A waiter earned $69.81 on a shift, and then bought himself a discounted meal for
$4.75. How much did he have left over, to the nearest dollar?
He had about $

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 probability that they are both left-handed is 0.01

Probability is the number of ways of achieving success.

the total number of possible outcomes.

Probability takes values between 0 (no chance) and 1 (certain) inclusive.

Complement Rule (probability that an event doesn't occur): P(A') = 1 - P(A) .

Addition rule: P(A ∪ B) = P(A) + P(B) – P(A ∩ B) .

Multiplication rule: P(A ∩ B) = P(A) × P(B) for independent events. P(A ∩ B)

For both, the persons selected at random are left-handed

10 % out of 100 % are left-handed.

Hence the probability that the person is left-handed

P(L) = 10 /100 = 1 / 10 = 0.1

where P(L) is the probability that the person is left-handed.

Therefore both the persons selected are left-handed

= 0.1 * 0.1

= (0.1)^2

= 0.01

Hence the probability that they are both left-handed is 0.01.

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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:

No 3

2x+4x+3x+12=0

9x+12=0

9x=0_12

9x=-12

divide by 9

x=1.333

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 value of b in the equation of common external tangent to both the given circles is 3.75.

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-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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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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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

The number √60 - 11 will be plotted between -3 and -4, but closer to -3 (Option A), as seen by number system.

Given: √60 - 11

The value of √60 - 11 is given as: √60 - 11 = 7.2 (approx.) - 11 = -3.2

Thus, as seen from the calculation of the value of the given number, √60 - 11 will lie between -3 and -4, but closer to -3 as -3.2 is closer to -3 than to -4.

Hence, The number √60 - 11 will be plotted between -3 and -4, but closer to -3 (Option A), as seen by number system.

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The measure of each angle is , ∠E = 117° and ∠F = 63°

In the geometry, angle is defined as the geometry formed by the multiple rays. Or we can also say that the angle is a figure formed by two rays with having same initial point. The rays are also known as the sides of the angle. A angle can have two rays.

Angles which are on the same line are supplementary angles. The sum of supplementary angles are always equals to 180 degree.

Some common terms related to angles :

In the given question:

Let measure of ∠E = x

and, measure of ∠F = y

as ∠E and ∠F are supplementary angles therefore their sum is 180

i.e. m∠E + m∠F = 180

=> x + y =180

also, m∠E is 54 more than m∠F

=> y+54 + y = 180

=> 2y + 54 = 180

=> y = 180-54 / 2 = 63

and , x = y + 54 = 63 + 54 = 117

Hence, ∠E = 117 degree and ∠F = 63 degree

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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

Avani needs 6 cups of yogurt.

To find the amount of yogurt required for specified number of smoothies, simple multiplication operation needs to be performed.

For 1 smoothie, the required amount of yogurt = 3/8 cups

So, the required amount of yogurt for 17 smoothies = (3/8) × 17

Performing multiplication and division to find the amount of yogurt required

Amount of yogurt required = 51/8 cups

Converting the fraction into fraction into decimal -

Amount of yogurt required = 6.375 cups

Rounding off the number of cups to convert it in simplest form -

Number of cups of yogurt required = 6 cups

Hence, the amount of yogurt for making 17 smoothies is 6 cups.

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The complete question is -

Avani is making smoothies. Each smoothie uses 3/8 cups of yogurt. How many cups of yogurt does she need to make 17 smoothies? Express your answer in simplest form.

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:

17/-11

Step-by-step explanation:

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

HOPE THIS HELPS

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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We take the value 2 for which y(2)=4 and [tex]y^{2}[/tex]=2 and see that y(x)=[tex]x^{2}[/tex] is a function and [tex]y^{2}[/tex]=x is a relation.

Domain is the set of values that a variable can take in an algebraic expression.For the equation y(x)=[tex]x^{2}[/tex], x can take any value from negative infinity to positive infinity so we can say that the domain for x is (-∞,∞). For the equation [tex]y^{2}[/tex]=x, x can take any value greater than or equal to zero. Since x=[tex]y^{2}[/tex] we can't take a negative value for x because squared numbers are always positive, so the domain of x will be [0,∞). The common domain for both the equations is [0,∞). Let us choose a value from this common domain,let's say 2. Then for

y(x)=[tex]x^{2}[/tex]⇒y(2)=4 ...(i)

[tex]y^{2} =x[/tex]=2 then y=±[tex]\sqrt{2}[/tex]...(ii)

A function always has an output variable and one or more input variables.For first equation, y is the output variable and x is the input variable. A relation states that two expressions are equal and one is not dependant on another. For equation (i) y is dependant on x but in equation (ii) both the variables are independant.

Thus we can conclude that y(x)=[tex]x^{2}[/tex] is a function and [tex]y^{2}[/tex]=x is a realtion.

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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:

120% = 162

10% = 13.5

100% = 135

so it's £135

hope this works :)

Answer:

your mixed fraction would be 12 37/100

Step-by-step explanation:

The number has two parts the whole number part is 12, and the decimal part is .37, 12 would be the whole number part of your mixed fraction and we will convert the .37 to become the fraction part of your mixed fraction.

You have to convert the decimal part into a fraction since there are two decimal places you will have 100 in the denominator .37 becomes 37/100 simplify this fraction if possible.

The rate of change of the surface area of the cylinder is approximately to 18.473 square meters per second.

In this question we find a formula for the surface area of a cone, of which we must estimate its rate of change by applying derivative rules and the concept of rate of change. The rate of change is the first derivative of the equation:

ds / dt = 2π · r · (dr / dt) + π · √(r² + h²) · (dr / dt) + π · r · [0.5 / √(r² + h²)] · [2 · r · (dr / dt) + 2 · h · (dh / dt)]

If we know that r = 3 m, h = 4 m, dr / dt = 0.5 m / s and dh / dt = 0.2 m / s, then the rate of change of the surface area of the cone is:

ds / dt = 2π · (3 m) · (0.5 m / s) + π · √[(3 m)² + (4 m)²] · (0.5 m / s) + π · (3 m) · [0.5 / √[(3 m)² + (4 m)²] · [2 · (3 m) · (0.5 m / s) + 2 · (4 m) · (0.2 m / s)]

ds / dt ≈ 18.473 m² /s

The rate of change of the surface area of the cylinder is approximately to 18.473 square meters per second.

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The equation of line passing through (1, -17) with slope 4 will be y = 4x - 21 .

What is the slope intercept form of a line ?

The equation of line that can be written as y = mx + c, where m is the slope and c is the line's y-intercept, is known as a slope intercept form.

The equation of a line which is passing through point (1 , -17) with slope m = 4 can be found by using the slope intercept form which is given by :

y = mx + c

Here ; m is the slope and c is the y - intercept of the line.

So ;

The point given is (x , y) = (1, -17) and slope m = 4. Let's use these values to find out the equation of the line. But before that let's find out the value of y-intercept (c).

-17 = (4 × 1) + c

c = - 17 - 4

c = -21

Hence , the equation of line passing through (1, -17) will be :

y = 4 ×  x + (-21)

or

y = 4x - 21

Therefore , the equation of line passing through (1, -17) with slope 4 will be y = 4x - 21 .

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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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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:

63°

Step-by-step explanation:

[tex]m\angle OZQ=m\angle OZP+m\angle PZQ \\ \\ 125^{\circ}=62^{\circ}+m\angle PZQ \\ \\ m\angle PZQ=63^{\circ}[/tex]

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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The area of the circle with the radius is 192 square feet

The figure represents the given parameter

On the figure, we have the radius (r) to be

r = 8 ft

The area of a circle is calculated as

A = πr^2

Where π is given as

π = 3

So, we have

A = 3 * 8^2

Evaluate the exponent

A = 3 * 64

Evaluate the product

A = 192

Hence, the area of the circle with the radius is 192 square feet

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the area of the circle is 201.06