It will take you 10 hours to paint your garage and it will take your brother 15 hours to paint your
garage. How long will it take to paint the garage if the two of you paint together?

The height of the water tower is found to be 54.66 meters.

A free-falling object is one that is falling solely due to gravity.

Some key features regarding the acceleration due to gravity are-

Now, according to the question;

It takes a watermelon 3.34 sec to reach the ground.

Use the equation of motion in straight line.

D  =  (1/2) x (gravity) x (time)²

D is the height of the water tower.

    =  (1/2) x (9.8 m/s²) x (3.34 sec)²

   =   (4.9 m/s²)  x  (11.16 sec²)

D = 54.66 meters.

Thus, the height of the water tower is estimated as 54.66 meters.

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The inverse of the function → y= f(x) = 1/7x - 1/7​ is -

f⁻¹(x) = 7x + 1.

We have -

y = f(x) = x/7 - 1/7

We have to find its inverse function.

Inverse of a function can be calculated by following the steps mentioned below -

Step 1 -  Replace 'y' with 'x' and vice - versa.

Step 2 - Rewrite the equation by solving for 'y'.

Step 3 - Replace 'y' with f⁻¹(x).

According to the question, the equation given is as follows

y = f(x) = x/7 - 1/7

Replace 'y' with 'x', we get -

x = y/7 - 1/7

Now, solve for y -

y/7 = x + 1/7

y = 7(x + 1/7)

y = 7x + 1

Replace 'y' with f⁻¹(x) -

f⁻¹(x) = 7x + 1

Hence, the inverse of the function → f(x) = 1/7x - 1/7 is -

f⁻¹(x) = 7x + 1.

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These questions are equations of one variable. An equation is an expression which has an equal sign, which is then evaluated isolating the variable in one side if the equation.

1) r + 12 = 36

r = 36 -12

r = 24

2) 22+ m = 24

m = 24 - 22

m = 2

3) -27 = n - 29

n = 2

4) -5 = b -26

b = 21

5) -17 = x -23

x = 5

6) v - 26 = - 4

v = 22

7) x+12 = 38

x = 26

8) 8= -12+ a

a = 20

9) b- 21 = 4

b = 25

10) 2 = x - 23

x = 25

11) x + 25 = 46

x = 21

12) -18 = x - 22

x = - 4

These questions are equations of one variable. An equation is an expression which has an equal sign, which is then evaluated isolating the variable in one side if the equation.

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The table that represents the linear function is table (B)

As a general rule, a linear function is any function that has a constant rate of change

This means that as the function independent value changes by a constant, the function dependent value changes by a constant

In other words, as the function x value changes by a constant, the function y value changes by a constant

Using the above as a guide, we can see the table B represents a linear function

This is so because, as x increases by 3, the y value decrease by -2

Hence, the table that represents the linear function is table (B)

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Answer:

She will give 78 students to the sixth student.

Step-by-step explanation:

The pattern is adding 6 each time.

Answer:

2

Step-by-step explanation:

Triangle side theorem states the sum of the lengths of any two sides of a triangle must be greater than the remaining side

3 + 2 = 5     third side would have to be LESS than 5

            so the only answer is 2 cm

Answer:

-3/5, -1/10, -0.8, 0.3, 1/2, 5/8

Step-by-step explanation:

negatives are always less than positive numbers. As you can see the first numbers that are negative count down and then once it turns positive the numbers count up. For example, it goes -3,-1,-0 then 0,1,5

Tim owns 74 socks, the colours of which are unknown.

He does, however, have an additional pair that is white rather than black.

Therefore, it suggests that we are working with the two hues white and black.

The result of dividing the total number of socks by two is:

= 74/2

= 37 socks, two pairs each for black and white.

But let's not forget that Tim has a pair of white socks in addition to his black pair.

The total number of white socks is equal to= 37+1= 38 socks.

Total black sock pairs= 37-1=36 socks.

Last but not least, the question asks us to count the number of single socks rather than pairs.

For white then:

There will be = (38x 2) socks per pair.

= 76 socks

For Black

The individual socks will be = (36 × 2)socks

= 72 socks

We can then deduce that there are 76 individual socks for white and 72 individual socks for black.

The solution would have to be four. Despite the large number of socks in the drawer, there are only three different colours, so if you take four socks, you will undoubtedly find at least one pair that matches.

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Answer:

[tex]y=0.1(2)^x[/tex]

where x is time in hours, and y is the number of bacteria in percent in decimal form.

Step-by-step explanation:

General form of an exponential function:

[tex]y=ab^x[/tex]

where:

Define the variables:

If the bacteria grows on food by doubling every hour then the growth rate b = 2.

If the bacteria initially covers 10% of the food then y = 10% when x = 0.

Therefore, a = 10% = 0.1.

Therefore, the equation is:

[tex]y=0.1(2)^x[/tex]

Substitute x = 3.3 into the found equation:

[tex]\begin{aligned}x=3.3 \implies y & =0.1(2)^{3.3}\\& =0.9849155307...\\& =1.0\:\sf (nearest\:tenth)\end{aligned}[/tex]

As 1.0 = 100%, this justifies the claim.

[tex]\begin{array}{|c|c|c|}\cline{1-3} x & y & y \\\cline{1-3} 0 & 10\% & 0.1\\\cline{1-3} 1 & 20\% & 0.2\\\cline{1-3} 2 & 40\% & 0.4\\\cline{1-3} 3 & 80\%\ & 0.8\\\cline{1-3} 4 & 160\% & 1.6\\\cline{1-3}\end{array}[/tex]

The density of the material in ounce per liter is 0.1059 ounce per liter.

The ounce per liter conversion selector on this page selects the density measurement unit to convert to starting from ounces per liter (oz/L).

Given that,

Density = 3 grams per fluid ounce

Convert grams to ounce.

1 grams = 0.0353 ounce

Then

Density = 3 * 0.0353 ounce per fluid grams

             = 0.1059 ounce per fluid grams

Convert fluid gram to liter

Density = 0.1059 ounce per 1000 liter

             = 0.0001059 ounce per liter

Hence, the density in ounce per liter is 0.0001059 ounce per liter.

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The inverse of a function when x = -1 is g^-1(-1) = -5/2

Linear functions are function that has a leading degree of 1. Given the expression below;

g(x) = 2x + 4

Determine the inverse

y = 2x + 4

Replace y with x

x = 2y + 4

Make y the subject of the formula

2y = x - 4

y = (x-4)/2

g^-1(x) = (x-4)/2

Substitute x = -1 into the equation

g^-1(x) = (-1-4)/2

g^-1(-1) = -5/2

Hence the inverse of a function when x = -1 is g^-1(-1) = -5/2

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Answer:

698,000

Step-by-step explanation:

7×10^5=700000

2×10^3=2000

700,000-2000=698,000

The given 7 * [tex]10^5[/tex] is 3.5*10² times larger than 2 * 10³.

Given that,

To determine, how many times larger is 7 x 10^5 than 2 x 10^3.

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
We have two values, here we have to determine the relationship between the two values.

[tex]ratio = 7*10^5 / 2 * 10^3\\Ratio = 3.5 * 10 ^2[/tex]
Implies,
[tex]7*10^5 = 3.5*10^2 (2 * 10^3)[/tex]

Thus, the given 7 * [tex]10^5[/tex] is 3.5*10² times larger than 2 * 10³.

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In dataset 60 is the data is spread more tightly around the mean than in other datasets. Accordingly, it would have a smaller standard deviation.

n dataset C, the data is spread more tightly around the mean than in other datasets. Accordingly, it would have a smaller standard deviation

Standard deviation is 60

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed. In contrast, a high or low standard deviation indicates that the data points are, respectively, above or below the mean. A standard deviation that is close to zero implies that the data points are close to the mean. The curve at the top is more dispersed and has a greater standard deviation than the curve at the bottom, which is more concentrated around the mean and has a lower standard deviation.

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Answer:

33.7

Step-by-step explanation:

Complementary angles are angles that when added, sum up to 90*

First, make the equation, x being the missing angle
90*= x + 56.3

Rewrite the equation to find the missing angle
90 - 56.3 = x

x= 33.7

Answer:33.7°

Step-by-step explanation:

To find the complement of an angle, subtract that angle's measurement from 90 degrees. The result will be the complement

90° - 56.3°

=33.7°

Answer:

I´m pretty sure it is 1.8 miles

Step-by-step explanation:

Answer:

36 = 2 x 2 x 3 x 3

Answer:

2 2/3 * 2 2/3 = 64/9 = 7 1/9 ≅ 7.1111111

Step-by-step explanation:

The result:

2 2/3 * 2 2/3 = 64/

9

= 7 1/

9

≅ 7.1111111

Spelled result in words is sixty-four ninths (or seven and one ninth).

How do we solve fractions step by step?

Conversion a mixed number 2 2/

3

to a improper fraction: 2 2/3 = 2 2/

3

= 2 · 3 + 2/

3

= 6 + 2/

3

= 8/

3

To find a new numerator:

a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/

3

= 6/

3

b) Add the answer from previous step 6 to the numerator 2. New numerator is 6 + 2 = 8

c) Write a previous answer (new numerator 8) over the denominator 3.

Two and two thirds is eight thirds

Multiple: 8/

3

* 8/

3

= 8 · 8/

3 · 3

= 64/

9

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(64, 9) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - eight thirds multiplied by eight thirds is sixty-four ninths.

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The number of tacos that is needed for 3 students is 8 tacos.

The first step is to determine the number of tacos that is needed for one student. To determine this value, divide the total number of tacos by the total number of students.

Division is the mathematical operation that is used to determine the quotient of two or more numbers. Division entails splitting a number into equal groups using another number. The sign used to denote division is ÷

Tacos that should be prepared for one student = total tacos / number of students

= 40 / 15

In order to determine the number of tacos needed for 3 students, multiply the result gotten in the previous step by 3. Multiplication is the process used in determining the product of two or more numbers. The sign used to denote multiplication is x .

Tacos needed for 3 students = (40 / 15) x 3 = 8

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A clockwise 360 degrees angle rotation will make the figure rotate onto themselves.

Any angle rotations other than a 0 degree or a 360 degree will change the figure and so does not rotate onto themselves.

To rotate onto themselves, which means the figure should not be changed after the rotation transformation, we have to rotate it 360 degrees.

We are asked for a clockwise angle rotation, so the require angle rotation is of 360 degrees.

0 degree angle rotation will not make a rotation. So we will go with a 360 degree rotation. Any figure after a 'full circle' clockwise rotation will goes onto themselves.

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Answer:

y = 2/3x - 8/3

or 2x = 3y + 8

Step-by-step explanation:

2x = 3y + 4

3y = 2x - 4

y = 2/3x - 4/3

If two lines are parallel, their slopes are equal

if m = 2/3, y = -2, x = 1

y = mx + b

-2 = 2/3(1) + b

-2 = 2/3 + b

b = -2 - 2/3 = -8/3

y = 2/3x - 8/3

or 3y = 2x - 8

or 2x = 3y + 8

Using translation concepts, the graph that shows that function f(x) = x with an input of f(x - 3) is given by:

A coordinate plane with a line passing through (negative 2, negative 5), (0, negative 3), and (3, 0).

The input of the function, of f(x - 3), is missing.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, the function is:

f(x) = x.

The translation is in the input, f(x - 3), meaning that the function is shifted 3 units right and defined by:

f(x - 3) = x - 3.

Hence three points on the graph are:

Hence the correct description is:

A coordinate plane with a line passing through (negative 2, negative 5), (0, negative 3), and (3, 0).

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Answer:

D

Step-by-step explanation:

The inequality form of the given expression is:

x < -8 or x > 0

The interval notation is : (−∞,−8)∪(0,∞)

Given, the expression is |x + 4| - 4 > 0

An inequality is a relationship that shows a non-equal comparison between two numbers or mathematical expressions.

Isolate the variable by dividing each side by factors that don't contain the variable.

⇒  |x + 4| - 4 > 0

⇒  |x + 4|  > -4

Remove mod.

⇒ x + 4 > -4 or  x - 4 > -4

⇒ x > -4 -4 or x > -4 +4

⇒ x <-8 or x > 0

Hence the internal notation is :

(−∞,−8)∪(0,∞)

The required graph is plotted.

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Answer:5/2 and 2 1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

2.5 as a mixed number is 2 1/2 since 1/2 = 0.5

2.5 as an improper fraction is 5/2

-5√3  - 11 is value of expression.

What do math Surds mean?

( 2 + √3) (√3 - 7)

First = 2√3

outer = 2(-7) = -14

inner = √3 √3 = 3

last = √3 (- 7)

= 2√3 + (- 14) + 3 + ( - 7√3)

= -5√3  - 11

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Answer:

17/-11

Step-by-step explanation:

why,because reciprocal in mathematics means changing the numerator to the denominator and denominator to numerator.

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Answer:

b = 0.5

Step-by-step explanation:

a = b x h

7 = 14b  Divide both sides by 14

0.5 = b

d. 15p + 100 = 30p + 75

The graph of the system of linear equations is shown in the image below, where the solution is: (3, 1)

The coordinates where x - 2y = 1 intersects the x-axis (horizontal axis) is: (-14, 0)

Given the linear equations:

5x – y = 14 ---> equation 1

x – 2y = 1 ---> equation 2

Rewrite both equations in slope-intercept form as y = mx + b, where b represents the y-intercept of the line and m represents the slope.

5x - y = 14

-y = -5x + 14

y = 5x - 14 (slope is 5 and y-intercept is -14)

x - 2y = 1

-2y = -x + 1

y = 1/2x - 1/2 (slope is 1/2, and the y-intercept is -1/2).

Therefore, the graph of the system of linear equations is shown in the image below, where the solution is: (3, 1)

The coordinates where x - 2y = 1 intersects the x-axis (horizontal axis) is: (-14, 0)

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Answer:

120% = 162

10% = 13.5

100% = 135

so it's £135

hope this works :)

Answer:

8 significant digits

Step-by-step explanation:

Let's count

6040.0050

⬇ ⬇⬇⬇.⬇ ⬇⬇ ⬇

1 234 567 8

therefore it's 8 significant figures

Answer:

The difference would be Unionville would have had 24.6 in. of rain and Arges only had 8.1 in

Step-by-step explanation: