Ms. Baker has a class of 15 students. She can spend $21 on each student to buy math supplies for the year. She first buys all of her students calculators, which
costs a total of $67.65, After buying the calculators, how much does she have left to spend on each student?

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{5})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x -4}{2}~~~ ,~~~ \cfrac{ y +5}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M} }{(5~~,~~-1)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -4 }{2}=5\implies x-4=10\implies \boxed{x=14} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +5 }{2}=-1\implies y+5=-2\implies \boxed{y=-7}[/tex]

Answer:

The answer is 53

Step-by-step explanation:

50+48+59+39+58=294

360-294=106

106/2=53

Answer:

53

Step-by-step explanation:

The sum of exterior angles of any polygon is 360 degrees

x + x + 59 + 48 + 50 + 39 + 58 = 360

2x + 254 = 360

x = (360 - 254)/2 = 53

Answer:

  C.  1/3

Step-by-step explanation:

You want to identify the rational number listed that cannot be a root of the given polynomial.

Possible rational roots will be off the form ...

  ± (divisor of the constant) / (divisor of the leading coefficient)

When the divisors are listed, this is ...

  ±{1, 3, 9}/{1, 2}

This shows you that 3 cannot be the denominator of any possible rational root.

  1/3 is not a possible zero of the function

__

Additional comment

The list of possible roots is ±{1/2, 1, 3/2, 3, 9/2, 9}.

As it happens, neither of the two real roots is rational.

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A

Step-by-step explanation:

The period of the sound wave created by the tuba is approximately 0.0134 seconds.

The speed of sound in air is given as 343 meters per second. The formula relating the speed of sound, wavelength, and period of a wave is:

v = λ × f

Where:

v = speed of sound (343 m/s)

λ = wavelength (4.61 m)

f = frequency (unknown)

To find the period, we need to determine the frequency of the sound wave. The period (T) is the reciprocal of the frequency (f), so we can rewrite the formula as:

v = λ / T

Rearranging the equation to solve for the period (T), we get:

T = λ / v

Substituting the given values, we have:

T = 4.61 m / 343 m/s

Calculating the value, we find:

T ≈ 0.0134 seconds

Therefore, the period of the sound wave created by the tuba is approximately 0.0134 seconds.

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The number of new health units is 937, and the number of improved health units is 1,137.

The number of improved health units exceeds the new ones by 200. In other words, I = N + 200.

We also know that the total number of health units counted in the report is 2,074.

Therefore, we have the equation N + I = 2,074.

Substituting the value of I from the first equation into the second equation, we can solve for N:

N + N + 200 = 2,074

2N + 200 = 2,074

2N = 1,874

N = 937

Now, we can substitute the value of N back into the first equation to find I:

I = N + 200

I = 937 + 200

I = 1,137

Therefore, the number of new health units is 937, and the number of improved health units is 1,137.

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Answer:

2

3

5

5

7

13

14

17

21

31

52

Step-by-step explanation:

but I think the town & is the best. I am not coming out of my reward.. this will be the last one day.. this will not go on. I am not coming to the office until tomorrow as I'm working for, and if I don't get any of that, I'll break it up with a choice. I am a bit worried, so I was 165 2762

The expressions are simplified to;

a. 4pq

b. t³

Algebraic expressions are defined as expressions that are made up of terms, variables, coefficients, factors and constants.

These algebraic expressions are also made up of mathematical or arithmetic operations, such as;

From the information given, we have that;

The expressions are;

1.  p x q x 4

Multiply the terms, we have that;

4qp

2.t x t x t

Multiply the terms, we get;

t³

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Answer:$2050.

Step-by-step explanation:

To find out how much a person will pay for renting a car for one day and driving it 100 miles using the given equation, you can substitute x = 100 into the equation y = 50 + 20x and solve for y:

y = 50 + 20x

y = 50 + 20(100)

y = 50 + 2000

y = 2050

Therefore, a person who rents a car for one day and drives it 100 miles will pay $2050.

The solution to the system of equations is x = 2 and y = -1.

To solve the system of equations:

2x - 5y = 9 ...(1)

3x + 4y = 2 ...(2)

Multiplying equation (1) by 4 and equation (2) by 5, we can eliminate the variable 'y':

8x - 20y = 36 ...(3)

15x + 20y = 10 ...(4)

Adding equation (3) and equation (4), the 'y' terms cancel out:

(8x - 20y) + (15x + 20y) = 36 + 10

23x = 46

Dividing both sides of the equation by 23, we find:

x = 2

Plugging the value of 'x'

2(2) - 5y = 9

4 - 5y = 9

Subtracting 4 from both sides of the equation:

-5y = 9 - 4

-5y = 5

y = -1

Therefore, the solution to the system of equations is x = 2 and y = -1.

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The ordered pair that is a solution of the system is (-3, -3), the second option.

There are two ways of finding this.

You can use your graph and identify which of the given pointes lies in the region where the two shaded areas intersect.

Another way, is replacing the values of the coordinate points in both inequalities and checking that both are true when evaluated in the point.

Here we will use the graph, because you already had it (and you can see a more precise graph in the image at the end).

We can see that the region os solutions is on the left side of the graph, and the only point that lies on there is (-3, -3)

So that point is the solution.

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Step-by-step explanation:

A LOT of different outfits !
8  x  5  x  4  x  2   = 320 outfit possibilities

Answer:

55°

Step-by-step explanation:

if angle 4 = 105°, then angle 3 must be 180 - 105 = 75° (angles in straight line add up to 180°).

angles in a triangle also add up to 180°.

so we expect angle 2 to be 180 - angle 6 - angle 3

= 180 - 50 - 75

= 55°.

Answer: 180

Step-by-step explanation:

Use the order of operations: PEMDAS

Parenthesis

Exponents

Multiplication/Division

Addition/Subtraction

3² x (-2)³ x 5               >There is nothing to simplify within parenthesis

                                   >Exponents are next in Order of Operations

(3)(3) x (-2)(-2) x 5       >This is the exponents expanded

9 x 4 x 5                      >Multiply from left to right

36 x 5

180

Evaluating the piecewise function we will get:

g(-1) = -2

g(2) = 0

g(3) = 1/2

To evaluate the piecewise function we need to use the correct part depending on the domains.

g(-1), here x = -1, then we need to use the second part of the function:

g(-1) = -(-1 - 1)² + 2 = -4 + 2 = -2

For the second one x = 2, we use the last part:

g(2) = (1/2)*2 - 1 = 0

For the last one, we have x = 3, again we need to use the last part:

g(3) = (1/2)*3 - 1 = 3/2 - 2/2 = 1/2

These are the 3 values.

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The man rotated the window by 45 degrees and covered one of the diagonals, resulting in a smaller square window with sides measuring 1 meter.

The man achieved the transformation of his square window by dividing it into two equal halves and boarding up one of them.

Let's analyze the steps he took to accomplish this:

Initially, the man had a square window with sides measuring 1 meter

This means that the window had an area of 1 square meter (1m x 1m = 1m²).

To reduce the amount of light coming through the window, the man decided to board up half of it.

This implies that he covered one of the equal halves of the square window, while leaving the other half open.

By boarding up half of the window, he effectively blocked off half of the area of the square window.

Since the original window had an area of 1 square meter, boarding up half of it reduces the effective area to 1/2 square meter (1m² ÷ 2 = 1/2m²).

The remaining open half of the window still retains its square shape, with sides equal to 1 meter.

Therefore, the man ends up with a square window that measures 1 meter in height and 1 meter in width, but with an area of only 1/2 square meter.

In summary, the man achieved the transformation by boarding up half of the square window, effectively reducing its area to half of the original size while maintaining the same dimensions for the remaining open half. This manipulation allows him to control the amount of light entering his house while preserving the square shape of the window.

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The required first answer u = [tex]x^{2}[/tex] + 1 and du = 2x  and second answer u = tanx and du = [tex]sec^2 x[/tex] .

Given that if  [tex]\int\limits {f(g(x)) g'(x)} \, dx[/tex]  then u = g(x) and du = g'(x),

[tex]\int\limits {\frac{x}{\sqrt{x^2+1} } } \, dx[/tex]  and [tex]\int\limits {tan^2 x sec^2 x} \, dx[/tex]

To find u and du by using the integral property

[tex]\int\limits {f(g(x)) g'(x)} \, dx = f(g(x))[/tex].

Consider  [tex]\int\limits {\frac{x}{\sqrt{x^2+1} } } \, dx[/tex]

The above integral can be expressed as

[tex]\int\limits {\frac{x}{\sqrt{x^2+1} } } \, dx = \int\limits {\frac{1}{\sqrt{x^2+1} } } \,x dx[/tex]

That implies, u = g(x) = [tex]x^{2}[/tex] + 1.

Differentiating with respect to x gives,

du = g'(x)

du = d/dx( [tex]x^{2}[/tex] + 1 )

du = 2x + 0.

du = 2x.

Consider  [tex]\int\limits {tan^2 x sec^2 x} \, dx[/tex]

The above integral can be expressed as

[tex]\int\limits {tan^2 x sec^2 x} \, dx = \int\limits {(tanx)^2 sec^2 x} \, dx[/tex]

That implies, u = g(x) = tanx.

Differentiating with respect to x gives,

du = g'(x)

du = d/dx( tanx )

du = [tex]sec^2 x[/tex].

du = [tex]sec^2 x[/tex].

Hence, the required first answer u = [tex]x^{2}[/tex] + 1 and du = 2x  and second answer u = tanx and du = [tex]sec^2 x[/tex].

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Answer: 97 degrees

Step-by-step explanation: 180-83=97

The value of probability P (A or B) is,

⇒ P (A or B) = 45

We have to given that;

To find the probability that either event will occur.

Now, By given figure we get;

P (A) = 25 + 5

P (A) = 30

P (B) = 5 + 15

P (B) = 20

P (A and B) = 5

Since, The formula is,

⇒ P (A or B) = P (A) + P (B) - P (A and B)

Substitute all the values we get;

⇒ P (A or B) = 30 + 20 - 5

⇒ P (A or B) = 50 - 5

⇒ P (A or B) = 45

Therefore, The value of probability P (A or B) is,

⇒ P (A or B) = 45

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Answer:

The GCF (Greatest Common Factor) of two numbers is the largest number that divides both of them. In this case, the GCF of 36 and 60 is 12.

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1. The percentage of data items below a z-score of 1.8 is 96.41%.

2. The percentage of data items above a z-score of 1.8, is 3.59%.

To find these percentages, we can look up the  z-score of 1.8 is located in the row labeled "1.8" and the column labeled "Percentile."

The value in this cell is 96.41. This means that 96.41% of the data items in the normal distribution table will have a z-score that is less than or equal to 1.8.

P(z = 1.8) = 96.41%.

To find the percentage above 1.8

100 - 96.41 = 3.59%.

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Answer:

[tex] {x}^{ - \frac{5}{3} } = \frac{1}{ {x}^{ \frac{5}{3} } } = \frac{1}{ \sqrt[3]{ {x}^{5} } } [/tex]

The measure of the angle ∠ADC is 36°.

Given that a circle T, the inscribed angle ∠ABC = 72°, we need to find the measure of the angle ∠ADC,

So, according to the inscribed angle theorem,

2 ∠ABC = arc AC

arc AC = 144°

Now, since the whole circumference is 360°,

So,

arc ADC = 360° - arc AC

arc ADC = 216°

So,

∠ADC = 1/2 [arc ADC - arc AC]

∠ADC = 1/2 [216° - 144°]

∠ADC = 36°

Hence the measure of the angle ∠ADC is 36°.

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Answer:

9

Step-by-step explanation:

You don't need to pass through each edge once.

If we name the top vertex 1 and the bottom vertex 2 then here are the possible combinations:

A-1-B

A-B

A-2-B

A-1-B-A-2-B

A-2-B-A-1-B

A-B-1-A-2-B

A-B-2-A-1-B

A-1-B-2-A-B

A-2-B-1-A-B

Some people say 6 because they think you need to pass through all the edges. But the only restriction with travelling on the edges is you can't pass one twice. The point is read the wording and it becomes easy.

Hope this helps!

The calculated values of the expected values are E(2x) = 8/3 and E(x²) = 2

From the question, we have the following parameters that can be used in our computation:

f(x) = 0.5x, 0 < x < 2

The expected value of 2x is calculated as

E(2x) = ∫2x * f(x) dx

So, we have

E(2x) = ∫2x * 0.5x dx

Evaluate

E(2x) = ∫x² dx

Integrate the function

So, we have

E(2x) = x³/3

Using the boundaries, we have

E(2x) = (2 - 0)³/3

Evaluate

E(2x) = 8/3

The expected value of x² is calculated as

E(x²) = ∫x² * f(x) dx

So, we have

E(x²) = ∫x² * 0.5x dx

Evaluate

E(x²) = ∫0.5x³ dx

Integrate the function

So, we have

E(x²) = 0.5x⁴/4

Using the boundaries, we have

E(x²) = 0.5 * (2 - 0)⁴/4

Evaluate

E(x²) = 2

Hence, the expected values are E(2x) = 8/3 and E(x²) = 2

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Amount of outstanding checks is $218

Given,

Bank balance = $683

Check book register balance = $462

Interest earned = $11

Service charge = $8

Now,

Form the linear equation,

Bank balance = Check book register balance + Interest earned + Amount of outstanding check - Service charge

Substitute the data given in the question,

$683 = $462 + $11 + Amount of outstanding check - $8

Amount of outstanding check = $218

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The boy is 630 meters south from his starting point.

We must take into account the southward component of his shift.

We can imagine a right-angled triangle where the hypotenuse represents the boy's total displacement of 1260 meters, the angle between the hypotenuse and the south direction is 120°, and the side next to the angle represents the southward displacement given that the boy walks 1260 meters on a bearing of 120°.

We can use trigonometric functions to calculate the displacement to the south. Since the adjacent side and hypotenuse of a right triangle are connected in this instance, we will use the cosine function.

cos(120°) = adjacent / hypotenuse

cos(120°) = adjacent / 1260

Solving for the adjacent side (southward displacement):

adjacent = cos(120°) * 1260

adjacent = (-0.5) * 1260

adjacent = -630

The negative sign indicates that the southward displacement is in the opposite direction or "south" relative to the starting point.

Therefore, the boy is 630 meters south from his starting point.

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Answer: Factor the problem

Step-by-step explanation:

Take out the common factor (-16), it will leave you with (t^2 - t - 30)

Factor (t - 6) (t + 5)

t - 6 = 0 or t + 5 = 0

t = 6 seconds

Answer: The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.