Monica paid sales tax of $1.40 when she bought a new bike helmet. If the sales tax rate was 7%, how much did the store charge for the bike helmet before tax?

Answer:

  (a) 43.6490°N, 70.3928°W

  (b) Baker's Field

Step-by-step explanation:

The locations are all within a 7-mile square, so we will make the assumption of a flat Earth with parallel longitude lines. Then the "central" location will be the weighted average of the latitude and longitude coordinates.

Total population is 16000 +22000 +36500 = 74,500. For purposes of the arithmetic, we will subtract 43 from latitude and 70 from longitude, then multiply each fraction by 10. Similarly, we will divide each population by 1000.

The weighted average location is found from ...

  (16/74.5)(6.769, 3.717) +(22/74.5)(5.781, 3.222) +(36.5/74.5)(6.795, 4.447)

  = (1.4537, 0.7983) +(1.7071, 0.9515) +(3.3291, 2.1787) = (6.490, 3.928)

The center of gravity is about 43.6490°N, 70.3928°W.

__

The coordinate differences from the center of gravity are (in (°lat, °long)) ...

  Baker's Field: (0.0294, -0.0101)

  Lonesome Acres: (-0.1371, -.0072)

Clearly, Baker's field is closer to the site of part (a).

_____

Additional comment

Distance calculations could be refined further by considering that a degree of longitude at this latitude represents about 0.72 times the distance of a degree of latitude. In this problem, the location of Lonesome Acres has a latitude difference that is several times any of the other coordinate differences, so it is clearly much farther away from the desired location.

The calculations done here are a sort of first-level approximation. The least-significant digits in the coordinates represent a distance of less than 50 feet. If you really want accuracy to that level, then the (approximately) spherical shape of the Earth needs to be accounted for. As a second-level approximation, some reference point needs to be identified, and coordinates in miles (or feet) need to be expressed in relation to that reference. The best accuracy would be obtained using spherical trigonometry to identify the distances.

We expect any school that is constructed to be somewhat larger than 50 feet in any direction, so accuracy to the 4th decimal place in these locations is probably not required--except to satisfy some answer-checker.

Answer:

see exp

Step-by-step explanation:

1.0, 1/3, 95%, 80%

Answer:

x+3/5=2

or,x+0.6=2

or,x=2-0.6

x=1.4

Answer:

HS = 5

Step-by-step explanation:

By the property of centroid, point S divides the median RP in the ratio of 2: 1: SR=2SP     HS = 1/2 SM

SP=4

SR + 2 = 2SP + 2 = 10 = SM

HS = 1/2*SM = 5

Answer:

I believe it'd 69.5

Step-by-step explanation:

if u use the equation 2x+5=134, you get 64.5 for Josh and 69.5 for eric

Answer:

7377.4

Step-by-step explanation:

Answer:

6 4/9

Step-by-step explanation:

You divide 58 and 8 and your answer would be 6.444444 repeating.

Answer:

The sum of 3/5 and Square root of 13 is irrational. Since square root of 13 is irrational. And when you add it gives u irrational.

Answer:

8/13 = 0.615

Step-by-step explanation:

Nolan is only using these numbers, not actual probabilities, to formulate his results. Therefore, only using these numbers, there is an 8/13 chance of Nolan flipping a head with his lucky coin, as he flipped heads 8/13 times.

Answer:

13 time /8 head

= 8/ 13

= 0.615

[tex]\dfrac{2 \tfrac 12 }{\tfrac 52}\\\\\\\\= \dfrac{\left(\tfrac 5 2\right)}{\left(\tfrac 52 \right) }\\\\\\\\=1[/tex]

Answer:

Last choice

Step-by-step explanation:

First, convert (sinx)^2 to 1-(cosx)^2 via trigonometric identity derived from (sinx)^2 + (cosx)^2 = 1

[tex]\displaystyle \large{\sin^2x + \cos^2x=1 \longrightarrow \sin^2x=1-\cos^2x}[/tex]

Thus, the rewritten inequality is [tex]\displaystyle \large{1-\cos^2x>1+\cos x}[/tex]

Notice how the inequality has a quadratic pattern since we have (cosx)^2 and cosx in the inequality, simply arrange degrees in order.

[tex]\displaystyle \large{1-\cos^2x>1+\cos x}\\\displaystyle \large{0>1+\cos x-1+\cos^2x}\\\displaystyle \large{0>\cos x+\cos^2x}\\\displaystyle \large{\cos^2x+\cos x < 0}[/tex]

Then we factor cosx since the expression has cosx as a common factor.

[tex]\displaystyle \large{\cos x(\cos x+1)<0}[/tex]

Then we have to consider each inequalities which are cosx<0 and cosx+1<0 then merge both intervals once obtaining the solutions.

(1) [tex]\displaystyle \large{\cos x < 0}[/tex]

This inequality means that we have to find the x-value(s) that satisfy(ies) it.

Since cosx becomes negative after π/2 (Refer to unit circle, cosx becomes negative in second quadrant and this quadrant), that means it becomes negative until it reaches or < 3π/2.

Thus, [tex]\displaystyle \large{\frac{\pi}{2}<x<\frac{3\pi}{2}}[/tex] is the solution to cosx > 0.

The another way to solve inequality is to find the intersections by solving the equation then joint the interval together.

[tex]\displaystyle \large{\cos x<0 \longrightarrow \cos x=0}[/tex]

From the unit circle, cosx becomes 0 at x = π/2 and x = 3π/2 between interval [0,2π]

Therefore:

[tex]\displaystyle \large{\cos x = 0 \longrightarrow x = \frac{\pi}{2}, \frac{3\pi}{2}}\\\displaystyle \large{\boxed{\frac{\pi}{2}<x<\frac{3\pi}{2}}}[/tex]

(2) [tex]\displaystyle \large{\cos x+1<0 \longrightarrow \cos x <-1[/tex]

For this inequality, it appears that there have no solutions because cosine function is defined between [-1,1] in range hence there are no x-values in real plane that make cosx even less than -1.

Because only π satisfies cosx = -1 but not cosx < -1, we restrict π and every values.

Hence no solutions which cause a break of interval between π and π/2 < x < 3π/2

If you substitute x = π in, the inequality is false and therefore the answer is:

[tex]\displaystyle \large{\frac{\pi}{2}<x<\pi, \pi<x<\frac{3\pi}{2}}[/tex]

Answer:

D.

Step-by-step explanation:

The first two don't work, so it's between the last two.

This equation doesn't work for 180, so the answer is the last choice.

:)

Step-by-step explanation:

hope it will help you......

Answer:

d four

Step-by-step explanation:

How many solutions does the nonlinear system of equations graphed below have?  

Look at the number of points where the graphs intersect each other...the points where the graphs of the functions cross each other are the solutions to the system.  

Upon looking, you should see 4 points where the graphs intersect, so there are 4 solutions to the non-linear system of equations.

Answer:

√13

Step-by-step explanation:

1/33 is a fraction, meaning it is rational

1.6... has a repiton, meaning it is rational

-5.43 is a integer meaning it is rational

Answer:

VI

Step-by-step explanation:

The letter "A" is a vowel and a capital letter, so this should be categorized in group VI, where the vowel circle and the capital letter circle overlap.

Answer:

F

Step-by-step explanation:

It is a capital letter and a vowel

Answer:

she will pay $19 for each day

Step-by-step explanation:

94-18=76

76÷4=19

The rental cost of each day Tara used the kayak is $19 if Tara stayed at the Merry Mountain campgrounds last weekend. She paid a rental fee to use a kayak for 4 days.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Tara stayed at the Merry Mountain campgrounds last weekend. She paid a rental fee to use a kayak for 4 days.

Let x be the rental cost of each day Tara used the kayak.

4x + 18 = 94

4x = 94 - 18

4x = 76

x = 76/4

x = $19

Thus, the rental cost of each day Tara used the kayak is $19 if Tara stayed at the Merry Mountain campgrounds last weekend. She paid a rental fee to use a kayak for 4 days.

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Answer:

Distributive Property

Step-by-step explanation (if you were to show the steps):

(x+2)(y+z)   (first expression)

xy + xz + 2y + 2z (Distributive Property of Multiplication)

yx + 2y + zx + 2z (use the Commutative Property of Addition and Commutative Property of Multiplication to group xy (also known as yx) and 2y together, and to group xz (also known as zx) and 2z together)

y(x + 2) + z(x + 2) (use factoring to get the rewritten expression at the end)

Answer:

2/3 = 4/6 = 8/12

Step-by-step explanation:

The equation which is equivalent to 60% of 25 are x • 1.6 = 25, 0.6 • 25 = x and x/25=60//100

Percentages can be expressed as decimals or fractions.

Given the expression 60% of 25, this can b expressed as:

where x is the result of the expression.

Expressing 60% as a decimal will give;

0.6 of 25  = x

0.6 * 25 = x

From the expression 60/100 * 25 = x, this can also be written as:

25 = 100/60 x

25 = 10/6 x

25 = 1.6x

Hence the equation which is equivalent to 60% of 25 are x • 1.6 = 25, 0.6 • 25 = x and x/25=60//100

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-1-1 or 2-4 or 3-5 or 6-8 or 7-9 or 8-10

Answer:

option 1

Step-by-step explanation:

(-2) (25/7)

-50/7 = -7 1/7

Answer:

Option A is correct.

Step-by-step explanation:

(-2) (3 4/7)​

=> (-2) x (3 4/7)​

=> -2 x 25/7

=> -50/7

=> -7 1/7

Therefore, Option A is correct.

all real numbers except the 90 and 270 because of cosx

Answer:

B.

Step-by-step explanation:

Range is all the set y values.

Answer:

See image

Step-by-step explanation:

The range is all of the y-values. Look at the points on the graph, and make a list of all the y's That will be the range.

Answer:

[tex]A=\left(-1\dfrac{5}{5}\right)=(-2)\\\\B=\left(-\dfrac{4}{5}\right)\\\\C=\left(\dfrac{3}{5}\right)[/tex]

Step-by-step explanation:

Look at the picture.

[tex]\dfrac{2}{10}=\dfrac{1}{5}[/tex]

Answer:

4

Step-by-step explanation:

Substitute: [tex]\frac{\frac{12}{2} +5*6}{3*3}[/tex]

Cross out the common factor: [tex]\frac{6+5*6}{3*3}[/tex]

Calculate the product or quotient: [tex]\frac{6 +30}{3*3}[/tex]

Calculate the product or quotient: [tex]\frac{6+30}{9}[/tex]

Calculate the sum or difference: [tex]\frac{36}{9}[/tex]

Cross out the common factor: [tex]4[/tex]

Answer: [tex]4[/tex]

Answer:

8 cm

Step-by-step explanation:

h = v/(pi r^2)

h = 904.78/ (3.1415 * 6^2)

Answer:

$28,875

Step-by-step explanation:

First, we would have to find 10% of $25,000

10% of $25,000 = $2,500

Now, we have to add the 2 values together

$25,000 + $2,500 = $27,500

Now, we can find the shipping fee, since it includes the engineering fee

5% of $27,500 = $1,375

Now, we can add the shipping fee to find the total

$27,500 + $1,375 = $28,875

Answer:

give the dimensions of the figure on the paper

Answer:

A. x = 96 and y = 42

Step-by-step explanation:

The required measure of the angle x and y is given as x =92° and y = 42°. Option A is correct.

Given that,
Tina wants to sew a piece of fabric into a scarf in the shape of an isosceles triangle as shown in the accompanying diagram what are the values of x and y is to be determined.

A triangle with two sides and two congruent angles that are equal each other is called an isosceles triangle.

Here,
For an isosceles triangle,
The measure of the angle opposite to the equal side is equal, So
y = 42°

Now,
The sum of the angles in the triangle° is equal to 180,
x + y + 42 = 180
x + 42 + 42 = 180
x = 96

Thus, the required measure of the angle x and y is given as x =92° and y = 42°. Option A is correct.

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