A route from point A to point B. 1 inch on the map equals 25 miles.

Manuel is leaving Boston to go on a hike at Mt. Monadnock, in New Hampshire. He mapped out a route with the map scale of 1 in. = 25 mi and found the total distance on the map to be about 3.2 inches. What is the actual distance Manuel will travel?

Answer:

120°

Step-by-step explanation:

A sector of a circle is the portion or region of a circle enclosed by two radii and an arc. The perimeter of a the sector of a circle is given by the formula:

Perimeter of sector = [tex]\frac{\theta}{360} *2\pi r[/tex] + 2r

Where θ is the angle which forms the sector and r is the radius of the circle.

Given that Perimeter of sector = 57.32 cm, radius (r) = 14 cm, we can find the angle θ using:

Perimeter of sector = [tex]\frac{\theta}{360} *2\pi r[/tex] + 2r

[tex]57.32=\frac{\theta}{360} *2\pi *14+2(14)\\\\57.32-28=\frac{\theta}{360} *2\pi *14\\\\29.32=\frac{\theta}{360} *2\pi *14\\\\ \frac{\theta}{360}=\frac{29.32}{2\pi *14} \\\\\frac{\theta}{360}=0.33\\\\\theta=120^o[/tex]

Answer: 6.68km/litre

Step-by-step explanation:

Distance(d) = 187km ( to 3 significant figures)

Petrol(p) = 28litres ( to 2 significant figures)

A number, x, rounded to 1 significant figure is 200

Write down the error interval for x

Calculating the lower and upper bound for both 'd' and 'p'

Upper bound 'd' = 187.5km

Lower bound 'd' = 186.5km

Upper bound 'p' = 28.5km

Lower bound 'p' = 27.5km

Therefore,

Petrol consumption (C) = d/p

Upper C = 187.5 / 28.5 = 6.57894

Lower C = 186.5 / 27.5 = 6.781818

Accuracy answer for C = (6.57894 + 6.781818) / 2 = 6.680379

= 6.68km/ litre ( to 3 significant figures)

To achieve a reasonable level of accuracy, the upper and lower bounds of P and D was used to calculate C, which was then averaged.

Using 3 significant figures ensure that we capture the C better, instead of early rounding.

Answer:

mark of the fifth exam = 60

Step-by-step explanation:

Mean = sum of all marks / number of exam

Mean = 70

Number of exam = 5

Let x =

Mean = sum of all marks / number of exam

70 = (65 + 80 + 76 + 69 + x) / 5

Cross product

70 × 5 = (290 + x)

350 = 290 + x

350 - 290 = x

x = 60

mark of the fifth exam = 60

Answer:

the answer is b

Step-by-step explanation:

12:

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

Given that,

Initial cost of a t-shirt = $30

Final cost of a t-shirt = $37.50

We need to find percent of change. The percentage change in any value is given by :

[tex]\%=\dfrac{\text{final value-initial value}}{\text{initial value}}\times 100\\\\=\dfrac{37.5-30}{30}\times 100\\\\=25\%[/tex]

Hence, the percentage error is 25%.

Answer:s=10.50 and p=27

Step-by-step explanation:

Answer:

I would need to know the number of radios she made each day.

Step-by-step explanation:

lets say she assembled 2 radios a day, which means we would do 0.54 x 2 (that would be 1.08) and then times it by 6 ***not incuding sunday***

you would get $6.48

then for sunday we would do 0.62 x 2 (that would be 1.24) .

now we add 6.48 and 1.24 to get $7.72 a week.

Answer:

n = 0.8

Step-by-step explanation:

3n + 3 = 5.4

-3 form each side

3n=2.4

÷3 for each side

n=0.8

Answer:

0.8

Step-by-step explanation:

3(n+1)=5.4

Divide both sides by 3

3(n+1)/3 = 5.4/3

simplify

n+1=1.8

subtract 1 from both sides

n+1-1=1.8-1

N=0.8

Answer:

(4, 22)

Step-by-step explanation:

y = 5x + 2

y  = 3x + 10

Since both equations are equal to y, we can have both equations equal to each other).

5x + 2 = 3x + 10

5x + 2 - 3x - 2 = 3x + 10 - 3x - 2

5x - 3x = 10 - 2

2x = 8

2x/2 = 8/2

x = 4

(Substitute the x value to any equation to solve for y).

y = 5x + 2

y = 5(4) + 2

y = 20 + 2

y = 22

So, the answer is (4, 22).

Hope this helped! <3

Answer:

The measure confirming that PQRS would be 25

Step-by-step explanation:

It's easier if you draw it down.

1. We need to make this shape a parallelogram and the way we will do that is by making angle Q and angle S the same, because in parallelograms those opposite angles are required to be the same.  

                             \

                        155 \

P \ -------------------------\ Q

    \                         25 \

      \                               \     so that's your shape  

   S   \______________\ R

2.We were given that the exterior angle of Q measures 155, and since exterior and interior angles combined make 180, then we can assume that the interior angle of Q is 25.

3. As mentioned before, in a parallelogram, opposite angles are the same and  therefore PSR (which is just asking for the middle letter, S) is equal to 25 because Q is also 25.  

Answer: i think its c

Step-by-step explanation:

Answer= s > 10/2

s > -10/-2

s > 10/2

Answer:

Step-by-step explanation:

The key to answering this is to know that the only time you'll change the direction of the sign is when you multiply or divide by a negative number.

-46 - 8x > 22

-8x > 22 + 46

-8x > 68

x < 68/-8        (we divided by -8 so the inequality changed direction)

x < -17/2

Step-by-step explanation:

-46 - 8x > 22: Original problem

-46 - 8x + 46 > 22 + 46: Bringing all the constants to one side of the inequality

-8x > 68: Simplification

x < 68/-8 : You have to flip the inequality symbol because you are dividing by                                

                  a negative number..

x< -8.5 : The answer!!!!!

Checking your answer....

-46 - 8x > 22 : Original problem

-46 - 8(-8.5) > 22 : Substitution

-46 + 68 > 22 : Simplification

22 > 22 : Answer check successful!!!

(22 is not greater than 22 but we know that the answer cannot be -8.5 because the inequality states that x is less -8.5. This process was only for the purpose of checking not for the purpose of proving)

Hope this helps!!!!

Given:

The expression is

[tex]13\sqrt {22b}-10\sqrt{22b}, b>0[/tex]

To find:

The equivalent expression.

Solution:

We have,

[tex]13\sqrt {22b}-10\sqrt{22b}[/tex]

Taking out common factors.

[tex]=(13-10)\sqrt {22b}[/tex]

[tex]=(3)\sqrt {22b}[/tex]

[tex]=3\sqrt {22b}[/tex]

The expression [tex]3\sqrt {22b}[/tex] is equivalent to the given expression.

Therefore, the correct option is D.

Answer:

look in explanation

Step-by-step explanation:

1) bisector means cutting an angle in half. the small lines between segment SM and MT mean they are congruent. this means MW is a bisector. Since both halves of ST are congruent, we know SM = 19. 19+19=38

2) same logic here, M bisects ST. set both halves of ST equal to each other and solve.

3x-6=x+8

2x+14

x=7

plug back in to find MT (7)+8=15. MT=SM so double 15 to get ST. ST=30

3) the bisector will be exactly halfway between the points.

4) find difference between x and y values, and divide by 2

2-2=0 0/2=0 x moves 0

13-1=12 12/2=6 y moves 6

so add 0 and 6 to 2,1 to get (2,7)

5) same process

6--6=12 12/2=6

6-0=6 6/2=3

add 6 and 3 to -6,0 to get (0,3)

6) find the change in x and y between the coordinate sets. (x: 1- -1=2) (y: 2-4=-2) take the opposite of those values and add them to M

(x:1-2=-1) (y:2+2=4)

(-1, 4) are the other coordinates for C

7) take the same steps

(x:3-1=2) (y:7-1=6)

use -2 and -6

(x:3-2=1) (y:7-6=1)

(1,1) are other coordinates for C

8) use distance formula

sqrt (x1-x2)^2 + (y1-y2)^2

sqrt(1--1)^2 +(2-4)^2

sqrt (2)^2 +(-2)^2

sqrt 4+4

sqrt 8

9) same process

sqrt (-1-3)^2+(-5--8)^2

sqrt (-4)^2 +(3)^2

sqrt 16+9

sqrt 25

5

Answer:

Step-by-step explanation:

The quotient of

it is -23 I think

Step-by-step explanation:

(-5)+(-18)=-23

Answer:

13.33 pink roses

Step-by-step explanation:

We are told the floral arrangements are proportional , hence:

6 white roses = 8 pink roses

10 white roses = x

Cross Multiply

6 white roses × x = 10 white rose × 8 pink roses

x = 10 white roses × 8 pink roses/6 white roses

x = 13.333333333 pink roses

x ≈ 13.33 pink roses

Answer:

I believe it is $21.24 im sure

Answer:

The equation is;

C = kg

c is the cost in $

k is the proportionality constant $/can

g is the number of cans

cost of 5 cans of coffee is $46.25

Step-by-step explanation:

From the question, 2 cans of ground coffee costs $18.50

Let c be the cost and g be the number of ground coffee

18.50 = k * 2

where k is the constant of proportionality;

k = 18.5/2

k = 9.25

So, the cost of 5 coffee cans will be;

c = 9.25 * 5 = $46.25

Answer:

x=5

Step-by-step explanation:

Angles in a triangle adds up to 180 degrees

so 105 + (6x+20) + (7x-10) = 180

simplify

115+13x=180

subtract 115 to each side

13x=65

divide by 13

x=5

check work

105 + (6(5) + 20) + (7(5) -10)

105 + (30 +20) +(35 - 10)

105 + 50 + 25 = 180

Answer:

12.90%

Step-by-step explanation:

Given ;

Original price = 171.50

Sale price = 149.37

To find the % markdown :

Markdown = Purchase price - sale price

171.50 - 149.37 = 22.13

(Markdown / purchase price) * 100%

(22.13 / 171.50) * 100%

0.1290379 * 100%

= 12.90%

Answer:

9 sleeves for 22.99

Step-by-step explanation

The first pack has a unit rate of $11.49/ 4 balls

=$2.8725

The second pack has a unit rate of $16.79/6balls

=$2.798 per ball

the third pack has a unit rate of $22.99/9balls

=2.554

So, I would definitely go for the third pack since it has the least cost.

Answer:

5

Step-by-step explanation:

Step-by-step explanation:

subtract b to get P-b=2a. divide each side by 2 to get (P-b)/2=a

Answer:

yes True

Step-by-step explanation:

thank you so much

Answer:

44°

Step-by-step explanation:

8x-4 = 6x+8

8x - 6x = 8 + 4

2x = 12

x = 12/2

x = 6

then:

8*6 - 4 = 48 - 4 = 44°

The measure of angle 1:

44°

Answer:

5 for the green box and 9 for the purple one

Step-by-step explanation:

Answer:

(2,1)

Step-by-step explanation:

2x - 2y = 2

5x + 2y = 12

2x + 5x = 7x

-2y + 2y = 0

2 + 12 = 14

7x = 14

7x/7 = 14/7

x = 2

2x - 2y = 2

2(2) - 2y = 2

4 - 2y = 2

-2y = 2 - 4

-2y = -2

-2y/-2 = -2/-2

y = 1

1. 1\10

2. 1/4

3.16

Step-by-step explanation:

your welcome

Step-by-step explanation:

sogzglzotsoypysotaota9t8ts

It would be 120 ye  f  = 8  E = 3 1/2