Mary bought an aquarium that is cuboid in shape. The bottom is a rectangle with sides of 50 cm and 70 cm. The height of the aquarium is 4 dm. Find how many gallons of water this aquarium can hold. How much a square decimeter of glass was used to make the aquarium when it was open at the top and the bottom was plastic?

Length be x

width be x-5

So

Area=Length×Breadth

Or

If x turned y

Option C

Option A can be true as per commutatI've property

Option B is true

Answer:

y² - 5y = 750

750 - y(y - 5) = 0

(y + 25)(y - 30) = 0

Step-by-step explanation:

Formula

Area of a rectangle = length × width

Given:

Substituting the given values into the formula and rearranging in different way:

Equation 1

⇒ 750 = y(y - 5)

⇒ y(y - 5) = 750

⇒ y² - 5y = 750

Equation 2

⇒ 750 = y(y - 5)

⇒ 750 - y(y - 5) = 0

Equation 3

⇒ 750 = y(y - 5)

⇒ y(y - 5) - 750 = 0

⇒ y² - 5y - 750 = 0

⇒ y² - 30y + 25y - 750 = 0

⇒ y(y - 30) + 25(y - 30) = 0

⇒ (y + 25)(y - 30) = 0

Answer:

Step-by-step explanation:

[tex]\frac{21}{26}*\frac{7}{26}\\ =\frac{147}{676}[/tex]

The probability of students who plays both basketball and baseball is 2/13

What is Set Theory Formula?

The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.

Given data ,

Let the number of students who plays basketball and baseball = n ( A ∩ B )

Let the number of students who plays basketball be = n ( A )

The value of n ( A ) = 21

Let the number of students who plays baseball be = n ( B )

The value of n ( B ) = 7

Now , 2 students does not play any sports out of the 26 students

So , n ( A ∪ B ) = 26 - 2

n ( A ∪ B ) = 24

Now , from the set theory formula ,

n(A∪B) = n(A) + n(B) - n(A⋂B)

Substituting the values in the equation , we get

24 = 21 + 7 - n ( A ∩ B )

Adding n ( A ∩ B ) on both sides , we get

n ( A ∩ B ) + 24 = 28

Subtracting 24 on both sides , we get

n ( A ∩ B ) = 4

So . the number of students who plays both basketball and baseball = 4

And , the probability that the student chosen plays both basketball and baseball = number of students who plays both basketball and baseball / Total number of students

Probability that the student chosen plays both basketball and baseball
= 4 / 26

= 2 / 13

Hence , The probability of students who plays both basketball and baseball is 2/13

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Answer:

About 969 dollars

Step-by-step explanation:

I kind of did it the long way. I divided $1,404 by 100 and multiplied by 19. Did the same thing with 12. Added the product of those together and subtracted from 1,404.

(1,404÷100)19 + (1,404÷100)12 = 435.24

1,404 - 435.24 = 968.76

Since it was an estimate I rounded it to the nearest whole number and got 969

Hope this helps. There are probably better methods to solve this problem but this was my way.

Answer:

8

Step-by-step explanation:

Concepts

The formula to find the slope of a line given two points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. These points represent the x- and y-coordinates of the points.

Application

To find the slope of these points, we need to take two points and use the aforementioned formula. Let's take (0, 8), and (1, 16).

Solution

Therefore, the slope is 8.

Answer:

slope = 8

Step-by-step explanation:

Take 2 points from the given table:

[tex]\textsf{let}\:(x_1,y_1)=(0,8)[/tex]

[tex]\textsf{let}\:(x_2,y_2)=(-1,0)[/tex]

Use the slope formula to find the slope:

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-8}{-1-0}=\dfrac{-8}{-1}=8[/tex]

Answer:

  7 cm

Step-by-step explanation:

The circumference of a circle is given in terms of its radius by the formula ...

  C = 2πr . . . . where r represents the radius

__

Using the given values in the formula, we can find the radius to be ...

  C/(2π) = r

  43.96/(2×3.14) = r = 7 . . . . cm

The radius of the circle is 7 cm.

What I notice about the lines p and q that are parallel is that they are both supplementary angles. Lines p and q are parallel because alternate exterior angles are congruent Lines l and m are parallel because same side interior angles are supplementary Lines l and m are parallel because alternate interior angles are supplementary

Answer:

C

Step-by-step explanation:

Recall that the volume of a sphere is given by:

[tex]\displaystyle V = \frac{4}{3}\pi r^3[/tex]

Because the sphere has a diameter of 30 cm, its radius is 15 cm. Therefore, its volume is:

[tex]\displaystyle \begin{aligned} V & =\frac{4}{3}\pi(15\text{ cm})^3 \\ \\ & = \frac{4}{3}\pi(3375\text{ cm}^3) \\ \\ & = 4500\pi\text{ cm}^3 \end{aligned}[/tex]

In conclusion, our answer is C.

The function is a quadratic function, and none of the given options is a factor of the graph of the function

The zeros of the function are given as:

-3 and 5

This means that:

x = -3 and x = 5

Rewrite as:

x + 3 = 0 and x - 5 = 0

Multiply both equations

(x + 3)(x -5) = 0 * 0

This gives

(x + 3)(x -5) = 0

Express as a function

f(x) = (x + 3)(x -5)

The above means that the factors of the function are (x + 3) and (x -5)

Hence, none of the given options is a factor of the graph of the function

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Answer: The final balance is $4,734.73

Answer:

solution

here;

answer D

Step-by-step explanation:

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's get started ~

According to question :

[tex]\sf \dashrightarrow y \propto \dfrac{1}{x} [/tex]

[tex]\sf \dashrightarrow y = k\dfrac{1}{x} [/tex]

Now, we have been given that when y = 11, x = 8

Let's plug these values in equation to find value of k ~

[tex]\sf \dashrightarrow 11 = k \cdot\dfrac{1}{8} [/tex]

[tex]\sf \dashrightarrow k = 11 \times 8[/tex]

[tex]\sf \dashrightarrow k =88[/tex]

we got the value of proportionality constant. now we have been asked to find the value of y when x = 16

So, let's use the equation ~

[tex]\sf \dashrightarrow y = k \cdot\dfrac{1}{x} [/tex]

[tex]\sf \dashrightarrow y = 88\cdot\dfrac{1}{16} [/tex]

[tex]\sf \dashrightarrow y = \dfrac{11}{2} [/tex]

[tex]\sf \dashrightarrow y = 5.5[/tex]

I hope you understood the whole procedure ~

Answer:

I hope you know what a rectangle is, but it is true.

Step-by-step explanation:

Answer:

a = 16    b = 4    c = 8     d = 16

e = 12    f = 36   g = 64

Step-by-step explanation:

a.

Equation =   [tex]y_x = 4x^{2} \\x = 1\\y_1 = 4(1)^{2} \\y_1 = 4^{2} \\y_1 = 16 \\[/tex]

b.

Equation:      [tex]y_x = 4^{x} \\x = 1\\y_1 = 4^{1}\\y_1 = 4[/tex]

c.

Equation:      [tex]y_x = 4x\\x = 2\\y_2 = 4(2)\\y_2 = 8[/tex]

d.

Equation:      [tex]y_x = 4^{x}\\x = 2\\y_2 = 4^{2}\\y_2 = 16[/tex]

e.

Equation:      [tex]y_x = 4x\\x = 3\\y_3 = 4(3)\\y_3 = 12[/tex]

f.

Equation:      [tex]y_x = 4x^{2} \\x = 3\\y_3 = 4(3)^{2} \\y_3 = 4(9)\\y_3 = 36[/tex]

g.

Equation:      [tex]y_x = 4^{x}\\x = 3\\y_3 = 4^{3}\\y_3 = 64[/tex]

The missing values for the function are

a= 4

b=4

c=8

d=16

e=12

f= 36

g=64

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable.

We have the table for three function.

Now, to find the following we have find the rate of change.

Function 1 : y= 4x

At x = 2 ; y= 8

At x= 3; y= 12

Function 2: y= 4x²

At x =1 ; y= 4

At x= 3; y= 36

Function 3 : y= [tex]4^x[/tex]

At x =1 ; y= 4

At x = 2 ; y= 16

At x= 3; y= 64

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Review Material:

[tex]\sqrt[n]{x^m} = x^{\frac{m}{n}}[/tex]

[tex]\frac{d}{dx}[x^n]=nx^{n-1}\\[/tex]

[tex]\frac{d}{dx}[\sin(x)]=\cos(x)\\[/tex]

 [tex]\frac{d}{dx}[\cos(x)]=-\sin(x)\\[/tex]

[tex]\frac{d}{dx}[constant]=0\\[/tex]

Step-by-step explanation:

(a)

[tex]F(x) = -2\cos(x) +x^{\frac{4}{3}} -3e\\ \text{Note: 3e is a constant}\\F'(x) = 2\sin(x) + \frac{4}{3}x^{\frac{1}{3}}\\F''(x) = 2\cos(x) + \frac{4}{9}x^{-\frac{2}{3}}[/tex]

(b)

[tex]F(x) = x^{-3} + \frac{1}{2}x^2-\sin(x)\\F'(x)=-3x^{-4} + x - \cos(x)\\F''(x) = 12x^{-5} + 1 + \sin(x)[/tex]

(c)

[tex]F(x) = 2x^{-3}+x^{\frac{3}{4}}-4x\\F'(x) = -6x^{-4} + \frac{3}{4}x^{-\frac{1}{4}}-4\\F''(x)= 24x^{-5} - \frac{3}{16}x^{-\frac{5}{4}}[/tex]

Answer:

[tex]h(-1)[/tex] ⇢ [tex]-h[/tex]

Answer:

They will cross the finish line together in 175 minutes.

Step-by-step explanation:

This question asks you to consider the 25 and 35 times table.

I listed the 25 and 35 times tables and tried to find the lowest common multiple.

You can see that on Josephs' 7th lap of the track he will cross the line simulatneously with Owuor who will be on his 5th lap.  So the answer should be 175 minutes.

25 × 1 = 25   35 × 1 = 35

25 × 2 = 50   35 × 2 = 70

25 × 3 = 75       35 × 3 = 105  

25 × 4 = 100   35 × 4 = 140

25 × 5 = 125   35 × 5 = 175

25 × 6 = 150     35 × 6 = 210

25 × 7 = 175

25 × 8 = 200

Answer:

Step-by-step explanation:

(d). V ≈ 3016

S.A. ≈ 2261

The 16% of these students are taller than 66.7 inches and 285 students are between 61.6 and 68.4 inches tall.

It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

We have:

Mean of 65 inches and a standard deviation of 1.7.

From the graph:

P(X> 66.7) = (13.5 + 2.35 + 0.15)%

P(X> 66.7) = 16%

P(61.6 < X < 68.4) = (13.5 +34 + 34 + 13.5)%  = 95%

= (300×95)/100

= 285 students

Thus, the 16% of these students are taller than 66.7 inches and 285 students are between 61.6 and 68.4 inches tall.

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The total tons of trash that was thrown away by the people is 3.9 tons.

The first step is to convert pounds to tons

1 pound  = 0.0005 tons

40 x 0.0005 = 0.02 tons

The second step is to multiply 0.02 by 195

0.02 x 195 = 3.9 tons

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Answer:

(2x−3z)(3y−1)

Step-by-step explanation:
6xy-2x+3z-9zy
2x(2xy-1)+3z-9zy
2x(-1+3y)+3z(1-3y)

(2x−3z)(3y−1)

The range is found by subtracting the smallest data value from the largest data value. Here, the smallest data value is 2.5 and the largest is 9.3. Therefore, the range is:

[tex]9.3 - 2.5 = 6.8[/tex]

Therefore, the answer is Option A.

Just for extra.

1. The steps that follow are also needed for finding the standard deviation. Start by writing the computational formula for the variance of a sample:

[tex]{s^2}= \frac{{\sum}{x^2} - \frac{({\sum}{x})^2}{n}}{n-1}[/tex]

2. Create a table of 2 columns and 14 rows. There will be a header row and a row for each data value. The header row should be labeled with x and x^2. Enter the data values in the x column, with each data value in its own row. In the second column, put the square of each of the data values, x^2.

x     y

8.2 67.24

3.1 9.61

5.9 34.81

2.5 6.25

6.2 38.44

5.1 26.01

7.6 57.76

9.3 86.49

8.1 65.61

7.4 54.76

7.8 60.84

6.5 42.25

8.7 75.69

3. Find the sum of all the values in the first column, [tex]{\sum}{x}[/tex].

[tex]\sum{x} = 86.4[/tex]

4. Square the answer from step 3, then divide that number by the size of the sample.

[tex]\frac{({\sum}{x})^2}{n} = \frac{7464.96}{13} = 574.22769230769[/tex]

5. Find the sum of all the values in the second column, [tex]{\sum}{x^2}[/tex].

[tex]{\sum}{x^2} = 625.76[/tex]

6. Subtract the answer in step 4 from the answer in step 5.

[tex]{\sum}{x^2} - \frac{({\sum}{x})^2}{n} = 625.76 - 574.22769230769 = 51.532307692308[/tex]

7. Divide the answer in step 6 by n - 1, one less than the size of the sample. This answer is the variance of the sample.

[tex]{s^2}= \frac{{\sum}{x^2} - \frac{({\sum}{x})^2}{n}}{n-1} = \frac{ 51.532307692308 }{12} = 4.294358974359[/tex]

To find the standard deviation, first write the computational formula for the standard deviation of the sample.

[tex]{s}= \sqrt{\frac{{\sum}{x^2} - \frac{({\sum}{x})^2}{n}}{n - 1}}[/tex]

Take the square root of the answer found in step 7 above. This number is the standard deviation of the sample. It is symbolized by [tex]s[/tex]. Here, we round the standard deviation to at most 4 decimal places.

[tex]{s} = \sqrt{4023.0714285714} = 63.4277[/tex]

If you catch 3.33 frogs. Then the number of the frogs that were caught by your friend will be 16.67.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

You and your friend got 20 frogs and your friend caught 5 times more.

Let you catch x frogs. Then the number of the frogs that were caught by your friend will be 5x.

x + 5x = 20

     6x = 20

       x = 3.33

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Let you caught x and friend caught 5x

Now

5x=16.67

Answer:

B

Step-by-step explanation:

The answer is B as this is a simple ration question.

All you need to do is convert the question into ration fraction form:

24/60 =x/1990

x is the number of people whose favourite ice-cream is chocolate.

Do cross multiply on both sides and you will get 47760=60x.

x= 796.

Thus, you get your answer.

Answer:

40° and 6

Step-by-step explanation:

25. Let's suppose the angles as 2x and 7x

Then,

2x + 7x = 180°

or, 9x = 180°

or, x = 180°/9

or, x= 20°

Now, 2x is smaller

So, 2x = 2× 20° = 40°

26. Solution,

Each exterior angle = 360°\n

or, 60° = 360°/n

or, 60°n = 360 °

or, n = 360°/60°

or, n=6

As, Hexagon has 6 sides.

#26

Any polygon has sum of exterior sides as 360°

No of sides

#25

Let the angles be 2x and 7x

Smallest angle=2(20)=40°

Answer:

88

Step-by-step explanation:

Answer:

for "A" the answer is 247$

For "B" the answer 11 hours

Step-by-step explanation:

If Liza takes 120 steps, then the number of steps taken by Pete will be 72.

A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A percentage is a mathematical expression in which two things are equal.

Pete, Lulu, and Liza are walking in the Boston downtown. Each time Pete takes 4 steps, Lulu takes 3 steps. Each time Lulu takes 5 steps, Liza takes 4 steps.

Then the relation between is given as

4 Pete → 4 Lulu

5 Lulu → 4 Liza

Then we have

[tex]\rm \dfrac{5}{3} \times 4 \ Pete \rightarrow \dfrac{5}{3} \ Lulu \rightarrow 4 \ Liza[/tex]

If Liza takes 120 steps, then the number of the step taken by Pete will be

[tex]\rm \dfrac{5}{3} \times 4 \ Pete \rightarrow 4 \times 120 \\\\Pete \rightarrow 72[/tex]

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