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What is the total cost of a $12 t-shirt if the sales tax is 6.5%?

Step-by-step explanation:

\( \underline{ \underline{ \text{Given}} }: \)

\( \underline{ \underline{ \text{To \: find}}} : \)

Let E ( -3 , 2 ) be ( x₁ , y₁ ) & H ( 1 , -1 ) be ( x₂ , y₂ )

\( \underline{ \underline{ \text{Solution}}} : \)

\( \sf{Midpoint = ( \frac{x_{1} + x_{2}}{2} \: , \frac{ y_{1} + y_{2}}{2} )}\)

⟶ \( \sf{( \frac{-3 + 1}{2} \: , \frac{2 + ( - 1)}{2} )}\)

⟶ \( \sf{( \frac{-2}{2} \:, \frac{2 - 1}{2} )}\)

⟶ \( \sf{( -1 \: ,\frac{1}{2} )}\)

\( \pink{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline{ \tt{(-1 \: , \: \frac{1}{2} )}}}}}}}\)

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Have a wonderful day / night ! ツ

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The number of water stations there are along the 13 1/2 miles long road race according to the task content is; Choice C; 18 water stations.

It follows from the task content that the number of water stations can be determined as follows;

13 1/2 ÷ 3/4

= 27/2 × 4/3

= 18 water stations.

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Answer: The square root of 216 is equal to approximately 6.485281.

Step-by-step explanation:

The square root of 216 is equal to the number that, when multiplied by itself, gives 216. The value of the square root of 216 can be found using several methods, including estimation, the long division method, and a calculator. Here, I'll provide a step-by-step explanation using estimation.

Step 1: Estimate the value of the square root.

One way to estimate the value of the square root of 216 is to find two perfect squares that are close to 216, and whose square roots are therefore close to the square root of 216. In this case, the perfect squares closest to 216 are 144 (12^2) and 225 (15^2). Since 216 is closer to 144, the square root of 216 is likely to be closer to 12 than to 15.

Step 2: Refine the estimate.

To refine the estimate of the square root of 216, we can average the two closest perfect squares and their square roots. In this case, the average of 12 and 15 is 13.5, and this is a better estimate of the square root of 216 than either 12 or 15 alone.

Step 3: Improve the estimate using a more precise method.

One method for finding an even more precise estimate of the square root of 216 is to use the Newton-Raphson formula for finding square roots. This formula involves repeatedly applying the following equation:

x_n+1 = (x_n + n/x_n) / 2,

where x_n is the nth estimate of the square root, and n is the number whose square root we are trying to find (in this case, n = 216). We can start with an initial estimate, such as x_0 = 13.5, and iterate the formula until the estimate converges to a desired level of precision.

Step 4: Use a calculator or other tools to find the exact value.

Finally, we can use a calculator or computer program to find the exact value of the square root of 216 to as many decimal places as desired. The exact value of the square root of 216 is equal to approximately 6.485281.

The measure of the other two angles of the quadrilateral are 15 and 85.

What are the angles of a quadrilateral?

Angles in a quadrilateral are the four angles that occur at each vertex within a four-sided shape; these angles are called interior angles of a quadrilateral. The sum of the interior angles of any quadrilateral is 360 360°. We can prove this using the angle sum of a triangle.

A quadrilateral is a polygon having four sides, four angles, and four vertices.  When we draw the diagonals to the quadrilateral, it forms two triangles. Both these triangles have an angle sum of 180°. Therefore, the total angle sum of the quadrilateral is 360°

Given, two angles of quadrilateral as  175° and 85°.

Let other 2 angles be x and y.

x + y + 175 + 85 = 360

x + y = 100

Given x/y = 3/17

x= 3/17(y)

So,

3y/17 + y = 100

20y = 1700

y = 85

x = 100 - 85 = 15

Hence other two angles of the quadrilateral are 15 and 85.

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Many states use a sequence of three letters followed by a sequence of three digits as their standard license-plate pattern. The required answer is 5036336.

Given that each three-letter three-digit arrangement is equally likely, the probability that such a license plate will contain at least one palindrome (a three-letter arrangement or a three-digit arrangement that reads the same left-to-right as it does right-to-left) is to be found.

Let's solve it.

The total number of such arrangements is

26 * 26 * 26 * 10 * 10 * 10 = 17,576,000,

and the number of palindrome arrangements is 26 * 10 + 26 = 286.

The probability that a plate will not contain any palindromes is 17,575,714 / 17,576,000.

Thus, the probability that a plate will contain at least one palindrome is:

1 - (17,575,714 / 17,576,000) = 286 / 17,576.

Therefore, the value of mm and nn are 286 and 17,576 respectively.

To obtain the answer, we need to find their product mm * nn, which is

286 * 17,576 = 5,036,336.

Hence, the required answer is 5036336.

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To duplicate angle ABC, draw a line segment, position the compass on point A, and then draw an arc that intersects the line segment. Next, position the compass on point B, and then draw a second arc that intersects the first arc at a point on the line segment. Finally, position the compass on the point where the two arcs intersect, but without changing the width, and draw a third arc that intersects the line segment.

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.

Common instruments used to measure angles are:

1. Protractor

2.Compass

3.Digital Angle finder

4.Angle finder

5.Clinometer

6. Inclinometer

You can take the following actions to copy angle ABC:

Create a line segment that will serve as the foundation for the new angle you're going to create.

Draw an arc that crosses the line segment you produced in step 1 by positioning the compass on point A.

Draw a second arc that crosses the previous arc at a point on the line segment by setting the compass on point B.

Place the compass on the intersection of the two arcs without adjusting the compass's width, then create another arc that crosses the line segment.

Point D is where the second arc crosses the line segment. To finish the new angle, join points D and C.

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Answer:

x = 13

Step-by-step explanation:

To find the value of x we need to isolate it! To do this we have to get rid of any other value around it...

Firstly we need to get rid of the ' -2 '. We have to add 2 to both sides!

Now we are left with 3x = 39 so we have to get rid of the 3. We have to divide 3 from both sides!

x = 13!

Hope this helps, have a lovely day! :)

The purpose of stories "Here at the given any rate is said the bachelor, and then collecting his belongings preparatory to leaving the carriage, then he kept them quiet for ten minutes, which was more than you were able to do."

Here we need to excerpt from the storyteller best supports the theme that the purpose of stories.

While we look the bachelor says at the end they said that he kept them quiet for ten minutes, which was more than you were able to do and then he is implying that no matter what she thought of his story and how much "better" she thought she could've done it, and then his was able to capture the attention of these kids and that is the matter of the issue because, therefore for a story and then entertaining is more important than proper form

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Answer:

Step-by-step explanation:

1024  Km/h  * 2.4 hours

= 2457.4 km

Answer:

The pair of numbers that has a product of ac and a sum of b = (+2, +8)

The factored form of the trinomial = (x+2) (x+8)

Step-by-step explanation:

ax² + bx + c = 0

This is in the form of a trinomial algebraic expression

Given trinomial: = ax² + 10x + 16

Where a = 1, b= 10, c= 16

To find the pair of numbers that has a product of ac and a sum of b, we would solve the equation.

Using factorisation method:

ac = a×c = 1×16 = 16

Let's find the factors of 16 whose sum gives +10 and product gives +16

Factors of 16 = 1, 2, 8, 16

+2 + +8 = +10

+2 × +8 = +16

The factors are +2 and +8

The pair of numbers that has a product of ac and a sum of b = (+2, +8)

x² + 10x + 16 = x + 2x + 8x + 16

x² + 10x + 16 = x(x+2) + 8(x+2)

= (x+2) (x+8)

The factored form of the trinomial = (x+2) (x+8)

Answer:

(x+2) (x+8)

Step-by-step explanation:

The largest number of matches she could have won before are 164 matches.

A ratio shows the relation between two amounts. For example, the ratio of apples to pears in a basket or the ratio of women to men in a town.

First represent the matches she had won, using n as a reference. This means:

\(\frac{n}{2n} = \frac{1}{2}\)

Then, based on this let's add the current ratio:

\(\frac{n+3}{2n+4} = \frac{503}{1000}\)

Based on this, let's solve this inequality to find out the number of matches the player won before. Follow these steps:

Based on the previous process, the number of matches the player could have won before the weekend began was 164 matches.

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Answer:

10x9+110x5+x4+1100x3

Step-by-step explanation:

calculator

The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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The area of the sector is 11.75 metres squared.

The area of the sector can be calculated as follows:

area of a sector = ∅ / 360 × πr²

where

Therefore,

r = 3 metres

∅= 150 degrees

Therefore,

area of the sector = 150 / 360 × 3.14 × 3²

area of the sector = 150 / 360 × 3.14 × 9

area of the sector = 4239 / 360

area of the sector = 11.775 metres squared

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The distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.

We can use the distance formula to find the distance between two points in a coordinate plane. The distance formula is:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the coordinates of M(6, 16) and Z(-1, 14), we get:

d = √((-1 - 6)² + (14 - 16)²) = √(49 + 4) = √53 ≈ 7.1

Therefore, the distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.

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Answer:

c. x-intercept is (6, 0) and the y-intercept is (0, 10).

Step-by-step explanation:

i hope this helps :)

Answer:

-90

Step-by-step explanation:

I took -90 divided it by 3 which gave me the answer of -30.

Answer:

I think it will be A.

Step-by-step explanation:

Because 9/3 =3 so 90/3 =30 . Same goes with Negative integers!

Answer:

The answer would be 92.8 but since we're rounding it'll be 90

Step-by-step explanation:

The expression is simplified to give 2(9x + 2√3x - 5)

First, we need to know that surds are mathematical forms that can no longer be simplified to smaller forms

From the information given, we have that;

(2√3x - 2)(3√3x + 5)

expand the bracket, we get;

6√9x² + 5(2√3x) - 6√3x - 10

Find the square root factor

6(3x)  + 10√3x - 6√3x - 10

collect the like terms, we have;

18x + 4√3x - 10

Factorize the expression, we have;

2(9x + 2√3x - 5)

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Answer:

I think is D

Step-by-step explanation:

hope it helps <3

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Range is about subtracting the lowest number from the highest number!

The lowest number is 54.

The highest number is 65.

65 - 54 = 11

Answer:

11

Step-by-step explanation:

Subtract the highest and lowest values 65-54, and you get 11

Answer:

1a)  1141/660

3/5 + 6/11 +7/12

   find the LCM of the denominators

the LCM of 5,11,12 is 660

after finding the LCM divide it with the denominator.

after dividing 660 by 5 i get 132. So i need to multiply it with 3. Now, i got 396. Do the same with the rest of the numbers.

u will get smth like this: 396+360+385/660

and the final answer will be1141/660.

b) 71/40

c) 211/28

d) 103/20

Answer:

20 seconds

Step-by-step explanation:

Given the following :

Alarm 1 (goes off every 10 seconds)

Alarm 2 (goes off every 5 seconds)

Alarm 3 (goes off every 4 seconds)

If they all go off now, how long will it take all to go off at the same time again.

Obtain the multiples of the time in seconds in which each alarm goes off and select the lowest multiple common to all three;

Multiples of 10 : 10, 20, 30, 40, 50,...

Multiples of 5 : 5, 10, 15, 20, 25, 30, 35, 40,...

Multiples of 4 : 4, 8, 12, 16, 20, 24, 28, 32, 36,....

Hence, the lowest multiple common to all three alarm times is 20.

Hence, all three alarms will go off at the same time again after 20 seconds

Answer: The value of m is 29.

Step-by-step explanation:

Given that, One term of \((x+y)^m\) is \(31,824x^{18}y^{11}\)  ...(i)

We know that that (r+1)th term in \((a+b)^n\) is given by :-

\(T_{r+1}=^nC_ra^{n-r}b^r\)  ...(ii)

On comparing (i) with (ii) , we get

\(a= x \text{ and } b= y \\n-r =18 \text{ and } r=11\\n=m\)

i.e.

\(m-r=18\Rightarow\ m-11=18\\\\\Rightarrow\ m=18+11=29\)

Hence, the value of m is 29.

\(2^{3x-4}=5\) => x = 2.106 , by properties of logarithm.

Given: \(2^{3x-4}=5\)

Taking logarithm on both sides:

log (\(2^{3x-4}\)) = log (5)

=> (3x - 4) log (2) = log (5) (As \(log_b(a)^m = m (log_b(a))\))

=> 3x - 4 = \(\frac{log5}{log2}\)

=> 3x - 4 = \(\frac{0.698}{0.301}\)

=> 3x - 4 = 2.318

=> 3x = 6.318

=> x = 2.106

Hence, \(2^{3x-4}=5\) => x = 2.106, by properties of logarithm.

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If each car hοlds 3 students and each bus hοlds 45 students. If 372 students went οn the trip, then the class used 4 cars and 8 buses fοr the field trip.

An algebraic expressiοn is a mathematical phrase that cοntains variables, cοnstants, and mathematical οperatiοns.

Let's use "c" tο represent the number οf cars and "b" tο represent the number οf buses used fοr the trip.

Frοm the prοblem statement, we knοw that:

The tοtal number οf vehicles used is 12:

c + b = 12

Each car hοlds 3 students and each bus hοlds 45 students:

3c + 45b = 372

Nοw we have twο equatiοns with twο variables. We can use substitutiοn οr eliminatiοn methοd tο sοlve fοr c and b. Let's use substitutiοn:

Rearrange the first equatiοn tο sοlve fοr οne variable:

c = 12 - b

Substitute this expressiοn fοr c in the secοnd equatiοn:

3(12 - b) + 45b = 372

Simplify and sοlve fοr b:

36 + 42b = 372

42b = 336

b = 8

Use the value οf b tο sοlve fοr c:

c = 12 - b = 12 - 8 = 4

Therefοre, the class used 4 cars and 8 buses fοr the field trip.

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We know that 7x - 1 must equal 125 because of Alternate interior angles. Now, let's solve for x.

Therefore, we can conclude that x = 18.

Hoped this helped.

\(BrainiacUser1357\)

\(\\ \tt\Rrightarrow 7x-1=125\)

\(\\ \tt\Rrightarrow 7x=125+1\)

\(\\ \tt\Rrightarrow 7x=126\)

\(\\ \tt\Rrightarrow x=126/7\)

\(\\ \tt\Rrightarrow x=18\)

Answer:

28.5 ft

Step-by-step explanation:

The height of a ball is given by the equation ƒ(x) = −16x² + 45x + 2.5 where x is the tome the ball travels. To find the height of the ball after a seconds, we substitute a in place of x, the equation becomes:

ƒ(a) = −16a² + 45a + 2.5.

Therefore if the height of the ball is needed to be found after 2 seconds, we find f(2).

ƒ(2) = −16(2)² + 45(2) + 2.5 = -64 + 90 + 2.5 = 28.5 ft

f(2) = 28.5 ft

The differential equation is dy/dt + 20y = 68 - 20t^2. The particular solution can be found by solving the equation for y.

Rearranging the equation, we have y = (68 - 20t^2) / (20). Therefore, the particular solution for this differential equation is y(t) = 3.4 - t^2.

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Answer:

(-5, 0)

Step-by-step explanation:

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