In Brooke’s class of 25 students, 15 students report that math is their favorite class and 40% of the students report that science is their favorite class. Do students prefer math or science

Final answer:

The surface area covered by the banner is 27,000 square meters. The side length of a square with the same area would be approximately 164.3 meters.

Explanation:

The office building is a right rectangular prism with a height of 200m, a length of 60m, and a width of 40m. The upper quarter of each vertical face needs to be covered with a large banner.

To find the surface area covered by the banner, we need to calculate the surface area of each vertical face. The surface area of a rectangular prism is given by the formula 2lw + 2lh + 2wh. Since we need to cover the upper quarter of each face, we can consider only three quarters of the height, resulting in a formula of 2lw + (3/4)lh + 2wh.

Plugging in the given values, we get:

Surface area = 2(60)(40) + (3/4)(200)(60) + 2(40)(200)

Simplifying the expression, we get the surface area covered by the banner to be 27,000 square meters.

If we want to represent the area as a square with the same area, we can take the square root of the surface area. In this case, the side length of the square representing the area would be approximately 164.3 meters.

only the last one since the others don’t pass the vertical line test

which is when you draw a straight line down your function and if it hits 2 or more points it is not a function

The correct graph should have x values that have no more than one y value.

Depending on the kind of function that is graphed, various graph types exist.

Linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal graphs are the eight most often used types.

Learn more about function graph https://brainly.com/question/9834848

here

#SPJ2

Answer: OPTION A

Step-by-step explanation:

To simplify the expression you must multiply the numerator and the denominator of the expression by √3.

As all the square roots have equal index, you can multiply the radicands, which are the numbers inside of the sqaures roots.

You also must keep on mind that:

[tex](\sqrt[n]{a})^n=a[/tex]

Therefore, you obtain:

[tex]\frac{6\sqrt{2}*\sqrt{3}}{\sqrt{3}*\sqrt{3}}=\frac{6\sqrt[]{6}}{3}=\frac{2\sqrt[]{6}}{3}[/tex]

Answer:

The correct answer is option B.  2√6

Step-by-step explanation:

It is given that an expression, 6√2/√3

To simplify the expression

6√2/√3

Multiplying numerator and denominator with √3

6√2/√3 = (6√2 x √3)/(√3 x √3)

  = [ 6 x √(2x3)]/3)                    (√2 x √3 = √(2 x 3)

  = 6√6/3  

  = 2√6

Therefore the simplified form of given expression 6√2/√3 is 2√6.

The correct answer is option B. 2√6

Answer:

multiplication

Step-by-step explanation:

See what is happening to the expression x - 4 and choose the opposite operation.

x - 4 is being divided by 5.

The opposite operation to division is multiplication, so you need to use multiplication to get x - 4 alone on the left side.

the answer to the question is multiplication

[tex]\huge\text{B. $\boxed{x+(y-z)}$}[/tex]

First, let's take a look at the terms in the original expression. Since its just addition and subtraction, we can get rid of the parentheses, leaving behind just [tex]x+y-z[/tex].

As long as an answer is made up of a positive [tex]x[/tex], a positive [tex]y[/tex], and a negative [tex]z[/tex], its correct!

Removing the parentheses in choice A leaves us with [tex]z+x+y[/tex], which has a positive [tex]z[/tex] rather than a negative [tex]z[/tex], so it's incorrect.

Removing the parentheses in choice B on the other hand gives us [tex]x+y-z[/tex], which means it's the correct answer! This is a good example of the associative property of addition in action.

The correct expression that is equivalent is option B.  x +(y − z)

Let's simplify each expression to see if they are equivalent to (x + y) - z:

A. ( z + (x + y))

We can rearrange the terms:

z + (x + y) = (x + y) + z

This is not equivalent to (x + y) - z  because the terms are added in a different order.

B. (x + (y - z))

We can expand the expression:

[tex]\[ x + (y - z) = x + y - z \][/tex]

This expression is indeed equivalent to (x + y) - z because the terms are arranged in the same order and operations are consistent.

So, the correct answer is:

[tex]\[ \text{B. } x + (y - z) \][/tex]

Answer:

Yes, it does.

Step-by-step explanation:

Every regular shaped figure will have rotational symmetry, since they are built with identical segments all around.

To find the answer, ask yourself « If I rotate the shape, is there a time where I’ll find the exact same shape again with a different angle? »

So, a square has rotational symmetry, but not a rectangle.

A equilateral triangle has rotational symmetry, but not any other type of triangle.

Answer:

2.1

Step-by-step explanation:

There were a total of 435 people in the House. 9 were neither Republican nor Democratic. Divide 9/435. multiply that by 100

Answer:

The answer is C.

Step-by-step explanation:

In 1997 U.S. House of Representatives there were 222 Republicans, 204 Democrats, 2 Independents, and 7 undecided.

So total number in the House = 222 + 204 + 2 + 7

= 435

Total number who is neither Republican nor Democrat = 2 + 7

= 9

Percentage of the total is neither Republican nor Democrat

= 9 / 435 * 100%

= 2.1%

Answer:

x = - 3[tex]\sqrt{2}[/tex], x = [tex]\sqrt{2}[/tex]

Step-by-step explanation:

Given

x² + 2[tex]\sqrt{2}[/tex] x - 6

To calculate the zeros equate to zero

x² + 2[tex]\sqrt{2}[/tex] x - 6 = 0 ( add 6 to both sides )

x² + 2[tex]\sqrt{2}[/tex] x = 6

One way is to use the completing the square method

add ( half the coefficient of the x- term )² to both sides

x² + 2[tex]\sqrt{2}[/tex] x + ([tex]\sqrt{2}[/tex])² = 6 + ([tex]\sqrt{2}[/tex])²

x² + 2[tex]\sqrt{2}[/tex] x + 2 = 6 + 2

(x + [tex]\sqrt{2}[/tex] )² = 8

Take the square root of both sides

x + [tex]\sqrt{2}[/tex] = ± [tex]\sqrt{8}[/tex] = ± 2[tex]\sqrt{2}[/tex]

subtract [tex]\sqrt{2}[/tex] from both sides

x = - [tex]\sqrt{2}[/tex] ± 2[tex]\sqrt{2}[/tex]

x = - [tex]\sqrt{2}[/tex] - 2[tex]\sqrt{2}[/tex] = - 3[tex]\sqrt{2}[/tex], or

x = - [tex]\sqrt{2}[/tex] + 2[tex]\sqrt{2}[/tex] = [tex]\sqrt{2}[/tex]

Answer:

Step-by-step explanation:

60 - 55 = 5, car B catches up to Car A 5 miles per hour, they are 5 miles closer every hour

10 / 5 = 2, 2 hours

car b would have driven 60 * 2 = 120

Answer:

1 and 8 are the ones you should choose.

Step-by-step explanation:

Answer: ∠1 and ∠8

Step-by-step explanation:

Given : Line b is parallel to line c .

In the given figure , a traversal line is passing through line b and c.

∠2=120°

Then , ∠1 +∠2=180°   [linear pair]

⇒ ∠1=180°-120°=60°

Now, ∠4 and ∠1 are vertical angles.

Since vertical angles are congruent.

∴ we have , ∠4 ≅ ∠1 =60°

Also, ∠4 and ∠8 are corresponding angles and corresponding angles are congruent.

∴ we have , ∠4 ≅ 8 =60°

∠2 cannot be congruent to ∠4, since both have different measures

∠7 cannot be congruent to ∠4, since ∠7 is congruent to ∠2 (Alternate exterior angles)

Answer:

196

Step-by-step explanation:

Divide 140 by 5 to find out how many miles she can drive with one gallon:

140/5 = 28

Multiply by 7:

28 x 7 = 196

hope this helps

Answer:

3 m^2

Step-by-step explanation:

The shaded area = Area of Sector - Area of Triangle

First we find area of sector = [tex]\frac{\theta}{360}*\pi r^2[/tex]

We know the angle is 60° (vertical angles are equal) and the radius is 6, so we find the area of sector to be:

[tex]\frac{\theta}{360}*\pi r^2\\\frac{60}{360}*\pi (6)^2\\=18.85[/tex]

Secondly, we find area of triangle (isosceles) = [tex]\frac{1}{2}abSinC[/tex]

where

a and b are the two sides bordering the known angle, so a=b=6, and

C is the angle which is 60°

Now we find the area to be:

[tex]\frac{1}{2}(6)(6)Sin(60)\\=15.59[/tex]

Hence, area of shaded = [tex]18.85 - 15.59=3.26[/tex]

Rounding to nearest whole number, area of shaded region = 3m^2

Answer:

The expression would be = to 0.

Step-by-step explanation:

Starting with -4(3s) + 2(-t), substitute (1/2) for s and (-3) for t:

                    -4(3/2) + 2(+3)

This gives us:

                       -12/2 + 6 = 0              

Answer:

-12

Step-by-step explanation:

3 times 1/2 is 1 1/2. 1 1/2 times -4 is -6. Then, -3 times 2 equals to -6. lastly -6 plus -6 equals to -12

Answer:

Option c

[tex]y\geq-3[/tex] or [tex]y \leq 21[/tex]

Step-by-step explanation:

The absolute value is a function that transforms any value x into a positive number.

Therefore, for the function [tex]f(x) = |x|[/tex]  x> 0 for all real numbers.

Then the inequation:

[tex]|y-9| \leq 12[/tex] has two cases

[tex](y-9)[/tex]    if [tex]y \geq 9[/tex]  (i)

[tex]-(y-9)[/tex]    if [tex]y < 9[/tex] (ii)

We solve the case (i)

[tex]y \leq 9 + 12\\y\leq21[/tex]

We solve the case (ii)

[tex]-y +9 \leq 12\\-y \leq 12-9\\y \geq -3[/tex]

Then the solution is:

[tex]y\geq-3[/tex] or [tex]y \leq 21[/tex]

Answer:

its c the answer above me is correct

Step-by-step explanation:

-4 < -12 would be my answer, just from looking at it. If you write it out on a number line, the number -4 is higher than -12. The higher the negative number, the lower it is on the line. So, -4 is greater than -12, not lower than.

The comparison which is not correct is Option (D) -4<-12

The inequality, greater than or lesser than between two numbers indicate that whether one number is greater than the other number or less than the other number. The inequality is represented by ">" and "<".

In number system, when comparing two numbers less than zero then the magnitude of smaller negative number is always greater than the magnitude of bigger negative number. Or in other words it is opposite to the positive number system .

For example,  -10<-4  or  -2<-1

Thus the comparison which is incorrect is Option (D)  -4 < -12.

To learn more about comparison between two numbers, refer -

https://brainly.com/question/2954013

#SPJ2

Answer:

2

Step-by-step explanation:

2 is actually a prime number because composite numbers have more than 2 factors but prime numbers don't.

The given equation is :

[tex]24x^{3}y^{2} -4x^{2}y +84x^{4}[/tex]

Now taking [tex]4x^{2}[/tex] common from all the terms, we get

[tex]4x^{2} (6xy^{2} -y+21x^{2} )=0[/tex]

Writing the equation in standard form we get:

[tex]21x^{2} +6xy^{2} -y=0[/tex]

Now we will use the formula of quadratic equations to solve this,

[tex]x1,2 = \frac{-b+\sqrt{b^{2}-4ac }} {2a}[/tex] and

[tex]x1,2 = \frac{-b-\sqrt{b^{2}-4ac }} {2a}[/tex]

Now putting a = 21, b = 6y² and c = -y and solving the equations, we get

[tex]x=\frac{-6y^{2}+\sqrt{36y^{4}+84y }}{42}[/tex] and

[tex]x=\frac{-6y^{2}-\sqrt{36y^{4}+84y }}{42}[/tex]

Answer:

The standard form of the quadratic equation is [tex]f(x)=-2x^{2}+12x-16[/tex]

Step-by-step explanation:

we know that

The standard form of a quadratic equation is

[tex]f(x)=ax^{2}+bx+c[/tex]

we have

[tex]f(x)=-2(x-3)^{2}+2[/tex]

convert to standard form

[tex]f(x)=-2(x-3)^{2}+2\\f(x)=-2(x^{2} -6x+9)+2\\f(x)=-2x^{2}+12x-18+2\\f(x)=-2x^{2}+12x-16[/tex]

Answer:

Step-by-step explanation:

Any one color would be 1/4 of the total. So the number of times you should get red is 1/4 of 160 = 40

Notice that this very odd problem does not depend on what the total is. It only depends on the number of times you make the draw. Unusual question.

Answer:

10) 40,80,160

11) 64, 256, 1024

12) 5, 2.5, 1.25

Step-by-step explanation:

Hope this helps. :)

Answer:

B

Step-by-step explanation:

Using the rule of exponents

[tex]\frac{a^{m} }{a^{n} }[/tex] ⇔ [tex]a^{(m-n)}[/tex]

Hence

[tex]\frac{3^{4} }{3^{2} }[/tex] = [tex]3^{(4-2)}[/tex] = 3² = 9 → B

The answer is 9

because 3 to the power of 4 is 81 and 3 to the power of 2 is 9 so it’s 81 divided by 9 which is 9

Answer:

3/10. 1/2 and 7/10

Step-by-step explanation:

For P(x) = x/10

When x = 3;

Then;

P(3) = 3/10

When x = 5

Then;

P(5) = 5/10

       = 1/2

When, x = 7

Then;

P(7) = 7/10

Answer:

[tex]P(3)=\frac{3}{10}=0.3\\\\P(5)=\frac{5}{10}=0.5\\\\P(7)=\frac{7}{10}=0.7[/tex]

Step-by-step explanation:

Probability is the possibility of happening of some event .

Probability = [tex]\frac{No.\,\,of\,\,outcomes}{Total\,\,no.\,\,of\,\,outcomes}[/tex]

Probability distribution links each outcome of an experiment with it's probability of occurrence .

Given: [tex]P(x)=\frac{x}{10}[/tex]

To find: Probability  distribution for the given function for x = 3 , 5 and 7

Solution:

For x = 3 :

On putting x = 3 in function [tex]P(x)=\frac{x}{10}[/tex] , we get

[tex]P(3)=\frac{3}{10}=0.3[/tex]

For x = 5 :

On putting x = 5 in function [tex]P(x)=\frac{x}{10}[/tex] , we get

[tex]P(5)=\frac{5}{10}=0.5[/tex]

For x = 7 :

On putting x = 7 in function [tex]P(x)=\frac{x}{10}[/tex] , we get

[tex]P(7)=\frac{7}{10}=0.7[/tex]

Answer:

7 units to the left

Step-by-step explanation:

Because if you move to the left you subtract 7 from the x-axis number or in this case 7, so 7-7=0.

Answer:

7 units to the left.

Step-by-step explanation:

Answer:

a) The volume of the dunking booth = 98 feet³

b) They will need 84 feet³ of water to fill 6/7 of dunking booth

Step-by-step explanation:

* Lets talk about the rectangular prism

- It has 6 rectangular faces each two opposite faces are congruent

- It has three dimensions Length, Width and Height

- Its volume = Length × Width × height

* In our problem the dunking booth is a rectangular prism

 with dimensions:

- Width = 3.5 ft

- Length = 3.5 ft

- Height = 8 ft

∴ Its volume = 3.5 × 3.5 × 8 = 98 feet³

a) The volume of the dunking booth = 98 feet³

* They want to fill 6/7 of the dunking booth with water

∴ The volume of the water will be 6/7 from the volume

   of the dunking booth

∵ The volume of the dunking booth = 98 feet³

∴ The volume of the water = 6/7 × 98 = 84 feet³

b) * They will need 84 feet³ of water

a) 98

b) 84

hope this helps!

Answer:

  yes, -6

Step-by-step explanation:

6/-1 = -36/6 = 216/-36 = -6

Adjacent terms have a common ratio of -6, so they comprise a geometric sequence.

Answer:

10^5

Step-by-step explanation:

100,000

= 10 x 10 x 10 x 10 x 10

= 10^5

Answer:

Yes, because 3^2 + 4^2 = 5^2

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

it doesn't have the same length so one sides gonna be longer

Here is your answer

D. 17, 18, 32

REASON:

Sum of any two sides of a triangle is always greater than the third side.

So,

17+18= 35

35>32

In other cases

a. 12+15= 27

27 <30

b. 14+16= 30

30 <34

c. 15+16= 31

31 <33

Hence other three can't be sides of a triangle.

HOPE IT IS USEFUL

The side lengths that could represent a triangle is 17, 18, 32

A triangle is a polygon with three sides and three angles. Type of triangles are isosceles, equilateral, scalene and obtuse.

For a triangle, the sum of any two sides must be greater than the third side. Hence:

For 12, 15 , 30; 12 + 15 < 30

For 14, 16 , 34; 14 + 16 < 34

For 15, 16 , 33; 15 + 16 < 33

For 17, 18 , 33; 17 + 18 > 33

The side lengths that could represent a triangle is 17, 18, 32

Find out more on triangle at: https://brainly.com/question/17335144

Answer:

15

Step-by-step explanation:

we need to write the equation. I came up with....

3(5 - x) = 30

so take the 3 away from the 30. I think your not supose to do the 3 because it out of the ( ). the opppisite of multiplication is division. so...

3 divided by 30 =10

rewrite

(5 - x) = 10

take the 5 away. the oppisite of subbtraction is addition.

5 + 10 = 15

check your; plug in x

3(5 - 15) = 30  This equation looks true!

Hope this helped! Please mark as brainliest! Thanks