A classroom floor has an area of
(30x3 + 8x2) ft, with a width of 2x feet.
What is the length of the floor?

Answer:

[tex]\sum_{n=5}^{\infty}n^2[/tex]

Step-by-step explanation:

The pattern given is:

25+36+49+64+...+n^2+...

The pattern can be written as

(5)^2+(6)^2+(7)^2+(8)^2+.....+n^2+....

The series is started with 5 and it continues up to infinity.

The summation notation for the given series is:

[tex]\sum_{n=5}^{\infty} n^2[/tex]

n= 1 and goes up to infinity and the series is made up of taking square of n,

The sum using summation notation, assuming the suggested pattern continues is :

     [tex]25 + 36 + 49 + 64 + ... + n^2 + ...=\sum_{n=5}^{\infty} n^2[/tex]      

We are given a series of numbers as

          25 + 36 + 49 + 64 + ... + n^2 + ...

To write the sum using summation notation means we need to express this series in terms of a general n such that there is a whole summation expressing this series.

Here we see that each of the numbers could be expressed as follows:

[tex]25=5^2\\\\36=6^2\\\\49=7^2\\\\64=8^2[/tex]

and so on.

i.e. the series starts by taking the square of 5 then of 6 then 7 and so on.

and the series goes to infinity.

Hence, the summation notation will be given by:

[tex]25 + 36 + 49 + 64 + ... + n^2 + ...=\sum_{n=5}^{\infty} n^2[/tex]

What composite shape? Where is the shape?

Answer:

6 squared cm

Step-by-step explanation:

The height of a triangle is length of the segment that is perpendicular to the base.  So that length is 2cm here.

The base and the height of the triangle should be perpendicular. So the base is 6cm

The area of a triangle is 1/2 * b * h.

1/2 * b  * h

1/2 *6   * 2

    3    *  2

        6

The answer is 6 squared cm

Answer:

Step-by-step explanation:

The formula of an area of a triangle:

[tex]A_\triangle=\dfrac{bh}{2}[/tex]

b - base

h - height

In ΔBCD we have b = 6cm, and h = 2cm.

Substitute:

[tex]A_{\triangle BCD}=\dfrac{(6)(2)}{2}=\dfrac{12}{2}=6\ cm^2[/tex]

Answer:

Eating dinner and eating dessert are dependent events because

P(dinner) . P(dessert) = 0.9 × 0.6 = 0.54 which is not equal to

P(dinner and desert) = 0.5 ⇒ answer A

Step-by-step explanation:

* Lets study the meaning independent and dependent probability  

- Two events are independent if the result of the second event is not

  affected by the result of the first event

- If A and B are independent events, the probability of both events  

 is the product of the probabilities of the both events

- P (A and B) = P(A) · P(B)

* Lets solve the question  

∵ There is a 90% chance that a person eats dinner

∴ P(eating dinner) = 90/100 = 0.9

∵ There is a 60% chance a person eats dessert

∴ P(eating dessert) = 60/100 = 0.6

- If eating dinner and dating dessert are independent events, then

 probability of both events is the product of the probabilities of the

 both events

∵ P(eating dinner and dessert) = P(eating dinner) . P(eating dessert)

∴ P(eating dinner and dessert) = 0.9 × 0.6 = 0.54

∵ There is a 50% chance the person will eat dinner and dessert

∴ P(eating dinner and dessert) = 50/100 = 0.5

∵ P(eating dinner and dessert) ≠ P(eating dinner) . P(eating dessert)

∴ Eating dinner and eating dessert are dependent events because

  P(dinner) . P(dessert) = 0.9 × 0.6 = 0.54 which is not equal to

  P(dinner and desert) = 0.5

To find a line that is parallel to another line and passes through a specific point, you first find the slope of the original line. Then, you use the point-slope form of a line equation to find the equation of the new line. The final equation is y = 5/3x - 10.

In order to find the equation of a line that is parallel to another and passes through a specific point, you first need to find the slope of the original line. The line given in the question is 5x - 3y = 6, which can be rearranged into slope-intercept form (y = mx + b) to become y = 5/3x - 2. The slope (m) of this line is 5/3. Parallel lines share the same slope, so the slope of the line we are trying to find is also 5/3.

Next, we use the point-slope form of a line equation, which is y - y1 = m(x - x1). The point given in the question is (6, -2), so x1 = 6 and y1 = -2. Substituting these into the equation, we find the equation of the line to be y + 2 = 5/3(x - 6).

Simplify this to y = 5/3x - 10, which is the equation of the line parallel to the given line and passing through the point (6, -2).

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To find an equation of a line parallel to a given line that passes through a specific point, you can use the point-slope form of a line. Find the slope of the given line, and use the slope and the given point to determine the equation of the parallel line.

We can find the equation of a line parallel to the given line by using the fact that parallel lines have the same slope. To find the slope of the given line, we need to rearrange the equation into the slope-intercept form, y = mx + b, where m is the slope:

5x - 3y = 6 → -3y = -5x + 6 → y = (5/3)x - 2

So, the slope of the given line is 5/3. Thus, any line parallel to this must also have a slope of 5/3.

Since we now have the slope and a point that the line passes through (6, -2), we can use the point-slope form of a line to find the equation:

y - y₁ = m(x - x₁) where (x₁, y₁) is the point given and m is the slope. Substituting the values in, we get:

y - (-2) = (5/3)(x - 6) → y + 2 = (5/3)(x - 6)

Simplifying this equation gives the final answer:

y = (5/3)x - 22/3

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Answer:

16 mph

Step-by-step explanation:

You should first form equations related to this information

Given,Tamara can go 4 mph faster than her sister, Samantha

Lets take speed to ride a bike for Samantha to be=  x mph

The speed to ride a bike for Tamara will be= x+4 mph

To cover a distance of 80 miles, Samantha takes 1 hour longer than Tamara

Introduce the formula for time; time=distance/speed=D/S where D is distance in miles and S is speed in miles per hour

Here time Samantha takes to cover a distance of 80 miles is 1 hour more than that taken by Tamara, hence

Time taken by Samantha

[tex]=\frac{80}{x}[/tex]

Time taken by Tamara

[tex]=\frac{80}{4+x}[/tex]

Equation for difference in time

[tex]=\frac{80}{x} -\frac{80}{4+x} =1[/tex]

Solve the equation for difference in time to get value of x which is samantha speed

[tex]=\frac{80}{x} -\frac{80}{x+4} =1\\\\\\=80(4+x)-80(x)=x(4+x)\\\\\\=320+80x-80x=4x+x^2\\\\\\=x^2+4x-320=0[/tex]

Solve quadratic equation by the quadratic formula where a=1,b=4 and c=-320

x=(-b±√b²-4ac)÷2a

x=(-4±√4²-4×1×-320)÷2×1

[tex]x=\frac{-4+/-\sqrt{4^2-4*1*-320} }{2} \\\\\\x=(-4+/-\sqrt{1296} )/2\\\\\\x=\frac{-4+36}{2} =\frac{32}{2} =16[/tex]

Samantha speed is 16 mph

Answer:

37*20 = 740/4 = 185 -> Spent on new CD's

740 - 185 = $ 555 -> Savings Account

Step-by-step explanation:

Answer:

Amount of money she spend on CDs: $185

Amount of money she is going to be in her savings account: $555

Step-by-step explanation:

She sold 37 pairs of earrings with each of them costing 20 dollars.

That means she made 20(37)=740 dollars.

She is going to use 1/4 of 740 dollars to buy new CDS. This means she is going to use 740/4 =185 dollars on CDs.

So what money is left from 740 dollars after spending 185 dollars?

740-185=555 dollars

She is going to put 555 dollars into savings.

Answer:

Segment GD is half the length of segment HC​ ⇒ answer D

Step-by-step explanation:

* Look to the attached file

Answer: D) Segment GD is half the length of segment HC​

Answer:

t=0                                  t = -10/3

Step-by-step explanation:

5|3t+5|=25

Divide each side by 5

5|3t+5| /5=25/5

|3t+5|=5

Now to get rid of the absolute value we get two equations, one positive and one negative

3t+5 =5           3t+5 = -5

Subtract 5 from each side

3t+5-5 =5-5           3t+5-5 = -5-5

3t =0                        3t = -10

Divide by 3

3t/3 = 0/3                   3t/3 = -10/3

t=0                                  t = -10/3

Answer:

C

Step-by-step explanation:

So the system is:

5x+13y=232

12x+7y=218

------------------

Let's look at the options to see which will work:

A) Multiply first equation by -13:  -65x-169y=-3016

& second equation by 7           :    84x+49y=1526

There are no opposites in the either one of the variable columns so not this option.

B) Multiply first equation by 7:  35x+91y=1624

& second equation by 13       : 156x+91y=2834

There are no opposites in the either one of the variable columns so this is not option unless we were asked to subtract the equations.

C) Multiply first equation by -12: -60x-156y=-2784

& second equation by 5           :   60x+35y=1090

There is a column that contains opposites here so when you add the equations the x-variable will get eliminated.

Answer:

3rd one

Step-by-step explanation:

[tex]y=20^x\Longleftrightarrow x=\log_{20}y[/tex]

Answer:

it is 4x=-9

Step-by-step explanation:

Answer:

c and a

because 3k has to add up the an even number so k by it self can not be an even number, and k/2 would still be an odd number because an off number divided by a even number still makes it odd

If 3k is an even integer then k is an even integer, and k and k - 1 are also integers. However, k/2 cannot be assured to be an integer unless k is a multiple of 4, making it the correct answer for what cannot be an integer.

If 3k is an even number, then k must also be an even number because an even number divided by 3 still leaves k as an integer. So, we can infer that k is an integer.

The option k - 1 must also be an integer because if k is an integer, subtracting 1 from it will result in another integer. The option 3k is given as an even integer, to begin with. However, the option k/2 cannot be an integer unless k is not only even but also a multiple of 4, because when you divide an even number that is not a multiple of 4 by 2, the result is not an integer.

Given the information provided in the question, we can conclude that k/2 is the option that cannot definitely be an integer without additional information specifying that k is indeed a multiple of 4.

Answer:

MW=CD

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The general rule for the quadratic function is

[tex]y=ax^2+bx+c[/tex]

Use the data from the table:

[tex]y(0)=6\Rightarrow 6=a\cdot 0^2+b\cdot 0+c\\ \\y(1)=4\Rightarrow 4=a\cdot 1^2+b\cdot 1+c\\ \\y(-1)=10\Rightarrow 10=a\cdot (-1)^2+b\cdot (-1)+c[/tex]

We get the system of three equations:

[tex]\left\{\begin{array}{l}c=6\\ \\a+b+c=4\\ \\a-b+c=10\end{array}\right.[/tex]

From the first equation

[tex]c=6,[/tex] then

[tex]\left\{\begin{array}{l}a+b=-2\\ \\a-b=4\end{array}\right.[/tex]

Add these two equations:

[tex]a+b+a-b=-2+4\\ \\2a=2\\ \\a=1[/tex]

So,

[tex]b=-2-a=-2-1=-3[/tex]

The quadratic function is

[tex]y=1\cdot x^2-3x+6\\ \\y=x^2-3x+6[/tex]

Answer:

12 * 50 = 600

Step-by-step explanation:

We have to multiply 12 by 50

Short cut method for multiplying a number by 50

Step 1: Take the half of the given number

Step 2: Multiply the result by 100

To find the short cut method to multiply 12 by 50

Here the number is 12

Step 1: divide the number by 2

12/2 = 6

Step 2: Multiply 6 by 100 we get 600

Therefore 12 * 50 = 600

Answer:

12 x 50= 600

Step-by-step explanation:

One way you can do is long and short. But the best way is to do it long because than you will get a better score and get the answer still.

Answer:

We have divided the bar into two parts. For example, x and y.

Step-by-step explanation:

So, we have

63cm=x+y    (1)

But one of those parts is 7 centimeters smaller than the other.We take y as the smallest part.Then:

y=x-7cm    (2)

we replace this information in the first equation

63cm=x+(x-7cm)

63cm=x+x-7cm

7 goes to add to the other side

63cm+7cm=2x

70cm=2x

2 goes to divide to the other side

35cm=x

from the second equation we have

y=x-7cm

y=35cm-7cm=28cm

Finally

x=35cm

y=28cm

x+y=35cm+28cm=63cm

Answer:

False

Step-by-step explanation:

A point has zero dimension, once two pints are connected then you get one dimension which is a line

B. False

A point is a fundamental concept in geometry and represents a location in space. It is considered zero-dimensional because it has no length, width, or height.

A point is often represented by a dot or a small symbol and is described by its coordinates in a coordinate system.

In a one-dimensional context, you would have a line segment or a line that consists of multiple points.

However, a single point on its own is considered to have no dimension and is therefore not classified as one-dimensional.

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Answer:

Step-by-step explanation:

Find the x-value that makes the denominator zero.  This x = a is the equation of the vertical asymptote.  Next, determine the behavior of the function as x increases without bound in either direction.  If there is a limiting value, then this y = d is the horizontal asymptote.

Consider the rational function

     [tex]f(x)=\frac{P(x)}{Q(x)}[/tex]

We will find the Domain of Rational function first, means those value of  rational function for which f(x) is defined, To do this we will evaluate those  point first for which, Q(x)=0.

So, The first Step is "Finding Domain of the rational function" as well as the point where function is not defined.

⇒Consider the function

    [tex]f(x)=\frac{x-3}{x-2}[/tex]

→Domain of the function is

x-2=0

x=2

=All Real Numbers , except at x=2.

=R- {2}

Answer:

[tex]\large\boxed{\dfrac{4}{3}}[/tex]

Step-by-step explanation:

Look at the picture.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the graph we have two points (0, -4) and (3, 0).

Substitute:

[tex]m=\dfrac{0-(-4)}{3-0}=\dfrac{4}{3}[/tex]

Answer:

-$1.9

Step-by-step explanation:

There are 47 pages.

Printing on both sides would divide the number of pages into half.

47/2 = 23.5

2 pages on each side would mean 4 pages on one sheet. Therefore, the number of pages will be further divided by 2.

23.5/2 = 11.75

There cannot be 11.75 pages so we will round it up to 12 pages.

Each page costs $0.25 so 12 pages will cost:

12 x 0.25 = $3

Faithi has $1.1 so new account balance will be:

1.1 - 3 = $-1.9

Therefore, Fathi's balance in his printing account would be negative $1.9.

!!

When Fathi prints a 47-page document using both sides of pages and printing 2 pages on each side, at a cost of $0.25 per sheet, his printing account balance will be -$1.90.

The question asks what will Fathi's balance be in his printing account after printing a document that is 47 pages long, with specific printing constraints. To solve this, we first need to figure out the number of pages he will print per sheet. Given that Fathi prints two pages on each side of a sheet, he will print 4 pages per sheet. As the document is 47 pages, he will need a total of 12 sheets (47 divided by 4 and rounded up to the nearest whole number).

Next, we need to calculate the cost of printing those sheets. As each sheet reduces his printing account by $0.25, and he's using 12 sheets, the cost will be $3.00 (12 multiplied by $0.25).

Finally, to find the balance in his printing account, we subtract the cost of printing from his initial balance. Fathi started with $1.10 in his printing account, so after deducting the cost of printing 12 sheets, his final balance will be $-1.90 (which means he owes this amount to replenish his account back to zero).

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Answer:

202,44

Step-by-step explanation:

We know that 41% of a number is 83, and we need to find the base number.  To do so, we're going to use the rule of three, as follows:

If 83 represents -----------------------------> 41% of a number

             X          <------------------------------ 100% of a number

Then:

X = (100 * 83)/41 = 202,44

Therefore, the base number is:  202,44 ✅

Answer:

Please look at the different answers. I wasn't 100% sure what your expression was.

Step-by-step explanation:

If you mean 2/(5x-1) then g(x) will take the fraction into account with a constant 2 for the numerator and a variable for the denominator since that is where our variable is so g(x)=2/x.

Now h(x)=5x-1 since if you plug in 5x-1 into 2/x where x is you will get our original expression.

Now if you did mean (2/5)x-1 I would take notice of where the variable is which is in (2/5)x so g(x)=x-1 where h(x)=(2/5)x since if you plug (2/5)x in place of the x in x-1 you will get the original.

Please let me know if I didn't interpret your expression correctly.

The required functions which satisfy the condition [tex]\ h (x) = g (f (x))[/tex] are,

[tex]h (x) = \dfrac{2}{5} x[/tex]  and [tex]g (x) = x - 1[/tex].

Used the concept of composition which states that,

The composition of a function is an operation where two functions say f and g generate a new function say h in such a way that;

[tex]\ h (x) = g (f (x))[/tex]

Consider the given function as

[tex]f (x) = \dfrac{2}{5} x - 1[/tex]

It is given that [tex]\ f (x) = g (h (x))[/tex] and neither [tex]g (x)[/tex] nor [tex]h (x)[/tex] is solely x.

Let us assume that,

The function h (x) is defined as,

[tex]h (x) = \dfrac{2}{5} x[/tex]

Then we get;

[tex]\ f (x) = g (h (x))[/tex]

= [tex]h (x) - 1[/tex]

Substitute [tex]h (x) = x[/tex] in the above function for the value of function g (x),

[tex]g (x) = x - 1[/tex]

Therefore, the required functions are [tex]h (x) = \dfrac{2}{5} x[/tex]  and [tex]g (x) = x - 1[/tex].

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Answer:

Dotted linear inequality shaded above passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5)

Step-by-step explanation:

we have

[tex]y > -x+4[/tex] ----> inequality A

The solution of the inequality A is the shaded area above the dotted line [tex]y=-x+4[/tex]

The dotted line passes through the points (0,4) and (4,0) (y and x-intercepts)

and

[tex]y \leq -(1/2)^{x} +6[/tex] -----> inequality B

The solution of the inequality B is the shaded area above the solid line [tex]y=-(1/2)^{x} +6[/tex]

The solid line passes through the points (0,5) and (-2,2)

therefore

The solution of the system of inequalities is the shaded area between the dotted line and the solid line

see the attached figure

Dotted linear inequality shaded above passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5)

Answer:

A i think

Step-by-step explanation:

The volume of a sphere that has a radius of 9 inches is 3053.63in³.

V≈3053.63in³

V=4

3πr3=4

3·π·93≈3053.62806in³

Answer:

Therefore, C ) [tex]\frac{4*pi}{3} (9)^{3}[/tex].

Step-by-step explanation:

Given :  A sphere that has a radius of 9 inches.

To find : Which equation can be used to find the volume of a sphere.

Solution: We have given

radius of sphere =  9 inches.

Volume of sphere = [tex]\frac{4*pi}{3} (radius)^{3}[/tex].

Plug the valu radius = 9 inches .

Volume of sphere = [tex]\frac{4*pi}{3} (9)^{3}[/tex].

Then equation c is correct answere.

Therefore, C ) [tex]\frac{4*pi}{3} (9)^{3}[/tex].

Answer:

78˚

Step-by-step explanation:

Triangle MNP is congruent to Triangle QST, and so their angle measures are the same.

If you look at the order of the letters in the triangle names, you will notice that angle N lines up with angle S, so that means their angle measures are the same. Therefore if angle N is 78˚, angle S will be 78˚ as well.

Answer:

∠S = 78°

Step-by-step explanation:

Corresponding angles are equal, that is

∠Q = ∠M = 66° and

∠S = ∠N = 78°

Answer:

Step-by-step explanation:

According to the given statement two pieces are of same length:

If the length of one piece is x,

Then the length of other piece is also x.

And one piece is 2 feet longer than the other two = x+2

Total length of a board = 10 foot

Now make the equation from these terms:

x+x+x+2= 10

This is the equation of the given question.

You can further solve this equation:

x+x+x+2=10

3x+2=10

Now combine the constants:

3x=10-2

3x=8

x=8/3

x=2.67

It means that the length of two pieces of same length is 2.67

And the length of one piece which is longer than the other two = x+2 = 2.67+2 = 4.67 ....

Final answer:

To cut a 10-foot board into three pieces where two are the same length and one is 2 feet longer, denote the shorter length as 'x', create the equation 2x + (x + 2) = 10, and solve for 'x'. The two shorter pieces will each be approximately 2.67 feet and the longer one will be approximately 4.67 feet.

Explanation:

The question involves dividing a 10-foot board into three pieces with one piece being 2 feet longer than the other two equal pieces. To solve this, let's denote the length of the shorter pieces as 'x'. Since there are two of these, we have '2x', and the longer piece would be 'x + 2' feet long. The sum of the lengths of all three pieces is equal to the length of the board, so:

2x + (x + 2) = 10

This simplifies to:

3x + 2 = 10

Subtracting 2 from both sides gives:

3x = 8

Dividing both sides by 3 gives:

x = 8/3 or approximately 2.67 feet.

Therefore, the two shorter pieces are each approximately 2.67 feet long and the longer piece is 2.67 + 2, which is approximately 4.67 feet long.

Answer:

The percentage of the calls lasted less than 8 min is 16%

Step-by-step explanation:

* Lets explain how to solve the problem

- To find the percentage of the calls lasted less than 8 min, find the

  z-score for the calls lasted

∵ The rule of z-score is z = (x - μ)/σ , where

# x is the score

# μ is the mean

# σ is the standard deviation

* Lets solve the problem

- The average phone call in a certain town lasted is 9 min

∴ The mean (μ) = 9

- The standard deviation is 1 min

∴ σ = 1

- The calls lasted less than 8 min

∴ x = 8

∵ z = (x - μ)/σ

∴ z = (8 - 9)/1 = -1/1 = -1

∴ P(z < 8) = -1

- Use z-table to find the percentage of x < 8

∴ P(x < 8) = 0.15866 × 100% = 15.87% ≅ 16%

* The percentage of the calls lasted less than 8 min is 16%

Answer:

The percentage of the calls lasted less than 8 min is 16%.

Step-by-step explanation:

We are dealing with a normal distribution with an average phone call of 9 min and a standard deviation of 1 min. Below we can observe the empirical rule applied with a mean of 9 and a standard deviation of 1. The number 8 represents one standard deviation below the mean, so, the percentage of observations below 8 is 16%. Therefore the percentage of the calls lasted less than 8 min is 16%.

Answer:

i think she should eat

I think ??????

Step-by-step explanation:

Answer:

-20x^2 +14x+12

The domain of f*g is all real numbers

Step-by-step explanation:

f(x) = -4x - 2

g(x) = 5x - 6.

f*g = (-4x-2) * (5x-6)

FOIL

first -4x*5x = -20x^2

outer -4x*-6 = 24x

inner -2*5x = -10x

last -2 *-6 = 12

Add them together

-20x^2 +24x-10x+12 = -20x^2 +14x+12

The domain of f is all real numbers, the domain of g is all real numbers

The domain of f*g is all real numbers

Answer:

[tex](f*g)(x)=-20x^2+14x+12[/tex]

Domain: All Real Numbers.

Step-by-step explanation:

Given the function f(x):

[tex]f(x) = -4x - 2[/tex]

And the function g(x):

[tex]g(x) = 5x - 6[/tex]

You need to multiply them. Then:

[tex](f*g)(x)=( -4x - 2)( 5x - 6)\\\\(f*g)(x)=-20x^2+24x-10x+12\\\\(f*g)(x)=-20x^2+14x+12[/tex]

Since we know that the domain is the set of all real values of the variable "x" that will give real values for the variable "y", the domain of [tex](f*g)(x)=-20x^2+14x+12[/tex] is ALL REAL NUMBERS.