Evaluate 1/3m-1-1/2n, when m=21 and n
=12

ANSWER

[tex]{( - 2)}^{ - 3} =- \frac{1}{ 8} [/tex]

EXPLANATION

We want to simplify;

[tex] {( - 2)}^{ - 3} [/tex]

Recall that,

[tex] {a}^{ - m} = \frac{1}{ {a}^{m} } [/tex]

[tex]{( - 2)}^{ - 3} = \frac{1}{{( - 2)}^{ 3}} [/tex]

We multiply out to get,

[tex]{( - 2)}^{ - 3} = \frac{1}{{- 2} \times - 2 \times - 2} [/tex]

[tex]{( - 2)}^{ - 3} = \frac{1}{ - 8} [/tex]

The correct choice is B.

ANSWER

[tex]P(A and B) = \frac{39}{200} [/tex]

EXPLANATION

If A and B are independent events, then,

P(A and B)=P(A)×P(B)

It was given that:

[tex]P(A) = \frac{3}{10} [/tex]

and

[tex]P(B) = \frac{13}{20} [/tex]

[tex]P(A \: and \: B) = \frac{3}{10} \times \frac{13}{20} [/tex]

[tex]P(A and B) = \frac{39}{200} [/tex]

the probability of events A and B occurring together, P(A and B), is 39/200 or, when simplified, 0.195.

The subject of the question is finding the probability of both independent events A and B occurring together, which is represented by P(A and B). To calculate this, you simply multiply the probability of event A by the probability of event B since they are independent. Given that P(A) = 3/10 and P(B) = 13/20, the calculation would be as follows:

Thus, the probability of events A and B occurring together, P(A and B), is 39/200 or, when simplified, 0.195.

Answer:

69

Step-by-step explanation:

To find the total sum of all the tests, you multiply 93 by 7 or 651. Multiplying 90 and 8, you get 720. So 720-651 is 69.

Folder = 1.25$

Notebook = 4.5 $

Folder =x

Notebook = y

The cost of one folder if the prices did not change between the days, for this case, is $1.25

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

Given that:

To find:

Cost of one folder.

Assume that:

Then, from the given condition, we get:

Amount spent in buying 3 folders and 1 notebook = 3x + 1y dollars = $8.25

And, amount spent in buying 2 folders and 3 notebook = 2x + 3y dollars = $16

Thus, we get two equations as:

[tex]3x + 1y = 8.25\\2x + 3y = 16[/tex]

From the first equation, getting 'y' in terms  of 'x', we get:

[tex]y = 8.25 - 3x[/tex]

Substituting this in second equation, we get:
[tex]2x + 3(8.25 - 3x) = 16\\2x +24.75 -3x = 16\\(2-9)x = 16 - 24.75\\-7x = -8.75\\7x = 8.75\\x = 8.75/7 =1.25 \: \rm dollars[/tex]

As we have Cost of one folder = $x

Thus, the cost of one folder if the prices did not change between the days, for this case, is $1.25

Learn more about forming equations here:

https://brainly.com/question/11938672

#SPJ2

there are 80 buttons

7/10

3÷24=8 8×7=56 56+24=80

The total number of buttons in the container is 60. This was calculated by setting up an equation using the given proportion of black buttons and the difference between the number of black and white buttons.

Let the total number of buttons in the container be x. Given that 7/10 of the buttons are black, this means 7/10 of x, or (7/10)x, represent the number of black buttons. The remaining 3/10 of x are white buttons. The difference between the number of black and white buttons is 24, so we can set up the following equation:

(7/10)x - (3/10)x = 24.

Simplifying the equation by subtracting the fractions results in (4/10)x = 24.

We can then simplify this further by dividing both sides by the coefficient of x, which is (4/10), to find x.

x = 24 / (4/10) = 24 * (10/4) = 24 * (2.5) = 60.

So, there are 60 buttons in the container in total.

Answer:

The measure of angle b (angle dbc) is [tex]54\°[/tex]

The measure of angle c is [tex]59\°[/tex]

The measure of angle d is [tex]67\°[/tex]

Step-by-step explanation:

Let

x-----> measure of angle b (angle dbc)

y----> measure of angle c

z----> measure of angle d

Remember that

The sum of the internal angles of a triangle must be equal to 180 degrees

so

[tex]x+y+z=180\°[/tex] -----> equation A

[tex]x=y-5[/tex] -----> equation B

[tex]z=y+8[/tex] ----> equation C

Substitute equation B and equation C in equation A and solve for y

[tex](y-5)+y+(y+8)=180\°[/tex]

[tex]3y+3=180\°[/tex]

[tex]3y=177\°[/tex]

[tex]y=59\°[/tex]

Find the value of x

[tex]x=59\°-5\°=54\°[/tex]

Find the value of z

[tex]z=59\°+8\°=67\°[/tex]

The measures of each angle of the triangle are

The measure of angle b (angle dbc) is [tex]54\°[/tex]

The measure of angle c is [tex]59\°[/tex]

The measure of angle d is [tex]67\°[/tex]

ANSWER

y=1

EXPLANATION

If (-1, y) lies on the graph of

[tex]y = 3^{x+1}[/tex]

then it must satisfy its equation:

We substitute x=-1 in to the equation to get:

[tex]y = 3^{-1+1}[/tex]

[tex]y = 3^{0}[/tex]

Any non-zero number exponent 0 is 1.

This simplifies to:

y=1

Therefore when x=-1, y=1

The third choice is correct.

Answer:

The correct answer option is 1

Step-by-step explanation:

We are given the following equation and we are to find the value of y when the point (-1, y) lies on the graph of the given equation:

[tex] y = 3 ^ { x + 1 } [/tex]

So we will substitute the given value of x from the point (-1, y) in the equation to get y:

[tex]y = 3^{-1+1}[/tex]

[tex]y=3^0[/tex]

We know that anything with power zero is equal to 1.

Therefore, y = 1.

Answer: 7 and 3

Step-by-step explanation: 7 + 3 = 10 and 7-3 = 4

The mean of the data is 4.5 and the median of the data is 5.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

To find the mean of the data, we add up all the values and divide by the total number of values:

2 + 7 + 5 + 4 + 3 + 3 + 5 + 5 + 6 + 5 = 45

There are 10 values, so:

mean = 45 / 10 = 4.5

Therefore, the mean of the data is 4.5.

To find the median of the data, we need to first put the values in order from smallest to largest:

2, 3, 3, 4, 5, 5, 5, 5, 6, 7

There are 10 values, which is an even number, so we take the average of the two middle values:

median = (5 + 5) / 2 = 5

Therefore,  the mean of the data is 4.5 and the median of the data is 5.

To learn more on Statistics click:

https://brainly.com/question/30218856

#SPJ3

Answer:

7/8

Step-by-step explanation:

Answer:

7/8

Step-by-step explanation:

Answer:

the answer is B.  145 sq. ft.

Step-by-step explanation:

find the area of the first 2 triangles

A = 1/2 bh

A = 1/2 ba

a = 1/2 (11 ft.) (5 ft)

a =  27.5 sq ft.

A = 1/2 cb

a = 1/2 (5 ft) (7 ft)

a = 17.5 sq. ft

find the area of the rectangle

A = lw

a = (11 ft.)(5 ft.)

a = 55 sq. ft

Then add all together

2(27.5 sq.ft) + 2(17.5 sq. ft) + 55 sq.ft. = 145 sq. ft.

Answer:

y =1/27

Step-by-step explanation:

Howdy!

If P = (-3, y) lies on the graph of y=3^x, then, to find the value of 'y' we need to substitute the point P into the equation:

To solve this, remember that [tex]a^{-b} = \frac{1}{a^{b}}[/tex]

Then:

y = 3^x

y = 3^(-3)

y = 1/27

So P= (-3, 1/27)

The correct option is y =1/27

Answer:

The correct answer option is 1/27.

Step-by-step explanation:

We are given the following equation and we are to find the value of y when the point (-3, y) lies on the graph of the given equation:

[tex] y = 3 ^ { x } [/tex]

So we will substitute the given value of x from the point (-3, y) in the equation to get y:

[tex] y = 3 ^ { - 3 } [/tex]

[tex] y = \frac { 1 } { 2 7 } [/tex]

Answer:

25%

Step-by-step explanation:

6.75 divided by 9 gives you 75%, if you want the discount then you subtract from 100 and get 25%

Answer:

25%

Step-by-step explanation:

Answer:

f(x) and g(x) are inverses

Step-by-step explanation:

* Lets check the inverse function

- If f(x) = y has a domain = x and a range = y, then f^-1 is the

  inverse of f with a domain  = y and a range = x

- f(x) = f^-1(x) = x

* Now lets solve the problem

∵ f(x) = 8/x

∵ g(x) = 8/x

∴ fg(x) = f(8/x)

∴ fg(x) = 8/(8/x) = 8 ÷ 8/x ⇒ change division sign to the multiplication

  sign and reciprocal the fraction after the division sign

∴ fg(x) = 8 × x/8 = x

* Now lets find gf(x)

∴ gf(x) = g(8/x)

∴ gf(x) = 8/(8/x) = 8 ÷ 8/x

∴ gf(x) = 8 × x/8 = x

∵ f(x) = f^-1(x) = x

* fg(x) = gf(x) = x

∴ f(x) and g(x) are inverses

Answer: 8.4 inches.

Step-by-step explanation:

We know that the circumference of a circle can be calculated with this formula:

[tex]C=2\pi r[/tex]

Where "r" is the radius of the circle.

We know that the circular cake (whose radius is 8 inches) is cut from the center into 6 equal pieces. Then, you need to divide the circumference of this circular cake by 6 to find the width of the outer edge of each piece of cake.

Therefore, this is (to the nearest tenth of an inch):

[tex]C=\frac{2\pi (8in)}{6}\\\\C=8.4in[/tex]

The width of the outer edge of each piece of cake  8.4 inches.

SOLUTION:

Given, a circular cake with a radius of 8 inches is cut from the center into 6 equal pieces. We have to find the width of the outer edge of each piece of cake.

We know that the circumference of a circle can be calculated with this formula: [tex]2\pi r[/tex] where "r" is the radius of the circle.

We know that the circular cake (whose radius is 8 inches) is cut from the center into 6 equal pieces.

Then, you need to divide the circumference of this circular cake by 6 to find the width of the outer edge of each piece of cake.

Therefore, this is (to the nearest tenth of an inch):

[tex]\text { Width }=\frac{2 \pi \times 8}{6}=\frac{\pi \times 8}{3}=\frac{8 \pi}{3}=8.377[/tex]

Hence, the cake piece is 8.4 inches wide.

The answer is:

[tex]Area_{circle}=\pi *radius^{2}[/tex]

or

[tex]Area_{circle}=\pi *(\frac{diameter}{2})^{2}[/tex]

We can calculate the area of any circle using the following formula:

[tex]Area_{circle}=\pi *radius^{2}[/tex]

Where,

π, is a constant used to calculate the area of the circle.

radius, is the distance from the center to any point of the circle.

Also, we have that:

[tex]radius=\frac{diameter}{2}[/tex]

So, we can rewrite the equation by the following way:

[tex]Area_{circle}=\pi *(\frac{diameter}{2})^{2}[/tex]

Have a nice day!

Answer:

Use formula:

[tex]Area of circle = \pi (radius)^2 =\pi (r)^2[/tex]

Step-by-step explanation:

We need to find about how to calculate the area of a circle.

And match with the given choices. Where given choices are:

Area of a circle is equal to the diameterdiameter

squaredradiusradius squared times diameterheightpiwidth.

I'm not sure what exactly you have typed as choices are not written in proper way.

But I can still answer that.

You just need to apply formula of the area of circle which is given by:

[tex]Area of circle = \pi (radius)^2 =\pi (r)^2[/tex]

Answer:

Step-by-step explanation:

The cost of each adult ticket is $28, but there is no solution for the cost of each student ticket in this case.

To solve this problem, we can set up a system of equations using the given information. Let's represent the cost of an adult ticket as 'a' and the cost of a student ticket as 's'. From the first equation, we know that 4a + 2s = 64. From the second equation, we know that 3a + 3s = 60. Now we can solve this system of equations.

Multiplying both sides of the second equation by 2 gives us 6a + 6s = 120. We can subtract the first equation from this equation to eliminate 's'.

6a + 6s - (4a + 2s) = 120 - 64

Expanding and simplifying the equation gives us 2a = 56. Dividing both sides by 2, we find that a = 28. Now we can substitute this value into either of the original equations to find 's'.

Using the first equation: 4(28) + 2s = 64

Simplifying the equation gives us 112 + 2s = 64

Subtracting 112 from both sides gives us 2s = -48. Dividing both sides by 2, we find that s = -24.

However, since we're talking about the cost of tickets, we can't have a negative value. Therefore, there is no solution for 's' in this case.

The cost of each adult ticket is $28, but there is no solution for the cost of each student ticket in this case.

https://brainly.com/question/23579483

#SPJ12

Answer:

15 apples

Step-by-step explanation: if you need 10 apples for two quarts, then you need 5 for 1. add those together and you get 15

Let's say Lily invested x amount of money in bonds and 2x in stocks. What the yield is annually from those is 6% of x plus 2 * 8% of x, as she gets 6% in bonds and 8% in stocks. Simplified is 0.06x + 0.16x. Add and you get 0.22x. Now you can solve a simple equation.

Equation:

0.22x = 325.6 (as annual income is $325.60)

----divide both sides by 0.22----

x = 1480

----multiply by 2 to get your answer----

2x = amount of stocks = 1480 * 2 = $2960

Okay I have the same question as you so first cross out A and C. Because negative numbers are to the left ,and the Answer is D

Answer:

6840

Step-by-step explanation:

Here, the order matters (1st, 2nd, and 3rd), so we need to use permutations.

There are 20 people who can get in first place.  After that, there are 19 people who can get in second place.  Finally, there are 18 people who can get in third place.  So:

20 * 19 * 18 = 6840

Number of the  ways can they finish in first, second, and the third-place is 6840

The linear arrangement of the set of the orders or the linear arrangements of the numbers is called the permutation.

Here, the order matters (1st, 2nd, and 3rd), so we need to use permutations.

There are 20 people who can get in first place.  After that, there are 19 people who can get in second place.  Finally, there are 18 people who can get in third place.  So:

20 x  19  x  18 = 684

Therefore Number of the  ways can they finish in first, second, and the third-place is 6840

To know more about Permutation follow

https://brainly.com/question/11732255

#SPJ2

Since the difference between steps 1 and 2 is that 2x was subtracted from both sides, i'm pretty sure the answer is B, the Subtraction property of equality. Hope this helps you!

Answer:

B) Subtraction property of equality

Step-by-step explanation:

4x - 7 = 2x + 9

Subtract 2x from each side using the subtraction property  of equality

4x -2x  - 7 = 2x-2x + 9

2x -7 = 9

Answer:

Step-by-step explanation:

You would take the area of half of a circle plus the area of a rectangle.  You don't have measures there, but the formula would be

[tex]A=\frac{\pi r^{2} }{2}+(l*w)[/tex]

Answer:

x=36

Step-by-step explanation:

The angle right under 3x is 2x, because alternate exterior angles between parallel lines are equal. Those two angles add up to 180, because they are formed by a strait line intersecting with another straight line. This means that 5x = 180 or x=36.

Answer:

Step-by-step explanation:

Same side interior angles

Answer:

Step-by-step explanation:

Observe in the image that [tex]\angle 1[/tex] and [tex]\angle 2[/tex] are inside the inclined pair of lines, that position is called interior angles, also notice that they are at the same side of the horizontal line.

Therefore, the correct description of that pair of angles is "same-side interior angles", because they are inside the pair of lines, and at the same side of the horizontal line.

Answer:

The answer is B 48 cm squared.

Step-by-step:

First divide into smaller sections. Then you will do Length times height.

9 x 4 = 36

6 x 2 = 12

36 + 12 = 48

Answer:

[tex]Area of circle = \pi (radius)^2 =\pi (r)^2[/tex]

Step-by-step explanation:

We need to find about how to calculate the area of a circle.

And match with the given choices. Where given choices are:

Area of a circle is equal to the diameterdiameter

squaredradiusradius squared times diameterheightpiwidth.

I'm not sure what exactly you have typed lol :)

But I can still answer that.

You just need to apply formula of the area of circle which is given by:

[tex]Area of circle = \pi (radius)^2 =\pi (r)^2[/tex]

Answer:

radius squared times pi

Step-by-step explanation:

edge

Answer:

b. Well, I've gotten y=5x+110 for the line of best fit.

To do so, create a line that fits best for a scatter plot. It's best if it's in the middle and hits most coordinates. So y=5x+110 is a good line.

c. To do so, insert 15 into x and solve from there.

y=5(15)+110

y=75+110

y=185

That is the number of people that might attend the reunion on the 15th year.

The surface area of the pyramid is 156 square inches. It is found by computing the area of the base, then adding it with the product of half of the base perimeter and the slant height.

The problem involves finding the surface area of a pyramid with a square base. The surface area of a pyramid is given by the formula Base area + 1/2 * Perimeter of the base * Slant height.

First, let's compute the area of the base, the base is a square with sides of 6 inches. This gives us 6 * 6 = 36 square inches.

Secondly, the perimeter of a square is simply the length of one side multiplied by 4, which gives us 6*4 = 24 inches. Then multiply this by the slant height, which is 10 inches, then by 1/2, we have 0.5 * 24 * 10 = 120 square inches.

Finally, adding the base area and the latter computation gives: 36 + 120 = 156 square inches. Therefore, the surface area of the wooden pyramid puzzle is 156 square inches.

https://brainly.com/question/40111598

#SPJ12

The surface area of the wooden pyramid puzzle with a base side length of 6 inches and a slant height of 10 inches is 156 square inches.

To find the surface area of the wooden pyramid puzzle, we need to calculate the area of each face and then sum them up. The base of the pyramid is a square with side lengths of 6 inches, so the area of the base is 6 inches multiplied by 6 inches, which gives us 36 square inches. The four triangular faces have the same area since the pyramid is symmetrical, so we just need to calculate the area of one triangular face.

The height of the pyramid is given as 10 inches, and since it is a right triangle, we can use the formula for the area of a triangle: (base x height) / 2.

The base of the triangle is the length of one side of the square base, which is 6 inches. Therefore, the area of one triangular face is (6 inches x 10 inches) / 2 = 30 square inches.

Since there are four triangular faces, the total area for all the triangular faces is 4 x 30 square inches = 120 square inches. Finally, we can sum up the areas of the base and the triangular faces to find the surface area: 36 square inches + 120 square inches = 156 square inches.

https://brainly.com/question/951562

#SPJ12