Mathematics College

Four circles, each with a radius of 2 inches, are removed from a square. What is the remaining area of the square? (16 – 4π) in.2 (16 – π) in.2 (64 – 16π) in.2 (64 – 4π) in.2Four circles, each with a radius of 2 inches, are removed from a square. What is the remaining area of the square? (16 – 4π) in.2 (16 – π) in.2 (64 – 16π) in.2 (64 – 4π) in.2vvvv

Answers

Answer 1

Answer: [tex]64-16\pi[/tex] unit square.

Step-by-step explanation:

Here, four circle are removing from a square from the square of edge 8.

Since, The area of the square= [tex]8^2=64[/tex] square unit  ( because, area of square=side×side)

The area of a circle with radius 2 = [tex]\pi(2)^2=4\pi[/tex] square unit.

The area of four circle of radius 2= [tex]4\times4\pi=16\pi[/tex] square unit.

According to the question, these four circle are removed by the above square.

Therefore remaining area of the square after removing these four circle=area of the square- area of four circle of radius 2= [tex]64-16\pi[/tex] square unit.


Answer 2

The remaining area of the square is 64 - 16π.

What is a circle?

A circle is a bounded figure in which points from its center to its circumference is equidistant.

Area of a circle = πr²

Where :

π = pi = 22/7

R = radius

Area of one circle = 2²π = 4π

Area of four circles = 4 x 4π = 16π

What is a square?

A square is a quadrilateral with four equal sides.

Characteristics of a square includes:

Area of a square = length²

= (2x4)²

= 64

The remaining area of the square = 64 - 16π

To learn more about the area of a circle, please check: https://brainly.com/question/14351152

Related Questions

How much time does it take light to travel from the moon to the earth, a distance of 384,000km?

Answers

Excellent question light travels 3x10^8 m/s or 3x10^5 km/s so 384000km/300000km/s = 1.28 sec

Quadrilateral ABCD is similar to quadrilateral EFGH the length of the three longest side in quadrilateral ABCD are 24 feet 16 feet and 12 feet long if the two shortest sides of quadrilateral EFGH feet long and 18 feet long how long is the fourth side on quadrilateral ABCD ?

Answers

check the picture below

solve for "x"

since we know the two smallest sides for EFGH are 9 and 18, 9 is the smallest of all, and 18 is the next small

thus, for the the quadrilateral ABCD, the smallest is "x" and the next small is given, is 12, since that's smaller than 16 or 24

When all sides of a quadrilateral are transformed, the resulting quadrilateral  will be similar to the transformed quadrilateral. The fourth side of ABCD is 6 feet

We have the lengths of ABCD in descending order to be:

[tex]Side\ 1 = 24[/tex]

[tex]Side\ 2 = 16[/tex]

[tex]Side\ 3 = 12[/tex]

We have the lengths of EFGH in ascending order to be:

[tex]Side\ 4 = 9[/tex]

[tex]Side\ 3 = 18[/tex]

The missing side of ABCD is the fourth side, and it can be solved using the following equivalent ratios:

Side 4 : Side 3 of ABCD = Side 4: Side 3 of EFGH

Substitute the values of the known sides

[tex]Side\ 4 : 12 = 9 : 18[/tex]

Express as fraction

[tex]\frac{Side\ 4 }{ 12} = \frac{9}{ 18}[/tex]

Multiply both sides by 12

[tex]Side\ 4 = \frac{9}{ 18} \times 12[/tex]

[tex]Side\ 4 = \frac{1}{2} \times 12[/tex]

[tex]Side\ 4 = 6[/tex]

Hence, the fourth side of ABCD is 6 feet

Read more about similar quadrilaterals at:

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If f(x) = x - 5, then match each of the following.

1. f(-1) -3
2. f(0) -6
3. f(1) -5
4. f(2) 0
5. f(5) 3
6. f(8) -4

Answers

f(-1) = -6
f(0) = -5
f(1) = -4
f(2) = -3
f(5) = 0
f(8) = 3
hello : 
1. f(-1) -3 = -1-5-3 = -9
2. f(0) -6   = 0-5-6 = -11
3. f(1) -5 = 1-5-5 =-9
4. f(2) 0 ??? +0 or : ×0
5. f(5) 3 ....
6. f(8) -4....
f(-1)-3 = f(1)-5

A carpenter is framing a window with wood trim where the length of the window is 9 1/3 feet. If the width of the window is 6 3/4 feet, how many feet of the wood is needed to frame the window?

Answers

This is not much of a question, because it doesn't take into account the width of the wood trim.  

So you are asked to find the perimeter of the window, ignoring the width of the trim.

P = Perimeter = 2L + 2W.

Here, P= 2(9 1/3 feet) + 2(6 3/4 feet) = 2(28/3 feet) + 2(27/4 feet)

So P = 2[28/3 + 27/4] feet.  LCD is 3*4 = 12.

Thus, P = 2 [ 28/3 + 27/4 ] feet.  Can you finish?  Add together the fractions 28/3 and 27/4.

Picture Perfect Physician’s has 5 employees. FICA Social Security taxes are 6.2% of the first $118,500 paid to each employee, and FICA Medicare taxes are 1.45% of gross pay. FUTA taxes are 0.6% and SUTA taxes are 5.4% of the first $7,000 paid to each employee. Cumulative pay for the current year for each of its employees are as follows. Compute the amounts in the table for each employee and then total the numerical columns.
Employee
Cumulative Pay
Pay subject to FICA- S.S.
6.2% (First $118,000)
Pay subject to FICA-Medicare 1.45%
Pay subject to FUTA Taxes 0.6% Pay subject to SUTA Taxes 5.4% (First $7,000)

Mary $6,800
Type answer here
Type answer here
Type answer here
Type answer here

Zoe $10,500
Type answer here
Type answer here
Type answer here
Type answer here

Greg $8,400
Type answer here
Type answer here
Type answer here
Type answer here

Ann $66,000
Type answer here
Type answer here
Type answer here
Type answer here

Tom $4,700
Type answer here
Type answer here
Type answer here
Type answer here

Totals
Type answer here
Type answer here
Type answer here
Type answer here


Answers

Employee                                 Mary      Zoe         Greg         Ann           Tom

Cumulative Pay                       $6,800   $10,500  $8,400    $66,000   $4,700

Pay subject to FICA S.S.         $421.60  $651.00  $520.80 $4092.00 $291.40
6.2%, (First $118,000)

Pay subject to FICA Medicare $98.60 $152.25    $121.80    $957.00    $68.15
1.45% of gross

Pay subject to FUTA Taxes      $40.80  $63.00     $50.40    $396.00  $28.20
0.6%

Pay subject to SUTA Taxes   $367.20  $567.00  $453.60  $3564.00 $253.80
5.4% (First $7000)

Totals                                     $928.20 $1,433.25 $1,146.60 $9,009.00 $641.55

Answer:

Employee                                 Mary      Zoe         Greg         Ann           Tom

Cumulative Pay                       $6,800   $10,500  $8,400    $66,000   $4,700

Pay subject to FICA S.S.         $421.60  $651.00  $520.80 $4092.00 $291.40

6.2%, (First $118,000)

Pay subject to FICA Medicare $98.60 $152.25    $121.80    $957.00    $68.15

1.45% of gross

Pay subject to FUTA Taxes      $40.80  $63.00     $50.40    $396.00  $28.20

0.6%

Pay subject to SUTA Taxes   $367.20  $567.00  $453.60  $3564.00 $253.80

5.4% (First $7000)

Totals                                     $928.20 $1,433.25 $1,146.60 $9,009.00 $641.55

Step-by-step explanation:

Suppose that 19 inches of wire costs 95 cents. At the same rate, how much (in cents) will 37 inches of wire cost?

Answers

0.95/19 = 0.05 cents per inch

37*0.05 = 1.85

it will cost $1.85

Help!
Write 0.78% as a decimal and as a fraction

A) 78; 39/500

B) 0.078; 39/50,000

C) 0.0078; 39/5,000

D) 0.78; 39/50

Answers

d 0.78 and 39/50 \ its logical

starting at home, luis traveled uphill to the hardware store for 30 minutes st just 8mph. he then traveled back home along the same path downhill at a speed of 24 mph. what is his average speed for the entire trip from home to the hardware store and back?

Answers

1.
The main formula we use is :

Distance traveled = average Speed * Time,

in short:    D = S * T

2.
"luis traveled uphill to the hardware store for 30 minutes at speed 8mph."

we have the speed and the time = 30 min = 1/2 h

so we can find distance:

D=ST=8 (mi/h) * 1/2 (h)  =  4 mi

3.
Now we have D, and the speed 24 mph, so we can find the time it takes Luis to travel back home:

D=S*T

T= D/S = 4 (mi) / 24 (mi/h) =1/6 h

4.

The total distance is D+D = 4 +4 = 8 (mi)

the total time is 1/2 +1/6 = 3/6 + 1/6 = 4/6 = 2/3 (h)

So we can find the average speed of the entire trip is:

S=8 / (2/3)= 8* (3/2)=4*3=12 (mph)


Answer : 12 mph 


The sales at a particular bookstore grew from $2090 million in 2000 to $3849 million in 2005. Find an exponential function to model the sales as a function of years since 2000. Give your answer using the form B=Boat

Answers

[tex]\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=I(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\to &2090\\ I=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\to &0\\ \end{cases} \\\\\\ 2090=I(1+r)^0\implies 2090=I\\\\ -------------------------------\\\\[/tex]

[tex]\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=I(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\to &3849\\ I=\textit{initial amount}\to &2090\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\to &\stackrel{2000-2005}{5}\\ \end{cases}[/tex]

[tex]\bf 3849=2090(1+r)^5\implies \cfrac{3849}{2090}=(1+r)^5\implies \sqrt[5]{\cfrac{3849}{2090}}=1+r \\\\\\ \sqrt[5]{\cfrac{3849}{2090}}-1=r\implies 0.129900823\approx r\implies 0.13\approx r\\\\ -------------------------------\\\\ A=2090(1+0.13)^t\implies \boxed{A=2090(1.13)^t}[/tex]

Write an algebraic equation for the following problem and then solve it.
The population of a country in 2015 was estimated to be 321.6321.6 million people. This was an increase of 22​% from the population in 1990. What was the population of the country in​ 1990?

Answers

let's say is the population in 1990 is "x".

well, in 2015, 25 years later, it ballooned to 321,6321.6, and we know that's 22% or 22/100 ( 0.22 ), more than 25 years ago.

if the amount on 1990 was "x", then 22% of "x" is just (22/100) * x, which is 0.22x.

so, whatever "x" may be, the sum of those two is 321,6321.6, thus

[tex]\bf 321,6321.6 = x + 0.22x\implies 321,6321.6 = 1.22x\\\\\\ \cfrac{321,6321.6}{1.22}=x[/tex]

Which of the following expressions represents a function?

x2 + y2 = 9
{(4, 2), (4, –2), (9, 3), (9, –3)}
x = 4
2x + y = 5

Answers

A. Not a function because it's a circle that doesn't pass the vertical line test

B. Not a function because we have x = 4 repeated more than once. Same for x = 9 as well.

C. Not a function. Any vertical line fails the vertical line test. Any vertical line is therefore not a function.

D. This is a function since it passes the vertical line test.

------------------------------------------------------

In summary, the final answer is choice D

D is the correct answer the other person who answered explains why.

a dime is flipped 3 times. What is the probability that TAILS occurred all 3 times?

Answers

1/2*1/2*1/2=1/8

Therefore, the probability of tails being occurred 3 times is 1/8.

Hope this helps!
For three tosses of the coin all the possible outcomes are:
.
H-H-H
T-H-H
H-T-H
H-H-T
T-H-T
T-T-H
H-T-T
T-T-T

These eight possible outcomes are the sample space.
To find the probability of tossing tails tree times look down the sample space list and find any outcome that has exactly two H's.
The possibilities are only T-T-T.
This means that one of the eight possible outcomes contain exactly three tails. Therefore,
the probability of throwing exactly two heads in three tosses of the coin is 1 out of 8,

convert to polar form y=3x^2

Answers

The polar form for the given expression is sin(θ)=3r−3rsin²(θ)

To convert the equation y = 3x² into polar form, we substitute[tex]\( x = r\cos(\theta) \) and \( y = r\sin(\theta) \)[/tex], where R is the radius and theta is the angle.

[tex]So, \( y = 3x^2 \) becomes:\[ r\sin(\theta) = 3(r\cos(\theta))^2 \][/tex]

Now, we can simplify this equation:

[tex]\[ r\sin(\theta) = 3r^2\cos^2(\theta) \]\[ r\sin(\theta) = 3r^2\cos^2(\theta) \]\[ \frac{r\sin(\theta)}{r^2} = 3\cos^2(\theta) \]\[ \frac{\sin(\theta)}{r} = 3\cos^2(\theta) \]\[ \frac{\sin(\theta)}{r} = 3(1 - \sin^2(\theta)) \]\[ \frac{\sin(\theta)}{r} = 3 - 3\sin^2(\theta) \]\[ \sin(\theta) = 3r - 3r\sin^2(\theta) \][/tex]

This equation describes the curve in polar coordinates.

1. Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x= 12.

y = -10 when x = 2

2. Graph the direct variation equation:

y=2x

Answers

[tex]\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \textit{\underline{y} varies directly with \underline{x}}\implies y=kx \\\\\\ \textit{we also know that } \begin{cases} y=-10\\ x=2 \end{cases}\implies -10=k2\implies \cfrac{-10}{2}=k \\\\\\ -5=k\qquad thus\qquad \boxed{y=-5x}\\\\ -------------------------------\\\\ \textit{what's \underline{y} when \underline{x} is 12?}\qquad y=-5(12)[/tex]

An arithmetic sequence is represented in the following table. Enter the missing term of sequence

Answers

In mathematics, numbered sequential patterns are distinguished as progressions. There are three types of progression: arithmetic, geometric and harmonic. Let's focus on the arithmetic progression.

The pattern in the arithmetic progression is the common difference, You will find that when you subtract two consecutive terms of the sequence, you would get a common difference. Let's investigate further:

28-44 = -16
12-28 = -16
-4-12 = -16

Thus, the common difference is -16. To know the last term, just simply add -16 to the very last known term. In this case, -4+-16 = -20. The answer is -20.

Answer:

The required 18th term of the given sequence will be -160

Step-by-step explanation:

The A.P. is given to be : 44, 28, 12, -4, ....

First term, a = 44

Common Difference, d = 28 - 44

                                       = -12

We need to find the 18th term of the sequence.

[tex]a_n=a+(n-1)\times d\\\\\implies a_{18}=44+(18-1)\times -12\\\\\implies a_{18}=44+ 17 \times -12\\\\\implies a_{18}=44-201\\\\\implies a_{18}=-160[/tex]

Hence, The required 18th term of the given sequence will be -160

at the beginning of the summer, Conan had $180 in the bank. Each week he deposits another $64 that he earns mowing lawns. Is his account balance proportional to the number of weeks since he started mowing lawns?

Answers

what's his account balance? give us a bit more information

Answer:

no, because the initial 180 gets in the way

Step-by-step explanation:

Suppose you value a special watch at $100. you purchase it for $75. on your way home from class one day, you lose the watch. the store is still selling the same watch, but the price has risen to $85. assume that losing the watch has not altered how you value it. what should you do?

Answers

I will search all the way back to class and if i couldn't find it i will buy a new one.

coz $10 is not a very big amount.

How do you solve 18-n divded by 2 (which is underneath the 18-n) is less than or equal to 6?

Answers

[tex]\dfrac{18-n}{2}\leq6\\ 19-n\leq12\\ n\geq7[/tex]

William invested $6000 in an account that earns 5.5% interest, compounded annually. The formula for compound interest is A(t) = P(1 + i)t.

How much did William have in the account after 6 years? (APEX)

Answers

[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+r\right)^{t} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$6000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\to &0.055\\ t=years\to &6 \end{cases} \\\\\\ A=6000(1+0.055)^6\implies A=(1.055)^6[/tex]

Answer:

William have $8273.057 in the account after 6 years.

Step-by-step explanation:

The given formula is [tex]A(t)=P(1+i)^t[/tex]

We have,

P = $6000

r = 5.5% = 0.055

t = 6

A =?

Substituting these values in the above formula to find A

[tex]A(t)=6000(1+0.055)^6\\\\A(t)=8273.057[/tex]

Therefore, William have $8273.057 in the account after 6 years.

You invest 5000 in an account at 5.5% per year simple intrest how much will you have in the account at the beginning of the 6th year

Answers

I=Prt  Simple interest is the principle times the rate times the time.

The balance will be the principle plus that interest so:

B=P(1+rt), since P=5000 and the rate is 0.055

B=5000(1+0.055t) so at the beginning of the sixth year you will have earned five years of interest.

B=5000(1+0.055(5))

B=$6375

When would it be useful to sort data in descending order? why?

Answers

when seeing who has the highest score on a test

A student ID number is a letter of the alphabet followed by 2 digits. How many different IDs are possible if the digits can be repeated?

Answers

Final answer:

There are 2600 different possible student IDs when a student ID consists of one letter followed by two digits that can repeat, calculated as 26 possible letters multiplied by 10 possible digits for each of the two digit positions.

Explanation:

The question asks how many different student IDs are possible if an ID consists of a letter followed by two digits, with the digits being allowed to repeat. To calculate the possible combinations, we multiply the number of options for each component of the ID. There are 26 letters in the alphabet and 10 possible digits (0-9) for each of the two positions that follow the letter, allowing for repetition.

The calculation is therefore 26 letters × 10 digits × 10 digits = 2600 possible combinations. Each component is independent of the others, so this follows the fundamental principle of counting in combinatorics.

Events A and B are mutually exclusive with P(C) = 0.3 and P(B) = 0.2. Then P(Bc) =

Answers

If 2 events are mutually exclusive then probability they both occur is 0.
Final answer:

The probability of the complement of event B, denoted as Bc, is 0.8.

Explanation:

To find the probability of the complement of an event B, denoted as Bc, we can use the formula: P(Bc) = 1 - P(B). Given that events A and B are mutually exclusive, P(B) = 0.2. Therefore, P(Bc) = 1 - 0.2 = 0.8.

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Melvin has game and education apps on his tablet. He noticed that he has 3 game apps for every 2 education apps. Which of the following is another way to write this ratio?

Answers

The ratio of game apps to education apps is 3:2

A large tank is filled to capacity with 600 gallons of pure water. brine containing 4 pounds of salt per gallon is pumped into the tank at a rate of 6 gal/min. the well-mixed solution is pumped out at the same rate. find the number a(t) of pounds of salt in the tank at time t.

Answers

If [tex]A(t)[/tex] is the amount of salt in the tank at time [tex]t[/tex], then the rate at which the amount of salt in the tank changes is given by

[tex]\dfrac{\mathrm dA(t)}{\mathrm dt}=\dfrac{4\text{ lbs}}{1\text{ gal}}\dfrac{6\text{ gal}}{1\text{ min}}-\dfrac{A(t)\text{ lbs}}{600\text{ gal}}\dfrac{6\text{ gal}}{1\text{ min}}[/tex]
[tex]\dfrac{\mathrm dA}{\mathrm dt}=24\dfrac{\text{lb}}{\text{min}}-\dfrac{A(t)}{100}\dfrac{\text{lb}}{\text{min}}[/tex]

Let's drop the units for now. We have

[tex]\dfrac{\mathrm dA(t)}{\mathrm dt}+\dfrac{A(t)}{100}=24[/tex]
[tex]e^{t/100}\dfrac{\mathrm dA(t)}{\mathrm dt}+e^{t/100}\dfrac{A(t)}{100}=24e^{t/100}[/tex]
[tex]\dfrac{\mathrm d}{\mathrm dt}\left[e^{t/100}A(t)\right]=24e^{t/100}[/tex]
[tex]e^{t/100}A(t)=\displaystyle24\int e^{t/100}\,\mathrm dt[/tex]
[tex]e^{t/100}A(t)=2400e^{t/100}+C[/tex]
[tex]A(t)=2400+Ce^{-t/100}[/tex]

We're given that the water is pure at the start, so [tex]A(0)=0[/tex], giving

[tex]A(0)=0=2400+Ce^{-0/100}\implies C=-2400[/tex]

So the amount of salt in the tank (in lbs) at time [tex]t[/tex] is

[tex]A(t)=2400\left(1-e^{-t/100}\right)[/tex]
Final answer:

To find the amount of salt in the tank at a given time, one can use the equation a(t) = Q - Qe^(-rt). In this case, Q (the quantity of salt at a steady state) equals the pump rate multiplied by the salt concentration (24lb/min), and r (the rate of inflow and outflow of the solution) is the rate at which water is pumped out divided by the volume of the tank (1/100 per min). Substituting these values into the equation gives the salt content at any given time.

Explanation:

The quantity of salt in the tank at any given time can be determined by the equation of the form a(t) = Q - Qe^(-rt), in which Q is the quantity of salt that would be in the tank at a steady state (i.e., if enough time had passed that the quantity of salt in the tank stopped changing), r is the rate of inflow and outflow of the solution, and t is the time at which you're trying to determine the number of pounds of salt in the tank.

In this case, Q = rate of inflow x concentration of the inflow, which is 6 gal/min x 4 lb/gal = 24 lb/min. This amount is reached after a sufficient amount of time has passed and the tank has reached a steady state.

The rate, r, is the rate at which the water is pumped out of the tank. In this situation, that's 6 gallons per minute. Since there are 600 gallons of water in the tank at the start, r = 6 gal/min ÷ 600 gallons = 1/100 min^-1.

Therefore, the number of pounds of salt in the tank at any time t is a(t) = Q - Qe^(-rt) = 24 lb/min - 24 lb/min * e^[-(1/100 min^-1)*t].

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The compound probability of two events, E and F 1/8 , is ; the probability of E is 1/2 and of F is 1/3 . In two or more complete sentences, explain why E and F are not independent.

Answers

If they are independent then it should hold true that P(A) X P(B) = P(A and B)
This is not the case for F and E in the questions so therefore they are independent.
Answer:

Event E and event F are not independent because:

        [tex]P(E\bigcap F)\neq P(E)\times P(F)[/tex]

Step-by-step explanation:

We know that two event A and event B are said to be independent if:

         P(A∩B)=P(A)×P(B)

Here we have two events as E and F such that:

[tex]P(E\bigcap F)=\dfrac{1}{8}[/tex]

[tex]P(E)=\dfrac{1}{2}[/tex]

and [tex]P(F)=\dfrac{1}{3}[/tex]

This means that:

[tex]P(E)\times P(F)=\dfrac{1}{2}\times \dfrac{1}{3}\\\\\\i.e.\\\\\\P(E)\times P(F)=\dfrac{1}{6}\neq P(E\bigcap F)[/tex]

        Hence, the events E and F are not independent.

Every evening Jenna empties her pockets and puts her change in a jar. At the end of the week she counts her money. One week she had 38 coins all of them dimes and quarters. When she added them up she had a total of $6.95

Answers

d = dimes

q = quarters

d+q = 38 coins

q=38-d

0.25q + 0.10d=6.95

0.25(38-d)+0.10d=6.95

9.5-0.25d+0.10d=6.95

-015d=-2.55

d=-2.55/-0.15 = 17

q=38-17 =21

21*0.25 =5.25

17*0.10 = 1.70

5.25+1.70 = 6.95

 she had 21 quarters and 17 dimes

Answer:

She had 17 dims and 21 quarters to make $6.95.

Step-by-step explanation:

Given : Every evening Jenna empties her pockets and puts her change in a jar. At the end of the week she counts her money. One week she had 38 coins all of them dimes and quarters.

To find : When she added them up she had a total of $6.95?

Solution :

Let d be the dims and q be the quarters.

She had 38 coins.

i.e. [tex]d+q=38[/tex] ......(1)

The value of d is 0.10 and q is 0.25.

The total she had of $6.95

i.e. [tex]0.10d+0.25q=6.95[/tex]  .......(2)

Solving (1) and (2),

Substitute d from (1) into (2)

[tex]0.10(38-q)+0.25q=6.95[/tex]

[tex]0.10\times 38-0.10q+0.25q=6.95[/tex]

[tex]3.8+0.15q=6.95[/tex]

[tex]0.15q=6.95-3.8[/tex]

[tex]0.15q=3.15[/tex]

[tex]q=\frac{3.15}{0.15}[/tex]

[tex]q=21[/tex]

Substitute in equation (1),

[tex]d+21=38[/tex]

[tex]d=38-21[/tex]

[tex]d=17[/tex]

Therefore, She had 17 dims and 21 quarters to make $6.95.

If you toss six fair coins, in how many ways can you obtain at least two heads?

Answers

1/3 that is the correct answer

What is 243.875 rounded to the nearest tenth,hundreth,ten,and hundred?

Answers

tenth: 243.9
hundreth: 243.88
ten: 240
hundred:200

hope this helps

The marching band is selling cases of fruit for $13 per case. (a) Write an algebraic expression for the cost of f cases of fruit. (b) Evaluate the expression for 250 cases.

Answers

(a) Each case of fruit costs $13
∴ $13 × f cases
= 13f

(b) Since f = 250
= 13(250)
= $3250

An algebraic expression for the cost of f cases of fruit will be (a) z = 13f and the cost for 250 cases will be (b) $3250.

How to form an equation?

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say the cost of the fruit is z

Given,

The marching band is selling cases of fruit for $13 per case.

So for f cases of fruit

z = 13f

And cost of 250 cases = z = 13(150) = $3250

Hence, the algebraic expression for the cost of f cases of fruit will be z = 13f and the cost for 250 cases will be $3250.

For more about the equation

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