The perimeter and area of a wall have the same value. If the base of the wall is 7 meters long, what is the height of the wall? ​

Answer:

Subtract - 3 in each term

3 - 3 < x+3 - 3 < 6- 3

0 < x < 3

Answer:

it would be y since both are common there

Answer:

hope it helps

Step-by-step explanation:

x+2=6

3x=10

6+3x=22

5-3x=15

3+x=6y I'm sure about this one

5+x=y/4=23

Answer:

(a) 1) When V = 1000 L, the height of the liquid in the tank is approximately 62 cm

2) When V = 5,000 L, the height of the liquid in the tank is approximately 106 cm

3) When V = 10,000 L, the height of the liquid in the tank is approximately 202 cm

b) The drawing of the spherical tank showing the height of the liquid level for each volume created with Microsoft Excel is attached

Step-by-step explanation:

(a) The height of the spherical tank = 3 m

The diameter of the spherical tank, d = 3 m

The capacity of the spherical tank = 14,000 L

The volume of a sphere, V = (4/3) × π × r³ =

Where, r = d/2

∴ r = 3 m/2 = 1.5 m

V = (4/3) × π × (1.5)³ ≈ 14.1371669412 m³

Using calculus, we have;

[tex]V = 2 \times \pi \times \int\limits^r_{0} {(r^2 - y^2)} \, dx = 2 \times \pi \times \left[r^2 \cdot y - \dfrac{y^3}{3} \right]^y_0[/tex]

For the two halves, we have;

[tex]V = \pi \times \left[r^2 \cdot y - \dfrac{y^3}{3} \right]^{\dfrac{y}{2}} _0 + \pi \times \left[r^2 \cdot y - \dfrac{y^3}{3} \right]^y_{\dfrac{y}{2}}[/tex]

[tex]V = 2 \times \pi \times \left[y^3- \dfrac{y^3}{3} \right]^y_0 = \dfrac{4 \cdot \pi \cdot y^3}{3}[/tex]

1) For V = 1000 L, we have;

[tex]1000 \ L = \dfrac{4 \cdot \pi \cdot y^3}{3}[/tex]

1000 L =

When V = 1000 L, we have;

[tex]y = \sqrt[3]{\dfrac{3 \times 1 \, m^3}{4 \times \pi } } \approx 0.62 \ m[/tex]

The liquid level, y ≈ 0.62 m = 62 cm

2) When V = 5,000 L, we have;

[tex]y = \sqrt[3]{\dfrac{3 \times 5 \, m^3}{4 \times \pi } } \approx 1.06 \ m[/tex]

The liquid level, y ≈ 1.06 m = 106 cm

3) When V = 10,000 L, we use the height of the unfilled volume at the top which is the volume of the sphere less the 10,000 L as follows;

For the volume of the sphere of 14,000 L, we have;

Volume at the top = 14,000 L - 10,000 L = 4,000 L = 4 m³

Therefore

[tex]y_{top} = \sqrt[3]{\dfrac{3 \times 4 \, m^3}{4 \times \pi } } \approx 0.985 \ m[/tex]

The height of the liquid in the tank, y = d - [tex]y_{top}[/tex]

∴ y = 3 m - 0.985 m = 2.015 m

The liquid level, y ≈ 2.015 m = 201.5 cm ≈ 202 cm

b) Please find attached the drawing of the spherical tank created with Microsoft Excel

a) (i) The level line for 1000 liters is set at a height of 0.486 meters.

(ii) The level line for 5000 liters is set at a height of 1.203 meters.

(iii) The level line for 10000 liters is set at a height of 1.926 meters.

b) The sphere is represented by the equation [tex]x^2+(y-1.5)^{2} = 2.25[/tex] and the level lines are represented by the linear functions [tex]y = 0.486[/tex], [tex]y = 1.203[/tex] and [tex]y = 1.926[/tex]. Please see the second image attached.

a) First, we derive an expression for the volume of a spherical section ([tex]V[/tex]), in cubic meters, in terms of tank radius ([tex]R[/tex]), in meters, and liquid height ([tex]h[/tex]), in meters. The volume can be found by using the slicing method integral equation:

[tex]V = \int\limits^{H}_{0} {A(h)} \, dh[/tex] (1)

Where:

If we know that [tex]A = \pi\cdot [R^{2}-(R-h)^{2}][/tex], then the volume formula is:

[tex]V = \pi\int\limits^H_0 {h\cdot (2\cdot R-h)} \, dh[/tex]

[tex]V = 2\pi\cdot R\int\limits^{H}_{0} {h} \, dh - \pi \int\limits^{H}_{0} {h^{2}} \, dh[/tex]

[tex]V = \pi\cdot R\cdot H^{2}-\frac{\pi\cdot H^{3}}{3}[/tex]

Then we obtain the following third order polynomial:

[tex]\frac{\pi\cdot H^{3}}{3}-\pi\cdot R\cdot H^{2}+V = 0[/tex] (2)

Now we proceed to solve numerically for each case:

[tex]H = 0.486\,m[/tex]

The level line for 1000 liters is set at a height of 0.486 meters. [tex]\blacksquare[/tex]

[tex]H = 1.203\,m[/tex]

The level line for 5000 liters is set at a height of 1.203 meters. [tex]\blacksquare[/tex]

[tex]H = 1.926\,m[/tex]

The level line for 10000 liters is set at a height of 1.926 meters. [tex]\blacksquare[/tex]

b) The sphere is represented by the equation [tex]x^2+(y-1.5)^{2} = 2.25[/tex]level lines are represented by the linear functions [tex]y = 0.486[/tex], [tex]y = 1.203[/tex] and [tex]y = 1.926[/tex]. By a graphing tool we have the following result. [tex]\blacksquare[/tex]

To learn more on volumes, we kindly invite to check this verified question: https://brainly.com/question/1578538

Answer:

permutation

Step-by-step explanation:

Analyzing the information in the question above, it is correct to say that it is necessary to use permutation, since the ORDER matters, since there is a need to program the band's appearances.

Permutation can be understood as an arrangement in which n = p, where n is the number of elements in the set and p is the number of available elements.

Therefore, the permutation of nine bands is:

Pn = n!

P9 = 9!

p9 = 362880

Answer:

28+ 20 = 48 because 48 take away 28 equals 20. so g is 20

Answer:

150 are girls.

Step-by-step explanation:

There is an important difference between the way counts are viewed in ratio to that in fractions.

The ratio of boys : girls

4:5

so you have 4 boys and 5 girls making the whole count in its simplest form.

4+5=9

So to change the ratio proportion into fraction proportion we have:

Boys: 4/9

Girls: 5/9

It is given that the whole is 270 therefore the count of girls is:

5/9 x 270 = 150

Answer:

[tex]x = 5[/tex]

[tex]R = C = 225[/tex]

Step-by-step explanation:

Given

[tex]C = 15x + 150[/tex]

[tex]R = 45x[/tex]

Required

The break even point

To do this, we make use of:

[tex]R =C[/tex]

[tex]45x=15x + 150[/tex]

Collect Like Terms

[tex]45x-15x = 150[/tex]

[tex]30x = 150[/tex]

[tex]x = 5[/tex]

Substitute 5 for x in [tex]R = 45x[/tex]

[tex]R = 45 * 5[/tex]

[tex]R = 225[/tex]

Hence, the break even point is:

[tex]x = 5[/tex]

[tex]R = C = 225[/tex]

Answer:

[tex]y<-4[/tex]

Step-by-step explanation:

Given

[tex]7y + 42 <14[/tex]

Required

Determine the true statement

Options are not given; but, the question can still be attempted.

[tex]7y + 42 <14[/tex]

Collect Like Terms

[tex]7y < 14 -42[/tex]

[tex]7y < -28[/tex]

Divide through by 7

[tex]\frac{7y}{7} < -\frac{28}{7}[/tex]

[tex]y<-4[/tex] -- This is true

Answer:

Matched pairs test, because we are interested in the difference in mean between the two groups - not the gain that each student has achieved.

Step-by-step explanation:

Due to the correlation which exists between the two Given samples, we need to examine the difference between the pair of each point in the dataset ; coach and uncoached point. Hence, in other to analyze the underlying pattern between each data point in the two categories, the matched pair test will be more appropriate due to the underlying relationship between the reported groups.

Answer:

ewannnnnnnnnnnnnn

Step-by-step explanation:

d q den alam d pa namin pinagaaralan yan, xenxia na godbless

Answer:

Graph.

y = x^ 2 − 2 x − 8

y = 0

Answer:

the value of x is 7.

Step-by-step explanation:

2+19=21

21÷3=7

Check:

3×7=21

21-2=19

Therefore, 7 is the answer.

Answer:

0.3125

Step-by-step explanation:

Answer:

5/16 or 0.3125

Step-by-step explanation:

Answer:

Step-by-step explanation:

I re wrote the question so its easier to understand. You should now be able to solve this problem using simple math.

3² + (3×8) ÷ 2 - (2×5)

work it out in steps, using the acronym PEMDAS <3

D. HA

1234567890oplkjhgrewsertyuiopoiuytr

Answer:

Step-by-step explanation:

Its

D and E

Answer:

-1295x -21

Step-by-step explanation:

srry if it wrong

Answer:

=12x2+−3x+−1296x3+−21

Answer:

=−1296x3+12x2−3x−21

Answer:

I think it is 275 if you are subtracting

Given:

A line passes through the points (1,-7) and (5,-25).

To find:

The y-intercept of the line.

Solution:

The line passes through the points (1-7) and (5-25). So, the equation of the line is

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-(-7)=\dfrac{-25-(-7)}{5-1}(x-1)[/tex]

[tex]y+7=\dfrac{-25+7}{4}(x-1)[/tex]

[tex]y+7=\dfrac{-18}{4}(x-1)[/tex]

[tex]y+7=-4.5(x-1)[/tex]

Subtracting 7 from both sides, we get

[tex]y=-4.5x+4.5-7[/tex]

[tex]y=-4.5x-2.5[/tex]

Putting x=0, we get

[tex]y=-4.5(0)-2.5[/tex]

[tex]y=0-2.5[/tex]

[tex]y=-2.5[/tex]

Therefore, the y-intercept of the given line is -2.5 and the vertex form of (0,-2.5).

Answer:

26-33-40-47-54-61-68-75-82-89-96

Answer:

line n

Step-by-step explanation:

Answer:

the 3 correct ones are b,c,e

Answer:

See below.

Step-by-step explanation:

He earns $20 per hour, so when you multiply 20 by h number of hours, you get the amount he earns for working h hours.

The equation is

e = 20h

A is false.

B

e = 20h

20h = 500

h = 25

B is true.

C is false. He earns $20 per hour, not 20h dollars per hour.

D

e = 20h

For 10 hours, h = 10.

e = 20 * 10 = 200

He earns $200 for 10 hours.

D is false.

E

If he raises his hourly rate by $2, he will earn $22 per hour. The new equation is

e = 22h

E is true.

Answer:

P-value = 0.0333

At 5% level of significance;

0.0333 < 0.05

Therefore, we reject null hypothesis H₀ at 5% level of significance,

We conclude that proportion of shoppers who bought bananas at least once in the past month is overstated

Step-by-step explanation:

 Given the data in the question;

To test whether population proportion p is overstated;

Null hypothesis H₀ : p = (75%) = 0.75

Alternative hypothesis H₁ : = < (75%) < 0.75

now, sample proportion p" = 64 / 100 = 0.64

from the dot plot below, we will determine the p-value for test { P(p" < 0.64)}

so, the number of times p"<0.64 in 150 simulations is 5

Hence; P(p" < 0.64 ) = 5 / 150 = 0.0333

P-value = 0.0333

At 5% level of significance;

0.0333 < 0.05

Therefore, we reject null hypothesis H₀ at 5% level of significance,

We conclude that proportion of shoppers who bought bananas at least once in the past month is overstated

This sample provide evidence that the grocery store manager overstated the true proportion P-value = 0.0333.

  Given data in the question:

Now, sample proportion p" = 64 / 100 = 0.64

From the dot plot below,

Therefore:

At 5% level of significance;

0.0333 < 0.05

Therefore, we reject null hypothesis H₀ at 5% level of significance,

We conclude that proportion of shoppers who bought bananas at least once in the past month is overstated.

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The answer to your question was..:

24.5

It is 100% correct, and I hope you get it right! :D

(Love your username! >:3)

Answer:

90 cm²

Step-by-step explanation:

since the ratio is 1:6 for every one little box the bigger box increases 6 times.

so  15·6= 90 cm²

Answer:

D. 90 square cm

Answer:

Step-by-step explanation: