Mathematics High School

The distance between two cities on a map is 3 1/2 inches. The actual distance between the two cities is 28 miles.
a. What is the scale used on the map?
b. If the scale on a different map of the same area is inch = 1 mile, how separate the same two cities?

Answers

Answer 1
part A= 3.5 inches is equal to 8 miles

Part B= if 1 inch is 1 miles then on this map the cities are 28 inches apart.

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Related Questions

Complete the general form of the equation of a sinusoidal function having an amplitude of 1, a period of pi/2 , and a vertical shift up 3 units.

Answers

Sinusoidal equations are trigonometric functions involving sine and cosine functions. Graphically, they look like wave patterns having amplitudes and periods. The general form of a sinusoidal equation is 

y = A sin(Bx + C) + D

where

A = amplitude
B = frequency
C = shift on starting angle
D = shift of wave on the y-axis

From the given problem, A = 1 and D = 3. There is no value for C because there is no mention of any shift in angle. About the frequency, you can obtain this by getting the reciprocal of the period. Thus, B = 2/π. The complete equation is

y = sin(2x/π) + 3

Answer:

y = sin(4x) + 3

Step-by-step explanation:

y = Asin(Bx + C) + D

A is amplitude = 1

B = 2pi/period = 2pi / (pi/2) = 4

C does not mention.

D: shift up or down = 3

=> y = sin(4x) + 3

A parachutist's speed during a free fall reaches
207
kilometers per hour. What is this speed in meters per second? At this speed, how many meters will the parachutist fall during 5 seconds of free fall?

Answers

1) Convert using online calculators.
    207km/h = 57.5m/s

2) Use the rate from question 1.
    Make an equation and cross multiply to solve for x.
    57.5/1 = x/5
    x = 57.5(5)
    x = 287.5
    So he fell 287 meters in just 5 seconds

What two steps are necessary to put this equation into standard form?
x^2-3x+27=8x-3

A. Add 3 to both sides and subtract 8x from both sides.
B. add 3 to both sides and add 8x from both sides.
C. the equation is already in standard form.
D. Subtract 3 from sides and subtract 8x from both sides.

Answers

x² - 3x + 27 = 8x - 3     аdd 3 to both sides  ⇒
           + 3          + 3
---------------------------
x² - 3x + 30 = 8x         subtract 8x from both sides ⇒
    - 8x          - 8x
--------------------------
x² - 11x + 30 = 0    ←  standard form


A. Add 3 to both sides and subtract 8x from both sides.

At maximum speed, an airplane travels 2,400 miles against the wind in 6 hours. Flying with the wind, the plane can travel the same distance in 5 hours. Let x be the maximum speed of the plane and y be the speed of the wind. What is the speed of the plane with no wind?

Answers

x - y  = 2400/6 = 400        where x = speed of plane and y = speed of wind.

x + y =  2400/5 = 480          - flying with the wind

adding the 2 equations 
2x = 880
x = 440

Speed of the plane with no wind = 440 mph

Answer: The speed of the plane with no wind is 440 miles per hour.

Step-by-step explanation:

Let the maximum speed of the plane be 'x'.

Let the maximum speed of the wind be 'y'.

Since we have given that an airplane travels 2400 miles against the wind in 6 hours.

As we know that

Downstream is given by

[tex]x+y=\dfrac{2400}{6}=400--------------(1)[/tex]

Since we have also given that flying with the wind, the plane can travel the same distance in 5 hours.

As we know tha t

Upstream is given by

[tex]x-y=\dfrac{2400}{5}=480-------------------(2)[/tex]

We just need to find the speed of the plane with no wind.

Using the elimination method,

[tex]x+y=400\\\\x-y=480\\\\-----------------------------\\\\2x=880\\\\x=\dfrac{880}{2}\\\\x=440[/tex]

Hence, the speed of the plane with no wind is 440 miles per hour.

Darien ordered soda for $2.75, a sandwich for $8.50, and a dessert for $3.85. Sales tax was $1.15. Use mental math to find the total amount of the bill. Explain

Answers

What I would do is start with the price of the dessert and the sales tax $3.85+ $1.15= $5. I started with this because when you add the cents they equal a dollar which makes it easier to continue.


Then I would add the 2.75. This would be 7.75.


Then add 7.75 + 8.50. To simplify this, you can add 7 + 8, then .75+ .50

Which would equal 15 + 1.25 + 16.25

This question is based on the mental math. Therefore, the total amount of bill is  $16.25.

Given:

Darien ordered soda for $2.75, a sandwich for $8.50, and a dessert for $3.85. Sales tax was $1.15.

We need to determined the  total amount of the bill.

Let  start with the price of the dessert and the sales tax $3.85+ $1.15= $5.  

Now,  added 2.75  to $5 .

We get,  

$2.75 + $5 = $ 7.75

Then, add 7.75 + 8.50.

We get,

= $16.25

Therefore, the total amount of bill is  $16.25.

For further details, please prefer this link:

https://brainly.com/question/2017990

If you have 5 distinct positive integers and the median is 17 and the mean is 12, what are the 5 numbers? How do you know for sure? Can you find 5 distinct positive integers with a median of 17 and a mean of 10? What whole-number means will work for 5 distinct positive integers with a median of 17? What medians will work for 5 distinct positive integers with a mean of 12?

Answers

1) Part 1: 5 distinctive positive integers with median 17 and mean 12

If the median is  17, that means that one number is 17, two numbers are greater than 17 and two numbers are less than 17.

Remember that the five numbers are distint positive integers.

If the mean is 12, that means that the sum of the five numbers is 12 * 5 = 60

The minimum values could be 1 and 2, with which the partil sum of the three first terms would be 1 + 2 + 17 = 20.

So, the partial sum of the two greater terms is 60 - 20 = 40.

That leads to these possibilities:

1, 2, 17, 18, 22
1, 2, 17, 19, 21

If the two smaller terms are 1 and 3, the possibilities are:

1, 3, 17, 18, 21
1, 3, 17, 19, 20.

If the two smaller terms are 2 and 3, the only possibility is:

2, 3, 17, 18, 20

If the smaller terms are 1 and 4, the only possibility is

1, 4, 17, 18, 20

Other options are:

1, 5, 17, 18, 19

2, 4, 17, 18, 19

You can realize that you cannot use other set of numbers.

2) Part 2: five distinctive numbers with median 17 and mean 10.

sum of the five numbers = 5 * 10 = 50

Given that 17 + 18 + 19 = 54, it is not possible to find those five distinctive numbers.

3) Part 3: What whole-number means will work for 5 distinctive integers with a median of 17.

=>the minimum whole-number means that will work is the whole number equal or greater than [1+2+17+18+19] / 5 = 11.4 => 12.

So, the whole-number means that will work are 12 or more.

4) Part 4. What medians will work for 5 distinctive positive integers with a mean of 12:

total sum = 5*12 = 60.

The smallest median would be 3, because the smaller values would be 1 and 2. The highest median would be.

Also, 1 + 2 = 3 => the median + the two greatest values = 60 - 3 = 57.

=> 18, 19, 20

=> 1, 2,18, 19, 20

So the median has to be between 3 and 18, inclusive.

Molly earns a rebate each month on her movie tickets and books. She earns $0.25 for each movie ticket and $2 for each book. Last month Molly purchased 4 movie tickets and earned $17. Part A: Create an equation that will determine the number of books she purchased. (3 points) Part B: Solve this equation justifying each step with an algebraic property of equality. (6 points) Part C: How many books did Molly purchase last month? (1 point)

Answers

r(m,b)=0.25m+2b  (rebate as a function of movie tickets, m, and books, b.

r(4,b)=0.25(4)+2b=17

1+2b=17 subtract 1 from both sides

2b=16  divide both sides by 2

b=8.

So Molly purchased 8 books last month.

You have ten fewer quarters than dimes and 5 fewer nickles than quarters. The total value of the coins is $4.75. How many quarters, nickles, and dimes do you have?

Answers

0.05n + 0.10d + 0.25q = 4.75
d = q + 10
n = q - 5

0.05(q - 5) + 0.10(q + 10) + 0.25q = 4.75
0.05q - 0.25 + 0.10q + 1 + 0.25q = 4.75
0.40q + 0.75 = 4.75
0.40q = 4.75 - 0.75
0.40q = 4
q = 4 / 0.40
q = 10 <=== quarters

d = q +10
d = 10 + 10
d = 20 <== dimes

n = q - 5
n = 10 - 5
n = 5 <== nickels


q=d-10, n=q-5, Solve the first for d and you have:

d=q+10 and n=q-5

.25q+.1d+.05n=4.75, then using d and n from above, this becomes:

.25q+.1(q+10)+.05(q-5)=4.75  perform indicated multiplications

.25q+.1q+1+.05q-.25=4.75  combine like terms

.4q+.75=4.75  subtract .75 from both sides

.4q=4  divide both sides by .4

q=10, since d=q+10 and n=q-5

d=20, n=5

So you have 10 quarters, 20 dimes, and 5 nickels.


In the formula that gives the circumference of a circle, which quantity is multiplied by 2Ï€ ?


A. Diameter
B. Radius
C. Area
D. Circumference

Answers

The circumference of an object is the total length of the line that forms the object. For a circle, the formula is:

C = 2 π r

We can see that in the formula, what is multiplied by 2 π is the radius (r).

Therefore the answer to this is

B. Radius

If​ (x,y) are the coordinates of a point p in the​ xy-plane, then x is called the​ _______ of p and y is the​ _______ of p.

Answers

The first coordinate of a point P is called the x-coordinate of P, 

and the second coordinate of a point P is called the y-coordinate of P.

So 

"x is called the​ ___x-coordinate____ of p and y is the​ ___y-coordinate____ of p."


Answer:

x-coordinate
y-coordinate
Final answer:

In a Cartesian coordinate system, the x-coordinate represents the horizontal position of a point, and the y-coordinate represents the vertical position of a point.

Explanation:

In a Cartesian coordinate system, the x-coordinate represents the horizontal position of a point, and the y-coordinate represents the vertical position of a point.

For example, in the point (3, 5), the x-coordinate is 3 and the y-coordinate is 5.

Together, the x and y coordinates specify the precise location of a point in the xy-plane.

what is the distance between the points (3,7) and (15,16) on a coordinate plane?

Answers

distance = Sqrt((x2-x1)^2 +(y2-y1)^2)


15-3 =12

16-7=9

12^2 = 144

9^2 = 81

144+81 = 225

square root of 225 = 15

 the distance is 15

Use the distance formula: [tex]distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

[tex]\sqrt{(15 - 3)^2 + (16 - 7)^2} \\ \\ \sqrt{12^2 + 9^2} \\ \\ \sqrt{144 + 81} \\ \\ \sqrt{225} \\ \\ 15[/tex]

So, 15 units is the answer.

Solve each system:

80x+60y=85
100x-40y=20

Answers

y = 3/4 (fraction)
x= 1/2 (fraction)

In a certain set of numbers, 12.5 is 1.5 units of standard deviation above the mean, and 8.9 is 0.5 units of standard deviation below the mean. what is the mean of the set?

Answers

Standard deviation is a statistical tool that is used to measure the spread or variation of a certain set of data. It is the square root is the variance. It determines the difference of each data relative to the mean. To calculate the mean, we do as follows:

12.5 is 1.5 units of standard deviation
So the value for the upper standard deviation would be:
12.5 - 1.5 = 11

8.9 is 0.5 units of standard deviation
So the value for the lower standard deviation would be:
8.9 + 0.5 =  9.4

So, the range of the standard deviation would be about 11 - 9.4 = 1.6 units. The mean would be located at the center of this range which is 0.8 from each of the values. Therefore, the mean would be 11-0.8 = 10.2.

Can someone help me figure this out: Factor 12y^2-27? I keep getting the steps confused.

Answers

Factor out the gcf first.

3(4y^2-9)

The binomial inside is a perfect square so keep factoring.

3(2y+3)(2y-3)

The pair of binomials cannot be further factored so stop there.

Answer for lady stole 100 from owner she bought 70 dollars worth of products and got back 30 how much did the owner lose

Answers

Answer: The total loss incurred by the store owner is 100$.

At first look, the answer might seem to be 200$ or 130$, but that's not the correct one. The explanation is below:

The lady stole 100$ from the owner therefore loss incurred is 100$.

The lady went back to the store  and:

Step 1 - The lady hands back the 100$ to the store owner. Loss incurred is back to 0$.

Step 2 - The store owner hands over merchandise worth 70$. Loss Incurred is now 70$.

Step 3 - The store owner hands over 30$ worth of change. Loss Incurred is (70 + 30)$ = 100$

The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4.
The four angles of the quadrilateral are °, °, °, and °, respectively.

Answers

Answer:

The four angles of the quadrilateral are 30°, 60°, 150°, and 120°, respectively.

Step-by-step explanation:

Given  : The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4.

To find : The four angles of the quadrilateral are °, °, °, and °, respectively.

Solution : We have given that  The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4.

Let the angle of the quadrilateral is x

Then all the  angles are  x  , 2x , 5x ,4x

Complete angle formed by circle is 360 °

Sum of all the angle are 360

x + 2x + 5x + 4x = 360 .

12 x = 360 .

On dividing both sids by 12.

x = 30 .

Then

2x =  60

5x = 5 * 30 = 150 .

4x = 4 *30 = 120 .

Therefore, The four angles of the quadrilateral are 30°, 60°, 150°, and 120°, respectively.

Answer:

for plato users the answers are 45,75,135,105

Step-by-step explanation:

Solve for x:p=12-x/1000

Answers

p=12-x/1000
1000p=12-x
1000p-12=-x
x=12-1000p

4⋅10 ​6 ​​ 4, dot, 10, start superscript, 6, end superscript is how many times as large as 1\cdot10^41⋅10 ​4 ​​ 1, dot, 10, start superscript, 4, end superscript?

Answers

The given problem is very confusing since it was copy pasted directly from the source so the equations look scrambled and plus it was one words. After my own translation, I believe the given numbers are:

4 ⋅ 10^6

and

1 ⋅ 10^4

The symbol ⋅ means that the two numbers are multiplied while the symbol ^ means an exponent of. Now we are asked to find how much the 1st number is larger than the 2nd number. To solve this, we simply have to divide the bigger number by the smaller number. Since 4 ⋅ 10^6 has bigger exponent than 1 ⋅ 10^4 then it is the bigger number.

Ratio = 4 ⋅ 10^6 / 1 ⋅ 10^4

Ratio = 4 ⋅ 10^2 = 400

Therefore 4 ⋅ 10^6 is 400 times bigger than 1 ⋅ 10^4.

 

Answer:

400 times

Having knowledge about potencies we will find that the final value will be greater than 400 times.

Recalling the properties of powers we find:

Multiplication of powers with the same base.Division of powers with the same base.Power of potency. Potency of a product.Quotient power.

Then we can write the two given powers as:

[tex]4 *10^6\\1 * 10^4[/tex]

We know that we have a multiplication and a power, so solving for each of them, we find:

[tex]Ratio = 4 *10^6 / 1 * 10^4\\Ratio = 4 * 10^2 = 400[/tex]

See more about power at brainly.com/question/1618040

3/8 of people at a fun fair were children 3/4 of the remaining people were men there were 140 more children than women how many people went to the fun fair

Answers

The fraction of children was 3/8
The remaining fraction was 1-3/8=5/8
the fraction of men was 3/4*5/8=15/32
the fraction of women=1/4*5/8=5/32
given that the there were 140 more children than women, the fraction represented by this is:
3/8-5/32
=7/32
thus the total number of people who were there was:
1/(7/32)*140
=640
The answer is 640

Ivanna deposits $600 into an account that pays simple interest at a rate of 3% per year. How much interest will she be paid in the first 2 years?

Answers

Given here,

Principle [P] = $600

Rate [R] = 3

Time [T] = 2

We know,

[tex]Simple Interest = \frac{Principle * Rate * Time}{100} [/tex]

[tex]= \frac{600*3*2}{100} = 36[/tex]


What would you look for in a word problem that might indicate that you need to use an absolute value inequality?

Answers

The words "magnitude" and "size" would suggest absolute value. The phrases "at most" and "at least" would suggest inequalities. The words "maximal" and "minimal" may suggest inequalities, depending on the context.

A rope 10 feet long is cut into two pieces. One piece is used to form a circle and the other used to form a square. Find a function representing the area of both square and circle as a function of the length of one side of the square.

Answers

10-x=C=2πr

(10-x)/(2π)=r

A=π(100-20x+x^2)/(4π^2)

A=(x^2-20x+100)/(4π)

...

x/4=s, x=4s  using this in the area of a circle we get:

A=(16s^2-80s+100)/(4π)

A=(4s^2-20s+25)/π

And of course the area of a square is s^2

A=(4s^2+πs^2-20s+25)/π

The functions representing the areas of the square and circle as functions of the length of one side of the square x are [tex]\[ A_s(x) = x^2 \][/tex] and [tex]\[ A_c(x) = \frac{(10 - x)^2}{4\pi} \][/tex] respectively.

Let's denote:

- [tex]\( x \)[/tex] as the length of one side of the square (in feet).

- [tex]\( 10 - x \)[/tex] as the length of the rope used to form the circle.

1. Area of the Square [tex](\( A_s \))[/tex]:

The area of a square is given by the formula: [tex]\( A_s = x^2 \)[/tex].

2. Area of the Circle [tex](\( A_c \))[/tex]:

The circumference of the circle, formed by the rope, is used to find the radius [tex]\( r \)[/tex] of the circle:

[tex]\[ \text{Circumference} = 2\pi r = 10 - x \][/tex]

Solving for [tex]\( r \)[/tex], we get: [tex]\( r = \frac{10 - x}{2\pi} \)[/tex]

The area of the circle is then given by the formula: [tex]\( A_c = \pi r^2 \)[/tex].

Substituting the value of [tex]\( r \)[/tex], we get:

[tex]\[ A_c = \pi \left(\frac{10 - x}{2\pi}\right)^2 \][/tex]

[tex]\[ A_c = \frac{(10 - x)^2}{4\pi} \][/tex]

Martin bought 30 shares of microsoft at the close price of $24.53. in a few years, martin sells all of his shares at $33.71. how much money did martin make?

Answers

The answer is $275.40

Answer:

Money that Martin make is $ 275.9

Step-by-step explanation:

Number of shares Martin Bought = 30

Cost Price of a share = $ 24.53

Total Cost price of all share = 30 × 24.53 = $ 735.9

Selling Price of a share = $ 33.71

Total Selling Price of all shares = 30 × 33.71 = $ 1011.3

Profit money that Martin make = 1011.3 - 735.9 = $ 275.9

Therefore, Money that Martin make is $ 275.9

Four times the complement increased by forty-six is the same as twice the supplement. find the measures of the angle, the complement, and the supplement

Answers

x = measure of anglecomplement: 90 -x
supplement: 180 - x

Four times the complement increased by forty-six = 4(90-x) + 46
twice the supplement: 2(180 - x)
so
Four times the complement increased by forty-six is the same as twice the supplement

 4(90-x) + 46  = 2(180 - x)
360 - 4x + 46 = 360 - 2x
                 2x = 46
                   x = 23

answer

measure of angle x = 23
measure of complement = 90 - 23 = 67
measure of supplement = 180 - 23 = 157

find the GCF 12, 18, 24

Answers

12= 2*2*3

18= 2*3*3

24= 2*2*2*3

The GCF would be equal to the product of all common multiples.

2*3=6

Final answer: 6
Hi, your answer would be 6. Hoped I helped!!!!!!

A bag contains 7 red marbles, 8 blue marbles, and 9 green marbles. What is the probability of choosing a blue marble when one marble is drawn?

Answers

Final answer:

The probability of choosing a blue marble from the bag is 1/3.

Explanation:

The probability of choosing a blue marble can be calculated by dividing the number of blue marbles by the total number of marbles in the bag. In this case, there are 8 blue marbles out of a total of 7 + 8 + 9 = 24 marbles.



So, the probability of choosing a blue marble is:



P(Blue Marble) = Number of Blue Marbles / Total Number of Marbles = 8 / 24 = 1/3

Final answer:

The probability of choosing a blue marble when one marble is drawn from the bag is 1/3 or approximately 0.333.

Explanation:

To find the probability of choosing a blue marble when one marble is drawn from a bag, we need to determine the number of favorable outcomes (blue marbles) and divide it by the total number of possible outcomes (all the marbles).

In this case, there are 8 blue marbles out of a total of 7 red + 8 blue + 9 green = 24 marbles. So the probability of choosing a blue marble is 8/24, which simplifies to 1/3 or approximately 0.333.

Therefore, the probability of choosing a blue marble when one marble is drawn is 1/3 or approximately 0.333.

What are the solutions of the equation 9x^4 – 2x^2 – 7 = 0? Use u substitution to solve.

Answers

[tex]9x^4 - 2x^2 - 7 = 0 \\ \text{substitution: } x^2=t, \ \ t\ \textgreater \ 0\\ 9t^2-2t-7\ \textgreater \ 0 \\ D=b^2-4ac=(-2)^2-4*9*(-7)=4+252 = 256 \\ t_{1,2}= \frac{-bб \sqrt{D} }{2a}= \frac{2б 16 }{18} \\ t_1=- \frac{14}{18} \ \ \ \ \O \\ \boxed{t_2=1} \\ \\x^2=1\\x=б \sqrt{1} \\ x=б1 [/tex]

Answer: x=-1, x=1

Zoey put a $1040 item on layaway by making a down payment of 13% of the purchase price. How much does she have left to pay after making the down payment?
A.$80
B.$135.20
C. $1040.00
D. $904.80

Answers

The amount of the down payment is
1,040×0.13=135.2

So the amount she has to pay after making the down payment is
1,040−135.2=904.8

It's d

Downpayment is the percent amount paid from a sum  of money. The amount left after the downpayment is  $904.80

Downpayment on a price

Downpayment is the percent amount paid from a sum  of money. If Zoey put a $1040 item on layaway by making a down payment of 13% of the purchase price, the amount he have left is;

Amount left = (100 - 13)% * 1040

Amount left .= 87% of 1040

Amount left = 0.87 * 1040

Amount left =  $904.80

Hence the amount left after the downpayment is  $904.80

Learn more on downpayment here: https://brainly.com/question/26173748

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At the beginning of the month a store had a balance of −$554. During the month the store lost another $600. What is the current balance?

Answers

$-1,154. All you have to do is subtract 600 from -554.
$-554 - $600 = $-1,154
So the stores current balance is $-1,154.
Please mark brainliest and have an amazing day.

How do you factor the quadratic equation 36^2= 25

Answers

This calculates to 1,296 = 25 which it is NOT.
Do you have the question typed correctly?

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