What is the sum of n natural numbers: 1+2+...+n?

So first you have to find the volume of the entire tank using the height of 6cm. Then you have to find the volume of just the water using the height of 4 cm. Then you subtract both of your volumes and that will represent the volume of the part of the tank that isn't filled with water

Answer:

432cm³

Step-by-step explanation:

First we need to find the volume.

Use the volume formula.

[tex]V=l*w*h[/tex]

Plug in the values.

[tex]V=18*12*6\\ \\ V=1296[/tex]

Now find the volume of water we filled up.

[tex]V=18*12*4\\ \\ \\V=864[/tex]

Now we can subtract to find how much more water we need.

[tex]V=1296-864\\ \\ \\V=432[/tex]

432cm³ of water is needed to fill up the tank completely.

Answer:

Mike is not right

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z----> the scale factor

x----> surface area of the enlarged rectangular prism

y-----> surface area of the original rectangular prism

[tex]z^{2}=\frac{x}{y}[/tex]

so

In this problem we have

[tex]z=2[/tex]

substitute

[tex]2^{2}=\frac{x}{y}[/tex]

[tex]4=\frac{x}{y}[/tex]

[tex]x=4y[/tex]

so

The surface area of the enlarged rectangular prism is 4 times the surface area of the original rectangular prism

therefore

Mike is not right

Verify with an example

we have a rectangular prism

[tex]L=5\ m[/tex]

[tex]W=2\ m[/tex]

[tex]H=3\ m[/tex]

The surface area of the prism is equal to

[tex]SA=2(LW)+(2L+2W)H[/tex]

substitute the values

[tex]SA=2*(5*2)+(2*5+2*2)*3=62\ m^{2}[/tex]

If he doubles each dimension of any rectangular prism

then

the new dimensions will be

[tex]L=5*2=10\ m[/tex]

[tex]W=2*2=4\ m[/tex]

[tex]H=3*2=6\ m[/tex]

The new surface area will be

[tex]SA=2*(10*4)+(2*10+2*4)*6=248\ m^{2}[/tex]

[tex]248/62=4[/tex]

therefore

The surface area of the enlarged rectangular prism is 4 times the surface area of the original rectangular prism

Answer:

x=60

Step-by-step explanation:

As the sides of the triangle are doubled (21 to 42 and 44 to 88) that means that the side of 30 is doubled to 60

Answer:

x=60

Step-by-step explanation:

Answer:

-1/2

Step-by-step explanation:

To find the slope we know that:

Slope = (Y2-Y1)/(X2-X1)

Then, given the two points, we have that:

(X1, Y1) = (-2,-2)

(X2, Y2) = (2, -4)

Then:

m= (Y2-Y1)/(X2-X1) = (-4-(-2))/(2-(-2)) = -4+2/2+2 = -2/4 = -1/2

So the slope of the function that passes through those points is: -1/2

Answer:

$18.00

Step-by-step explanation:

75% of 80$ is 60$ .    

80$-60$=20$

10%of20$=2$

20$-2$=18$

18$

She spend $18 on the swimsuit and she gets total 77.5 percent off.

Given local clothing shop is marking down all of its summer clothes by 75%.

And Sarah would like to purchase a swimsuit that is originally priced at $80.

So, the markdown price of swimsuit will be ( $80 - 75 % of $80).

Now 75% of $80 is equals to $60.

So the markdown price of swimsuit will be ($80 - $60) or $20.

Again, when she gets to the register, she signs up for a loyalty cars that saves her an additional 10%.

So 2% of $20 dollar will be $2.

Now the final markdown price of swimsuit will be ($20-$2) or $18 .

Total discount she get is of ($80 - $18) or $62.

The percent amount she gets off = [tex]\frac{62}{80} \times100%[/tex] %.

=[tex]0.775 \times100[/tex]%.

[tex]=77.5[/tex]%.

She spend $18 on the swimsuit and she gets total 77.5 percent off.

For more details on percentage follow the link:

https://brainly.com/question/16797504

The answer is:

[tex]-2(2x+5)-3(x-1)=-7x-7\\[/tex]

To solve the problem, we need to perform the operations and then, add like terms.

We need to apply the distributive property, which is defined by the following way:

[tex]a(b+c)=ab+ac[/tex]

Also, we need to remember how to add like terms. Like terms are terms that share the same exponent and the same variable, for example:

[tex]3x+5x+x^{2}=8x+x^{2}[/tex]

We were able to add only the first two terms since they are like terms, both are sharing the same exponent and the same variable.

So, we are given the expression:

[tex]-2(2x+5)-3(x-1)[/tex]

Then, solving we have:

[tex]-2(2x+5)-3(x-1)=-4x-10-(3x-3)\\\\-4x-10-(3x-3)=-4x-10-3x+3\\\\-4x-10-3x+3=-4x-3x-10+3\\\\-4x-3x-10+3=-7x-7[/tex]

Hence, we have that the answer is:

[tex]-2(2x+5)-3(x-1)=-7x-7\\[/tex]

Have a nice day!

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

The formula of a slope:

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

We have the points (-3, -1) and (1/2, 2). Substitute:

[tex]m=\dfrac{2-(-1)}{\frac{1}{2}-(-3)}=\dfrac{3}{3\frac{1}{2}}=\dfrac{3}{\frac{7}{2}}=3\cdot\dfrac{2}{7}=\dfrac{6}{7}\\\\y-(-1)=\dfrac{6}{7}(x-(-3))\\\\y+1=\dfrac{6}{7}(x+3)}[/tex]

Convert to the standard form Ax + By = C:

[tex]y+1=\dfrac{6}{7}(x+3)[/tex]           multiply both sides by 7

[tex]7y+7=6(x+3)[/tex]              use the distributive property

[tex]7y+7=6x+18[/tex]                subtract 7 from both sides

[tex]7y=6x+11[/tex]             subtract 6x from both sides

[tex]-6x+7y=11[/tex]

Answer:

I believe 40 is the height from which the ball was dropped

In the expression \( 40(0.75)^x \), the number 40 represents the initial height from which the ball is dropped. This initial height refers to the height of the ball above the ground before it experiences any bounces.
The expression itself describes a geometric sequence where the height of the ball after each bounce is a certain fraction of the height from the previous bounce. In this particular case, after each bounce, the ball reaches a height that is 75% (or 0.75 times) of the height of the previous bounce.
To break it down further:
- \( 40 \) is the initial height (in meters, feet, or another unit of measurement) where the ball was dropped from the top of the building.
- \( 0.75 \) is the common ratio, representing the fact that the ball loses 25% of its height with each bounce. It means that the ball only reaches 75% of the height it reached after the previous bounce.
- \( x \) is the number of bounces.
So, after the first bounce (when \( x = 1 \)), the height of the ball would be \( 40 \times 0.75 \). After the second bounce (when \( x = 2 \)), the height would be \( 40 \times 0.75^2 \), and so on for each subsequent bounce, following the pattern of a geometric sequence.

Answer: Option D

[tex]P (B | A) =\frac{4}{5}[/tex]

Step-by-step explanation:

Call A to the event in which a student advances to the second round.

We know that:

[tex]P (A) = 75\% = 0.75[/tex]

Call B the event in which a student advances to the third round.

We know that:

[tex]P (B) = 60\% = 0.6[/tex]

We then look for the probability of B given A. This is:

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

In this case, the probability of B and A is equal to the probability of B, since the students who advance to the third round also advanced to the second round before

[tex]P (B | A) =\frac{P(B)}{P(A)}[/tex]

[tex]P (B | A) =\frac{0.6}{0.75}[/tex]

[tex]P (B | A) =\frac{4}{5}[/tex]

C+6=23 just go step by step dawg

Answer:

Undefined

Step-by-step explanation:

Slope form:

m (slope) = (y₂ - y₁)/(x₂ - x₁)

Let:

(x₁ , y₁) = (4 , 4)

(x₂ , y₂) = (4 , 9)

Plug in the corresponding numbers to the corresponding variables.

m = (9 - 4)/(4 - 4)

Simplify

m = (5)/(0)

m = undefined

Undefined is your answer, for there cannot be a 5/0. You cannot have 5 parts of nothing.

~

Interest=Principal×Rate×Time

I=PRT/100

I= 79000×15×1

100

I= 1185000

100

I= $11850

To confirm

11850/79000 ÷ 100

= 0.5 ×100

= 15% (rate)

The interest of one year is $11850.

easy interest is based on the essential amount of a loan or the primary deposit in a savings account.

calculation:-

Amount of money borrowed by Linda = $79000

rate of interest =15%

Interest amount= $79000*15/100

  The interest of the year =$11850

Learn more about simple interests here:-https://brainly.com/question/2294792

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Answer:

The sides of the new triangle compared to the original are 4 times smaller.

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

Let

z-----> the scale factor

x----> the corresponding side of new triangle

y----> the corresponding side of the original triangle

[tex]z=\frac{x}{y}[/tex]

we have

[tex]z=\frac{1}{4}[/tex]

substitute

[tex]\frac{1}{4}=\frac{x}{y}[/tex]

[tex]x=\frac{1}{4}y[/tex]

therefore

The sides of the new triangle compared to the original are 4 times smaller.

Answer:

C

Step-by-step explanation:

The correct answer is B.

1/9 can be converted into 2/18. 2/3 can be converted into 12/18. 2/18 + 12/18 + 5/18 = 19/18. The answer is B

hw: 3/2hrs = 3×30 = 90mins

chores: 1/2hr = 1×30 = 30mins

sleep: 17/2hrs = 17×30 = 510mins

90+30+510=630mins=10.5hrs/day

Answer:

21/2

Step-by-step explanation:

khan academy got right

Answer:

241

Step-by-step explanation:

Answer:

Option D. ET=IT

Step-by-step explanation:

we know that

The Side Angle Side postulate (SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent

In this problem

the included angle ∠ETK of triangle TEK is congruent with the included angle ∠KTI of triangle TIK

the side KT is a common side both triangles

therefore

ET must be equal to IT to prove that triangles TEK and TIK are congruent by SAS postulate

Hi

The probability of landing a green side up is 2 / 6 .

Hope this helps

Answer:

C. 2/6

Step-by-step explanation:

We know that a block has 6 sides.

There are 2 green sides.

Now all we do is put the number of green sides over the number of sides the block has.

2/6 is our answer.

Answer:3*6

Step-by-step explanation: It is (40*6)+(3*6) you have to break it down

Answer:69.38

Step-by-step explanation: Sue = 15.5 allie = 23.25 carol = 15.5+32.25 - 8.12 2.   15.5+32.25=38.75-8.12=  30.63 now all together 23.25+15.5+30.63= 69.38

The girls danced for a total of 30 minutes and 33 seconds.

First, we need to calculate the total time Sue and Allie danced combined:

Sue danced for 15.5 minutes, which can be written as [tex]\(\frac{155}{10}\)[/tex] minutes.

Allie danced for 23.25 minutes, which can be written as [tex]\(\frac{2325}{100}\)[/tex] minutes.

To combine these times, we need a common denominator, which is 100:

Sue's time in minutes: [tex]\(\frac{155 \times 10}{100} = \frac{1550}{100}\)[/tex]

Allie's time in minutes: [tex]\(\frac{2325}{100}\)[/tex]

Now we add Sue's and Allie's times:

[tex]\(\frac{1550}{100} + \frac{2325}{100} = \frac{3875}{100}\)[/tex]

Converting this back to mixed numbers:

[tex]\(\frac{3875}{100} = 38\)[/tex] minutes and [tex]\(\frac{75}{100}\)[/tex] minutes, which is 45 seconds.

Now, Carol danced for 8 minutes and 12 seconds less than the combined time of Sue and Allie. We need to subtract this time from the total time Sue and Allie danced:

[tex]\(38\)[/tex] minutes and [tex]\(45\)[/tex] seconds [tex]\(-\) \(8\)[/tex] minutes and [tex]\(12\)[/tex] seconds.

Subtracting the minutes:

[tex]\(38 - 8 = 30\)[/tex] minutes.

Subtracting the seconds:

[tex]\(45 - 12 = 33\)[/tex] seconds.

Therefore, Carol danced for 30 minutes and 33 seconds. Since Sue and Allie's combined time was 38 minutes and 45 seconds, and Carol danced for 8 minutes and 12 seconds less, the total time the girls danced altogether is:

[tex]\(38\)[/tex] minutes and [tex]\(45\)[/tex] seconds [tex]\(-\) \(8\)[/tex] minutes and [tex]\(12\)[/tex] seconds [tex]\(=\) \(30\)[/tex] minutes and [tex]\(33\)[/tex] seconds.

Thus, the girls danced for a total of 30 minutes and 33 seconds.

The answer is y=1/2x-2

Answer:

1/8

Step-by-step explanation:

If you need 1/4 cup for the full recipe and you're making half, you have to divide 1/4 by 2. Dividing 1/4 by 2 is the same as multiplying 1/4 by 1/2 since you take the reciprocal (opposite or flip) of 2. 1/4 times 1/2 is 1/8. I hope this helps!

Answer:

1/8

Step-by-step explanation

(1/4)÷2 is the same as saying (1/4)×(1/2)

Multiply the numerators (1×1)

Multiply the denominator (4×2)

and you get (1/8)

The right answer is y + 8= -5 (x-2).

Answer:

[tex]y+8=-5(x-2)[/tex]

Step-by-step explanation:

Slope of the line =-5

To get point slope form of the line , we use the point that passes through the line. LEts pick the point (2,-8)

Point slope form of a line is

[tex]y-y_1=m (x-x_1)[/tex]

(x1,y1) is (2,-8) and slope m = -5

[tex]y-(-8)=-5(x-2)[/tex]

[tex]y+8=-5(x-2)[/tex] is the equation of the line in point slope form.

The addition equation or a subtraction equation to describe the diagram is (-9)—(-4) = -13

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have a line graph shown in the picture.

The small arrow represents the length of 4 but as it is indicating negative direction, so we take -4

Similarly, the big arrow represents the length of 9 as it is indicating negative direction, so we take -9

The sum of the lengths:

(-9)—(-4) = -13

Thus, the addition equation or a subtraction equation to describe the diagram is (-9)—(-4) = -13

Learn more about the arithmetic operation here:

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Answer:

x² + 8x + 16

Step-by-step explanation:

(x + 4)² = (x + 4)(x + 4)

Each term in the second parenthesis is multiplied by each term in the first parenthesis, that is

x(x + 4) + 4(x + 4) ← distribute both parenthesis

= x² + 4x + 4x + 16 ← collect like terms

= x² + 8x + 16 ← perfect square trinomial

you can use inverse operations and add 37 to 82 and get y=119

Y= 119 because if you add 82 and 37 you get 119

To check: 119-37=82

i believe the answer would be x > 1?

Answer:

x > 1

Step-by-step explanation:

3(x-1)<-3(2-2x)

=> 3x +3 < 6x

=> 1<x

Answer:

hello : x = 2 +√17    or  x = 2 -√17

Step-by-step explanation:

(5x-2)^2=17

5x-2 = √17     or 5x-2 =  - √17

x = 2 +√17    or  x = 2 -√17

It's B A(n)= 350 + (n - 1) (0.04 · 350); $504.00

Answer:

Option B.

Step-by-step explanation:

Gracie invest $350 at the beginning of the year 1 at annual simple interest rate of 4%.

the balance at the beginning of the year 12. Interest will be calculated for 11 years.

Formula for simple interest : A = P(1 + rt)

By putting the value : A = 350(1 + 0.04 × 11)

                                   A = 350 ( 1.44 ) = $504.00

So the best answer would be option B.

Answer:

4th option is correct; Each distribution has a different mean and a different standard deviation

Step-by-step explanation:

For the mean to be same in all three distributions, all graphs must be centered around the same number, so mean is not same.

The width of each graph shows how much data deviate from the mean. Since the width is different in all three distributions, standard deviation is different in all three distributions

Answer:

D

Step-by-step explanation:

E2020