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Answer:

The rational number representing the average change in the volume of water each day is:

[tex]\frac{0.875 liters}{1 day}[/tex]

Step-by-step explanation:

Rational numbers are those that can be represented as the quotient of two integers. That is, rational numbers can be represented by a fraction [tex]\frac{a}{b}[/tex], where a is the numerator and b is the denominator that must be other than zero. To express the set of these numbers, mathematicians use a capital Q.

In this case we know that Finn's pool leaked a total 3.5 L in 4 days, so the rate can be written as:

[tex]\frac{3.5 liters}{4 days}[/tex]

Now you must make this division or quotient, where the denominator will be 1 because you must know the number of liters drained per day:

[tex]\frac{3.5 liters}{4 days}=\frac{0.875 liters}{1 day}[/tex]

So the rational number representing the average change in the volume of water each day is:

[tex]\frac{0.875 liters}{1 day}[/tex]

Answer:

Step-by-step explanation:

Given the formula ui = xi - 25 / 10

Note that the general formula for calculating ui = xi-A/n where;

A = assumed mean

n = class size

On comparison with the given equation, A = 25 and h = 10

Also arithmetic mean  x = A + {h * sigma(fiui) /sigma(fi)} where;

sigma(fiui) = 20 and  sigma fi = 100

Substituting the given value to get the mean x;

x = 25+ (10*20/100)

x = 25 + (200/100)

x = 25 + 2

x = 27

The arithmetic mean is 27

Answer:

Answer is option d) 2

Step-by-step explanation:

[tex]given \: that \: x = 2 \: \: \: and \: \: \: y = 4 \\ value \: of \: \frac{2x + 3y}{4} - 2 \\ = \frac{2(2) + 3(4)}{4} - 2 \\ = \frac{4 + 12}{4} - 2 \\ = \frac{16}{4} - 2 \\ = 4 - 2 \\ = 2[/tex]

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For the given expression (2x + 3y) ÷ 4 - 2, If x = 2 and y = 4, the value of expression is, 2

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The expression, (2x + 3y)/4 - 2

The value of expression, when  x = 2 and y = 4

⇒ (2×2 + 3×4)/4 - 2

⇒  (4+12)/4 -2

⇒   16/4  - 2

⇒  2

Hence, the value of expression is 2

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Answer:

The equivalent fraction is:   [tex]\frac{5-\sqrt{10x} }{5-2x} }[/tex]

which agrees with the second answer in the list of options

Step-by-step explanation:

Recall that in order to rationalize a denominator of this type (remove the square roots), we need to multiply numerator and denominator of the fraction we have by the conjugate of the binomial. That is, multiply top and bottom of the fraction by the expression:  

[tex]5-\sqrt{10\,x}[/tex]

Therefore we have:

[tex]\frac{5}{5+\sqrt{10\,x} } =\frac{5\,(5-\sqrt{10x} )}{(5+\sqrt{10\,x})\,(5-\sqrt{10x})} =\frac{5\,(5-\sqrt{10x} )}{(25-10x)} }=\frac{5\,(5-\sqrt{10x} )}{5\,(5-2x)} }=\frac{5-\sqrt{10x} }{5-2x} }[/tex]

Then this is the equivalent rationalized expression:

[tex]\frac{5-\sqrt{10x} }{5-2x} }[/tex]

Answer:

B.

Step-by-step explanation:

A P E X

Answer:

the answer is B, because triangle BCA is a rotation of triangle XYZ.

Step-by-step explanation:

Answer:

7+42x

Step-by-step explanation:

7(1+6x)

Distribute

7*1 + 7*6x

7+42x

Answer:

7 + 42x

Step-by-step explanation:

Use the distributive property

7 + 42x

Answer:

2.375m

Step-by-step explanation:

Length of box = 8 m

Width of box = 3 m

Height of box = 2.4 m

It initially contains water of volume 37 m³. 20 m³ of water is added to it.

So, New volume = 37+20 = 57 cubic m

Volume of water = Length \times Width \times Height = 8 \times 3 \times Height

So, 8 x 3 x height = 57

Height = 57/ 8x3

Height =2.375 m

hence the depth of the water in the through after 20 m³ of water is added to it is 2.375m

Answer:

3

Step-by-step explanation:

72/9 = 8 ( The quotient of 72 and 9)

8-5 = 3 (Decrease by 5)

Answer:

a. x = 1.2, b. A = 32.1°

Step-by-step explanation:

1.41²-.75²=x²

a. x = 1.2

sin A = 0.75/1.41

b. A = 32.1°

Answer:

It would be 14/11

when you make it a mixed number, it'll be 1 3/11

Step-by-step explanation:

You can't simplify it more than 3/11 so

1 3/11

Answer:

fraction represented by model = 5/8

fraction less than model = 2/4

The fraction that is less than the fraction represented by the model is 2/4, the correct option is D.

A fraction is a number that is the part of the whole.

It is represented in the form of p/q, where q is not equal to zero.

The figure has a circle in which sections have been divided.

There are some shaded sections and some non-shaded sections.

The number of shaded section is 5.

The number of non-shaded section is 3.

The total sections are 8.

The fraction that is represented by the model is 5/8.

The model shown is a visual way to represent and understand fractions.

The fraction = 0.625

The fraction in the options are,

3/4 = 0.75

11/16 = 0.6875

13/16 = 0.8125

2/4 = 0.5

0.5 < 0.625

2/4 < 5/8

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Answer:

So you can divide by 2 for the picture. 4/2 = 2

So you can get 2 x 2 picture. The ratio would be 1

if you have a variable it would always be

x by x.

If you want to cover whole wall multiply by 4/3 on the 4 x 4 picture

The original needs to be scaled up by a factor of 75.

Given that, reproducing a 4 cm × 4 cm picture on a 3 m × 3 m wall.

We need to find what ratio we should use.

Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another.

We know that 1 m=100cm, then 3 m=300 cm.

The picture on the wall is (300 cm)/(4 cm) = 75 times as large in each dimension as the original.

Therefore, the original needs to be scaled up by a factor of 75.

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Answer:

y = 62°

Step-by-step explanation:

z represents the mid segment of the triangle.

Since, midsegment is parallel to the third side of the triangle.

[tex] \therefore \: y = 62 \degree...(correspnding \: \angle s) \\ [/tex]

Answer:

12 cm

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

We know the diameter is 6 so the radius is d/2 = 6/2 = 3

108 pi = pi (3)^2 h

108 pi = 9pi h

Divide each side by 9pi

108 pi /9pi = 9pi h/9pi

12 = h

Answer:

12cm in height

Step-by-step explanation:

Answer: The angle of depression would be 26.57°

Step-by-step explanation: Please refer to the attached picture for further details.

What harry has done has effectively led to the formation of a right angled triangle. As shown in the diagram, the camera has been mounted at a height of 8 feet above the ground. Also he mounts the camera at a horizontal from the entrance, which puts the camera at 16 feet away from the entrance (not from the ground). In order to capture every movement at the entrance, the camera range would be determined by an angle which covers everything from top to bottom of the entrance. That gives you the angle of depression which is at the point labelled CAMERA in the triangle.

Having determined two sides and an angle (unknown) in a right angled triangle, we shall use the trigonometric ratios as follows;

Tan ∅ = Opposite/Adjacent

Where the opposite is 8 (side facing the reference angle) and the adjacent is 16 (side that lies between the reference angle and the 90 degree angle)

Tan ∅ = 8/16

Tan ∅ = 0.5

By use of a calculator,

∅ = 26.5650

∅ ≈ 26.57

Therefore the angle of depression of the surveillance camera should be 26.57°

Answer:

0.267[tex]mm^3[/tex]

Step-by-step explanation:

Radius of the Bubble = 0.7 mm

Volume of the bubble is given by the formula :

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

Taking cube on both sides

[tex]V=\frac{4\pi\times r^3 }{3}\\\\ V=\frac{4\times3.14\times(0.7)^3}{3}\\\\V=\frac{12.56\times 0.064}{3}\\\\ V=\frac{0.804}{3}\\\\V=0.267mm^3[/tex]

Answer:

1/1

Step-by-step explanation:

Answer:

c)

Step-by-step explanation:

The equation of the circle that has a center (-1, 2) and radius of 8 will be (x + 1)² + (y – 2)² = 64. Then the correct option is D.

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at the (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x – h)² + (y – k)² = r²

A circle with center (-1, 2) and radius of 8.

Then the equation of the circle will be

(x – h)² + (y – k)² = r²

(x + 1)² + (y – 2)² = 8²

(x + 1)² + (y – 2)² = 64

Thus, the equation of the circle that has a center (-1, 2) and radius of 8 will be (x + 1)² + (y – 2)² = 64.

Then the correct option is D.

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Answer: Yes it's possible for Joshua to meet his goal of having $5,000 after 4 years.

Step-by-step explanation:

From the question, Joshua has $4,200 to invest for college which he invests $4,200 for 3 years and earns $630.

Interest = (Principal × Rate × Time)/100

630 = (4200 × R × 3)/100

630 = 12600R/100

12600R = 630 × 100

12600R = 63000

Interest rate =63000/12600 = 5%

Joshua's goal is to have $5,000 after 4 years. Is this possible if he invests with a rate of return of 6%?

Interest = (Principal × Rate × Time)/100

Interest = (4200 × 6 × 4)/100

= 100800/100

= $1008

At the end of 4 years, Joshua will have:

= $4200 + $1008

= $5208

Yes it's possible.

This would make a right triangle. Use the Pythagorean theorem to solve.

X = sqrt(14^2+ 3^2)

X = sqrt( 196 + 9)

X = sqrt(205)

X = 14.3178

Rounded = 14.3 miles

Answer:

"If two arcs are both equal in measure and they're segments of congruent circles, then they're congruent arcs"

Step-by-step explanation:

Answer: all of them

Step-by-step explanation:

Rational numbers are represented as dividing two integers, which is a fraction or decimal. Therefore, the numbers stated (134, 49, 9, etc.) are rational numbers since they are all whole numbers.

Answer:

b) 15 winners

Step-by-step explanation

if 3 winners get $720,000 each that means there is $2,160,000 total. So if each winner gets $144,000 each that means there are 15 winners.

(2,160,000/ 144,000)

Answer:

1hr 37min 18 sec

Step-by-step explanation:

Jack can mow the baseball grounds in 6 hours

Jack rate = 1/6 job/hr

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

Mike can mow the same grounds in 5 hours

Mike rate = 1/5 job/hr

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

Chris can mow the grounds in 4 hours.

Chris rate = 1/4 job/hr

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

Together rate = 1/x job/hr

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

Equation:

rate + rate + rate = together rate

[ 1/6 + 1/5 + 1/4] = 1/x

x[(5*4 + 6*4+ 6*5)/(6*5*4)] = 1

----

x(74/120) = 1

x = 120/74 = 1.62 hours = 1 hr 37 min 18 sec

Answer:

4.75

Step-by-step explanation:

u = 10  a = -2  t = 0.5 (half)

need to work out u times t add 0.5 times a times t ^2

so 10 x 0.5 + 0.5 x -2 x 0.25

= 4.75

Answer:

s=4.5 m

Step-by-step explanation:

in the equation s=ut+1/2at squared, u=10, a=-2, and t==1/2. So substitute the given values by the units u, a and t.

[tex]s=ut+\frac{1}{2} at^{2} \\s=10*\frac{1}{2}+-2*\frac{1}{2}^{2}\\ s=5+(-2)*\frac{1}{4}\\ s=5+\frac{-2}{4}\\ s=\frac{5*4-2}{4}\\ s=\frac{20-2}{4}\\ s=\frac{18}{4}\\ s=4.5 m[/tex]

Answer:

square root of 26 (sorry couldn't get the symbol)

Step-by-step explanation:

C^2 = A^2 + B^2 (Pythagoras Theorem)

C^2 = 5^2 + 1^2

C^2 = 26

take square root of both sides

C =

[tex] \sqrt{26} [/tex]

Answer:

it might come from 9/n = 10/m

Answer:

9/m=10/n

Step-by-step explanation:

Answer:

(a). Range is 6 (b). Mode is 5.75

Step-by-step explanation:

Finding range: Subtract the smallest value (2) from the largest value (8).

Finding mode: Add all the values (for each "x" you add the value that it corresponds to) and then divide them by the number of x's.

Answer:

1) (2,2)

2) (2,-1)

3) (-4,1)

Step-by-step explanation: