5) = (x1,y1)

(7,-1)= (x2,y2)

midpoint = (mx,my)

To find the first coordinate of the midpoint (xm) we have to add both x coordinates (x1 and x2) and divide them by 2

midpoint x = (x1+x2)/2 = (-3+7)/2 = 4/2 = 2

**xm=2**

Same for the y coordinate:

Midpoint y= (y1+y2)/2 = (5+(-1))/2= 4/2 = 2

**ym=2**

**Midpoint= (2,2)**

23. A jury pool consists of 31 people, 19 men and 12 women. Compute the probability that a randomly selected jury of 12 people is all male.

### Answers

We have a pool of 31 people of which 19 are men.

We have to find the probability of selecting a jury of 12 persons and all of them are male.

In this case, we are selecting from the pool and the chosen person does not return to the pool, so the composition of the pool changes.

The first place has a chance of 19 in 31 of being occupied by a man.

The second place has a chance of 18 in 30, as one of the men has been already selected: we take one unit from the count of men and also from the total.

Generalizing, the nth place will have (20-n) in (32-n) chances of being occupied by a man.

The chances of multiple independent events is equal to the product of the chances of each individual event, so we can write:

[tex]\begin{gathered} P=\prod P_i \\ P=\frac{19}{31}\cdot\frac{18}{30}\cdot\frac{17}{29}\cdot\frac{16}{28}\cdot\frac{15}{27}\cdot\frac{14}{26}\cdot\frac{13}{25}\cdot\frac{12}{24}\cdot\frac{11}{23}\cdot\frac{10}{22}\cdot\frac{9}{21}\cdot\frac{8}{20} \\ P=0.613\cdot0.600\cdot0.586\cdot0.571\cdot0.556\cdot0.538\cdot0.520\cdot0.500\cdot0.478\cdot0.455\cdot0.429\cdot0.400 \\ P=0.000357056 \end{gathered}[/tex]

*NOTE: note how the probabilities of the last places is much smaller than the first places, as there are less men to be selected in proportion to the women.*

**Answer: the probability that a 12-people jury is all male is P = 0.000357056.**

lena has $70,000 in a savings account that earns 15% interest per year. The interest is not compounded. How much interest will she earn in one year

### Answers

lena has $70,000 in a savings account that earns 15% interest per year. The interest is not compounded. How much interest will she earn in one year

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

[tex]I=P\mleft(rt\mright)[/tex]

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest

t is Number of Time Periods

in this problem we have

P=$70,000

r=15%=15/100=0.15

t=1 year

substitute in the given formula

[tex]\begin{gathered} I=70,000(0.15\cdot1) \\ I=\$10,500 \end{gathered}[/tex]

A bag contains 3 red, 4 yellow, and 5 blue marbles. Two marbles are randomly selected from the bag with replacement .1) Find the probability that:They are the same color 2) at least one is red

### Answers

Answer:

The probability that they are of the same colour is 19/66

The probability that at least one is red is 5/11

Explanation:

Given that there are:

3 red, 4 yellow, and 5 blue marbles

Total number of marbles = 12

Two marbles are randomly selected,

1.

The probability that they are of the same colour is:

(Probability that both are red) plus (the probability that both are yellow) plus (the probability that both are blue)

[tex]\begin{gathered} =(\frac{3}{12}\times\frac{2}{11})+(\frac{4}{12}\times\frac{3}{11})+(\frac{5}{12}\times\frac{4}{11}) \\ \\ =\frac{1}{22}+\frac{1}{11}+\frac{5}{33} \\ \\ =\frac{19}{66} \end{gathered}[/tex]2.

The probability that at least one is red is:

1 - probability that non is red.

[tex]\begin{gathered} =1-(\frac{9}{12}\times\frac{8}{11}) \\ \\ =1-\frac{6}{11} \\ \\ =\frac{5}{11} \end{gathered}[/tex]

r u real? whats 1×288

### Answers

**Step 1 :** Let's review the information given to us to answer the exercise correctly.

Amount of lemonade Greg made = 2/3 of a gallon

Number of friends = 4

**Step 2: **Let's calculate the amount of lemonade that each friend will get, using the Direct Rule of Three, as follows:

Lemonade (gallon) Friends

2/3 4

x 1

________________________________

4* x = 2/3 * 1

4x = 2/3

Dividng by 4 at both sides:

4x/4 = (2/3) / 4

x = 2/3 * 1/4

x = 2/12

**x = 1/6** (Simplifying)

**Step 3: **Each friend will get 1/6 of a gallon of lemonade

Answer: 288

Step-by-step explanation: anything multiplied by 1

Would stay the same as the bigger number

can you help me to find midpoint

### Answers

The expression for the mid point with the given two point is :

[tex]x=\frac{x_1+x_2}{2}\text{ \& y=}\frac{y_1+y_2}{2}[/tex]

From the given figure we have 2 points : A(5,7) & B(9,-1)

Substitute the value and solve for x & y

[tex]\begin{gathered} x=\frac{x_1+x_2}{2}\text{ \& y=}\frac{y_1+y_2}{2} \\ x=\frac{5+9}{2}\text{ \& y =}\frac{7+(-1)}{2} \\ x=\frac{14}{2}\text{ \& y=}\frac{6}{2} \\ x=7\text{ \& y =3} \end{gathered}[/tex]

So, the mid points are **(x, y) = (7, 3)**

Thus, the graph will be :

The graphs of f(x) and g(x) are shown below What are the solutions to the equation f(x) = g(x)?-A. x= -1,5.4B. x= -3,4C. X= -1,2D. x= -10, 12

### Answers

As given by the question

There are given that the graph of f(x) and g(x)

Now,

From the graph, we have to solve equation f(x)=g(x)

In the graph f(x) and g(x) will be equal at the point where they meet each other

Since y will be the value of f(x) and g(x).

So,

We need the same value of y for both f(x) and g(x) and the same value for y will be at a point where both functions meet each other.

Now

Looking at the graph, we can see that graph of function f(x) and g(x) intersect at two-point (-1, -10) and (5.5, 12)

Hence, the value of x from pair of solution is x=-1, 5.4

So, **option A is correct.**

The graph below shows the solution to which system of inequalities? 5 15 -5 O A. ys 2 and y2 and ysx OD. y>2 and ysx.

### Answers

First, let's evaluate the first statements.

You have:

y ≤ 2

y ≥ 2

x > 2

y > 2

As we can see:

* The graph is limited by a line y = 2 (red line).

* The drawing part corresponds to the part in which y > 2.

* The line is continuous, so 2 is also included in the interval.

In summary:

y ≥ 2

Second, let's evaluate the second part.

You have:

y < x

y < x

y ≤ x

y ≤ x

So, to find if it is "less than" (<) or "less than or equal to" (≤):

* Observe the line that limits this interval. The line is y = x

* Since it is a dotted line, the extreme is not included.

In summary:

y < x

**Answer: **

**B. y ≥ 2 and y < x**