When you listen to the sound of a bouncing ping-pong ball that has been dropped onto a cement floor, what mathematical pattern do you hear? Explain,

Answer:

Tom has $36 after paying his dad and buying the drink.

Answer:

36

Step-by-step explanation:

because if you  take away 12 from 55 you would have  43 and if you take away 7 you would have 36

a. Yes, the amount of water in the pool is a function of the number of minutes. b. The domain of the function is  0 < x ≤ 588. The domain is continuous c. The required graph has been attached below.

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

a. Yes, the amount of water in the pool is a function of the number of minutes. This is because, for each input value of the number of minutes, there is a unique output value of the amount of water in the pool.

Where the function is y = 17x  

b. The domain of the function is the set of all possible values of the input, which in this case is the number of minutes. The domain is continuous because it includes all possible values within a range (in this case, all possible values of the number of minutes), rather than only a set of specific, discrete values.

Assume that the capacity of the swimming pool with water is 10000 gallons.

So it completed fully fills with water in 588.2 (=10000/17) minutes

Thus, the domain of the functin is 0 < x ≤ 588.

c. Here is a graph of the function using its domain:

Where the vertical axis represents the amount of water in the pool and the horizontal axis represents the number of minutes.

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Answer:

You have to first convert them to improper fractions, by multiplying the whole with the denominator (bottom number). And then you add the answer with the numerator (top number). This answer is then the numerator of the improper fraction, and the denominator remains the same. Then you add the two improper fractions. If the denominators are different, you find the lowest common multiple (LCM) of the denominators and multiply both the numerator and denominator so that the new denominator is the lowest common multiple. Then you add the numerators and keep the denominator the same

Example:

5[tex]\frac{3}{6}[/tex] + 3[tex]\frac{3}{4}[/tex]

5[tex]\frac{3}{6}[/tex]

= 5 x 6 = 30

= 30 + 3 = 33

= [tex]\frac{33}{6}[/tex]

3[tex]\frac{3}{4}[/tex]

= 3 x 4 = 12

= 12 + 3 = 15

= [tex]\frac{15}{4}[/tex]

[tex]\frac{33}{6}[/tex] +    [tex]\frac{15}{4}[/tex]

LCM of 6 and 4 is 12

[tex]\frac{33}{6}[/tex]

= 33 x 2 and 6 x 2

= 66 and 12

= [tex]\frac{66}{12}[/tex]

     [tex]\frac{15}{4}[/tex]

= 15 x 3 and 4 x 3

= 45 and 12

= [tex]\frac{45}{12}[/tex]

[tex]\frac{66}{12}[/tex] +  [tex]\frac{45}{12}[/tex] = [tex]\frac{111}{12}[/tex]

Answer: Jacob will be 16 (16.5) years old, which is half of Todd's age, in 4 years.

I respect the Todoroki profile pic :)

Step-by-step explanation:

33 ÷ 2 = 16.5

1/2 of Todd's age = 16.5 (16)

16 - 12 = 4 years (4.5 years to be specific)

Using leaner equation we find that After 12 years from now will Jerry's age be (2/3) of the combined ages of his brother and sister at that time.

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

Let Jerry's brother present age be X years,

Then Jerry's present age will be 2x

And his sister's present age will be 2X - 6

And let y be  the  number of years from now when Jerry's age = (2/3) of combined age of his brother and sister.

So we have that,

(2X + y)  = (2/3) [(X + y) + (2X - 6 + x)]

simplify the above equation

2X + y = (2/3) [3X + 2y - 6]

multiply through by 3/2

3X + (3/2)y = 3X + 2y - 6

subtract  3X from both sides

(3/2)y = 2y - 6

subtract 2y from both sides

-1/2y = -6

divide both sides by -1/2

y = 12 years

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Answer:

  (a)  $1049.15

Step-by-step explanation:

You want to know the interest earned by an account that pays 3.2% interest compounded semiannually if the balance is $6049.15 after 6 years.

The formula for the balance of an account earning compound interest is ...

  A = P(1 +r/n)^(nt)

where P is the principal invested, r is the annual interest rate, n is the number of times per year interest is compounded, and t is the number of years.

We have ...

  6049.15 = P(1 +0.032/2)^(2·6) = P(1.016^12)

The amount of interest earned is the difference between the account balance and the principal:

  interest = 6049.15 -(6049.15/1.016^12) ≈ 1049.15

The total amount of interest earned is $1049.15.

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The age of Kate will be 16 years.

The age of Leo will be 20 years.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Kate is 4 years younger than Leo.

And, Twice Kate's age minus 3 is the same as Leo's age plus 9.

Now,

Let the age of Leo = x

So, The age of Kate = x - 4

Here, Twice Kate's age minus 3 is the same as Leo's age plus 9.

Hence, We can formulate;

⇒ 2 (x - 4) - 3 = x + 9

Solve for x as;

⇒ 2x - 8 - 3 = x + 9

⇒ 2x - x = 9 + 11

⇒ x = 20 years

Thus, The age of Leo = x

                                 = 20 years

So, The age of Kate = x - 4

                               = 20 - 4

                               = 16 years

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Answer: y = 2x

Step-by-step explanation:

Write in slope-intercept form,

y = mx + b.

y = 2x

On a graph, the coordinates will be:

(2,4);(4,8) Just like you had said above.

Hope this helped!

The values of a, b and c are a= 2, b = 3, c = -10

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We have been given an Cos Ф = 1/8

Cos Ф = 4x/y

Cos Ф = 4x/y = 1/8

x/y = 1/32

We need to write given expression in the form y² = ax² +bx+c, where a, b and c are numbers.

2x² + 12x + 8

=  2x² + 12x + 18 - 18 + 8

= (√2x + 3√2)² - 10

= (√2)² (x + 3)² - 10

= 2(x + 3)² - 10

Comparing with expression where a, b and c are numbers.

a = 2, b = 3 and c = -10

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If you're given a false equation and you multiply both sides by the same non-zero number, the resulting equation will also be a false equation.

If you're given a false equation and you multiply both sides by the same non-zero number, the resulting equation will also be a false equation.

This is because the equation was already unbalanced, and multiplying both sides by the same non-zero number does not change that.

For example, consider the equation 2 + 3 = 6. This is a false equation. If we multiply both sides by 2, we get:

(2 + 3) × 2 = 6 × 2

4 + 6 = 12

The resulting equation 4 + 6 = 12 is also a false equation.

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Yes, because 225 minutes is greater than 205 minutes.

In this question answer is

Yes, because 225 minutes is greater than 205 minutes.

This can be determined by using the outlier rule

which states that any data point that is more than 1.5 times the interquartile range (IQR) away from the upper quartile (Q3) is considered an outlier.

The IQR is calculated as Q3 - Q1,

which in this case is

110 - 15 = 95. Therefore,

1.5 times the IQR is 95 x 1.5 = 142.5.

The upper quartile (Q3) is 110,

so any data point more than 205 (110 + 142.5) is considered an outlier, including 225.

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Yes, because 225 minutes is greater than 205 minutes.

Outlier rules, also known as outlier detection algorithms, are algorithms designed to detect the presence of outliers in a dataset.

Outliers are data points that are significantly different from the rest of the data, and can be caused by measurement error, experimental error, or some other anomaly.

Outlier rules are used to identify and remove outliers from data sets in order to improve the accuracy of data analysis and modeling.

Outlier rules typically use some combination of statistical measures, such as mean, median, and standard deviation, to detect the presence of outliers in the data.

In this question answer is

Yes, because 225 minutes is greater than 205 minutes.

This can be determined by using the outlier rule

which states that any data point that is more than 1.5 times the interquartile range (IQR) away from the upper quartile (Q3) is considered an outlier.

The IQR is calculated as Q3 - Q1,

which in this case is

110 - 15 = 95. Therefore,

1.5 times the IQR is 95 x 1.5 = 142.5.

The upper quartile (Q3) is 110,

so any data point more than 205 (110 + 142.5) is considered an outlier, including 225.

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The checkpoint Odalis will be when they catch up to Jaquan is 0.1 km.

Given that, Jaquan passed a checkpoint jogging at a constant speed of 9 km/hr.

2 minutes later Odalis passed the same checkpoint.

Odalis runs at a constant speed of 12 km/hr.

We know that, 1 hour = 60 minutes

So, 2 minutes = [tex]\frac{2}{60}[/tex] hour

= [tex]\frac{1}{30}[/tex] hour

So, the distance = [tex]9\times\frac{1}{30}[/tex]

= [tex]\frac{3}{10}[/tex] km

When the speed is 12 km/hr, we get

Distance = [tex]12\times\frac{1}{30}[/tex]

= [tex]\frac{2}{5}[/tex] km

Now, [tex]\frac{2}{5} - \frac{3}{10}[/tex]

= [tex]\frac{4}{10} - \frac{3}{10}[/tex]

= [tex]\frac{1}{10}[/tex] km

= 0.1 km

Therefore, the checkpoint Odalis will be when they catch up to Jaquan is 0.1 km.

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Answer:

1.2

Step-by-step explanation:

none

The value of x is 6, f(x) an absolute minimum is (5, -16, 328.4475).

The derivative of f is  [tex]$& f(x)=e^x\left(-x^3+3 x\right)-3[/tex]

[tex]& f(x)=-e^x x^3+3 x e^x-3\end{aligned}$$[/tex]

Domain for: [tex]$0 \leq x \leq 5$[/tex] is [0,5]

[tex]$& \frac{d}{d x}[f(x)]=\frac{d}{d x}\left[-e^x x^3\right]+\frac{d}{d x}\left[3 x e^x\right]+\frac{d}{d x}[-3] \\$$[/tex]

[tex]\\& f^{\prime}(x)=\left(-e^x\right)\left(3 x^2\right)+\left(x^3\right)\left(-e^x\right) \\& +(3 x)\left(e^x\right)+\left(e^x\right)(3)+0 \\\\[/tex]

[tex]& f^{\prime}(x)=-3 x^2 e^x-x^3 e^x+3 x e^x+3 e^x \\[/tex]

[tex]& f^{\prime}(x)=e^x\left[-x^3-3 x^2+3 x+3\right]\end{aligned}$$[/tex]

Set the first derivative equal to zero and

solve for x to find the critical number.

[tex]$$-x^3-3 x^2+3 x+3=0$$[/tex]

x=-3.601679 (outside of the domain) not valid here

x=-0.6601231 (outside of the domain) not valid here

x=1.2618022 ... TEST this one

Now to find the absolute extremes, test the critical numbers and the endpoints by plugging their x-values back into the f (x) function to find their y - value.

Testing x = 0

x = 1.2618022

x = 5

Finding their y-values:

[tex]& f(0)=e^0\left[-(0)^3+3(0)\right]-3=0-3=-3 \\\\& f(1.2618022)=e^{1.2618022} \cdot\left[-(1.2618022)^3+3(1.2618\right. \\\\& f(1.2618022)=3.273978192[/tex]...Highest y-value.

absolute maximum: (1.2618022,3.273978192)

Where x==1.2618022

[tex]& f(5)=-e^5(5)^3+3(5) e^5-3 \\\\ f(5)=-125 e^5+15 e^5-3 \\\\& f(5)=-110 e^5-3=-16,328.4475 \\[/tex]

absolute minimum: (5, -16, 328.4475)

where x = 5.

Therefore, the absolute minimum of F(x) is (5, -16, 328.4475) and x is 5.

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The acceleration of Object B should be 5 times the acceleration of Object A in order to make the table true.

We have a table that gives the values of mass, acceleration and force of object A and object B.

We have to find by how many times greater must the acceleration of Object B be than the acceleration of Object A to make the table true.

The formula to calculate the force is -

F = m x a

From the table,

Mass = 40 Kg

Force = 1800 N

By substitution

a =F/m  = 1800/40  = 45 m/s²

The acceleration of Object A is 9m/s² .  On comparing the acceleration of both the objects, we can see that the acceleration of Object B is 5 times the acceleration of Object A.

Hence, the acceleration of Object B should be 5 times the acceleration of Object A in order to make the table true.

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The value of the hypotenuse y = 9, and the value of the opposite side of the right angle triangle x = 4.5

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

Considering the angle 30° in the right angle triangle, the hypotenuse is y, the opposite side is x and the adjacent side is 9√3

cos 30° = √3 = adjacent/hypotenuse

sin 30° = 1/2 = opposite/hypotenuse

√3 = 9√3/y {cross multiply}

y = 9√3/√3 {cancel out √3}

y = 9

1/2 = x/9 {cross multiply}

x = 9/2

x = 4.5

Therefore, by proper application of trigonometric ratios for the right angle triangle, the hypotenuse y is equal to 9 and the opposite side x is equal to 4.5.

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Answer:

a) 4

b) 8

Step-by-step expla nation:

a) 3.2 ÷ 0.8 = 4

b) 7.5 + 0.5 = 8

Answer: Its y-intercept is obtained when the x coordinate is 0, so that the function crosses the y-axis. Therefore, it means that x=0 . Note that the y value that corresponds to this intercept is y=f(0) y = f ( 0 ) . Thus, an ordered pair that represents the y-intercept is (0,f(0)) ( 0 , f ( 0 ) )

Step-by-step explanation:

Answer: $180 for 4 shirts and 360 for 8 shirts (this includes the 10% discount for both answers)

Step-by-step explanation: First, we have to multiply 50 by 4, since each shirt is $50 and there are 4 shirts to purchase. The answer is $200, but you have a 10% discount to consider. 10% of 200 is 20, so subtract $20 from 200, and you get $180 for 4 shirts. To find out the amount of money it costs to pay for 8 shirts, you can simply add 180 and 180 together and it'll give you 360.  This way, the 10% discount will not be left out.

Let me know if this is right! :)

The diameter is twice the radius, so it is decreasing at a rate of [tex]$2(1.26 \times 10^{-2} \ \text{cm}/\text{hr}) = \boxed{2.52 \times 10^{-2} \ \text{cm}/\text{hr}}$[/tex]

The volume of the grindstone is [tex]$\pi r^2 h = \pi \cdot 100^2 \cdot 10 = 3141600 \ \text{cm}^3$[/tex], so the rate at which it is wearing away is  [tex]$\frac{50}{3141600} = 1.59 \times 10^{-4} \ \text{cm}^3/\text{hr}$[/tex]

The grindstone is a cylinder, so its volume is proportional to its radius squared. Therefore, the radius is decreasing at a rate proportional to [tex]$\sqrt{1.59 \times 10^{-4}} = 1.26 \times 10^{-2} \ \text{cm}/\text{hr}$[/tex].

The diameter is twice the radius, so it is decreasing at a rate of [tex]$\sqrt{1.59 \times 10^{-4}} = 1.26 \times 10^{-2} \ \text{cm}/\text{hr}$[/tex].

A diameter is a line segment that passes through the centre of a circle or other curved shape and has its ends at the circumference. The length of a diameter is twice the length of the radius of the circle. A radius is a line segment joining the centre of a circle or other curved shape to any point on its circumference. The length of a radius is half the length of the diameter of the circle. Both the diameter and radius are fundamental measurements in determining the size and shape of a circle or other curved shape.

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The diameter of the grindstone is decreasing at a rate of 5/(πr) cm/hr.

Therefore the answer is b) 5/ (πr) cm/hr.

The grindstone is losing material at a rate of 50 cm³/hr, and since it is a cylinder, we can use the formula for the volume of a cylinder to find the rate at which its diameter is decreasing.

The volume of a cylinder is given by:

[tex]V= \frac{ \pi D^{2} h}{4}[/tex]

where V is the volume, d is the diameter and h is the height (in this case the thickness of the grindstone).

We know that the grindstone is losing material at a rate of 50 cm³/hr, and that the grindstone's thickness is 10 cm. To find the rate at which the diameter is decreasing, we need to find the rate at which the radius is decreasing, which we can find by differentiating the volume equation with respect to time.

So

[tex]\frac{dV}{dt} = -50\ cm^{3}/hr[/tex]

[tex]\frac{d(\frac{\pi\\D^{2}h }{4}) }{dt} = -50\ cm^{3}/hr[/tex]

[tex]\frac{2}{4}\pi Dh\frac{dD}{dt} = -50\ cm^{3}/hr[/tex]

Substitute the known values,

[tex]\frac{2}{4}\pi *(D)*(10cm)\frac{dD}{dt} = -50\ cm^{3}/hr[/tex]

[tex]\frac{dD}{dt}= (-50 cm^3/hr)*\frac{4}{2\pi *(D cm)*(10 cm)}[/tex]

[tex]\frac{dD}{dt}= \frac{-10}{\pi D}cm/hr[/tex]

We know D = 2r

[tex]\frac{dD}{dt}= \frac{-10}{\pi*(2r)}cm/hr[/tex]

[tex]\frac{dD}{dt}= \frac{-5}{\pi r}cm/hr[/tex]

--The question is incomplete, answering to the question below--

"A 10 cm thick grindstone is initially 200 cm in diameter, and it is wearing away at a rate of 50 cm³/hr. At what rate is it's diameter decreasing?

a. 5/ (2πr) cm/hr

b. 5/ (πr) cm/hr

c. 5/ (2π) cm/hr

d. 5/ π cm/hr"

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Percentage error in the area is 79.84 %

Percentage error is defined by the difference between actual value and estimated value while comparing to the actual value and expressed in percentage.

given, sides of a rectangle are 6.2 cm and 4.8 cm.

actual length = 6.2 cm

actual width = 4.8 cm

hence, area of rectangle = length × width

                                       = 6.2 cm x 4.8 cm

actual area = 29. 76 square centimeters.

measured length = 2 cm

measured width = 3 cm

measured area = 2 x 3 = 6 square cm

percentage error in the area = (actual area - measured area) / actual area ×100

                                                      =(29.76 - 6) / 29.76 × 100

                           percentage         error               = 79.84 %

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The Coordinates of point D(3,1) ,after reflection along, line, y=x, will be=(1,3).

What are coordinates?

coordinates can be defined as the pair of numbers which are used to determine the position of a given point.

Rule of reflection along line, y=x.

Suppose a point (a,b) is reflected along line, y=x,the coordinates of point after reflection along the line will be (b,a),that is abscissa and ordinate interchange their place, after reflection.

Coordinates of point D =(3,1)

→→Coordinates of point D(3,1) ,after reflection along, line, y=x, will be=(1,3).

Hence, The Coordinates of point D(3,1) ,after reflection along, line, y=x, will be=(1,3).

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Answer:

X =56

Step-by-step explanation:

Total angles of a triangle = 180

Since it's the total, we add these three angles

[tex](x - 31) + (x) + (x + 43) = 180[/tex]

Next, we combine like terms

[tex]3x + 12 = 180[/tex]

Next, you can subtract 12 from both sides to get numbers on one side

[tex]3x = 168[/tex]

Last step is to divide by 3 to get the X alone

[tex]x = 56[/tex]

Answer:  

x = 56

F = 25

R = 99

O = 56

Step-by-step explanation:

all triangles equal 180 degrees

that means that when you add angle F, O, + R, you will get 180

create the formula based on this info:

F + R + O = 180

x - 31  + x + 43 + x = 180

solve:

-31+43+x+x+x = 180

12 + 3x = 180

3x = 168

x = 56

now plug in x and find each angle

F = x - 31

F = 56 - 31

F = 25

R = x + 43

R = 56 + 43

R = 99

O = x

O = 56

By evaluating the quadratic equations we will get:

3c(a-4)+3d(a+5) =  3*(a^3 - 8a^2 + 102a + 22)

Here we have two quadratic functions:

c(x)=x^3-2x and d(x)=4x^2-6x+8

And we want to find the value of the expression:

3c(a-4)+3d(a+5)

First, let's evaluate the functions in these values:

3*c(a - 4) = 3*[ (a - 4)^3 - 2*(a - 4)] = 3*(a - 4)*[ (a - 4)^2 - 2]

               = 3*(a -4)*(a^2 - 8a + 16 - 2)

               = 3*(a - 4)*(a^2 - 8a + 14)

               = 3*(a^3 - 12a^2 + 46a - 56)

3*d(a + 5) = 3*[ 4*(a + 5)^2 - 6*(a + 5) + 8]

                = 3*[ 4a^2 + 40a + 100  -6a - 30 + 8]

                = 3*[4a^2 + 36a + 78]

Then the expression is:

3c(a-4)+3d(a+5) = 3*(a^3 - 12a^2 + 46a - 56) + 3*[4a^2 + 36a + 78]

                           = 3*(a^3 - 12a^2 + 46a - 56 + 4a^2 + 36a + 78)

                           = 3*(a^3 - 8a^2 + 102a + 22)

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Answer:

[tex]\huge\boxed{\sf Perimeter = 42\ cm}[/tex]

Step-by-step explanation:

Here,

Perimeter = 7 cm + 7 cm + 7 cm + 7 cm + 7 cm + 7 cm

[tex]\rule[225]{225}{2}[/tex]

Answer:

The slope is 4.

Step-by-step explanation:

y=mx+b says that m is the slope and b is the y intercept. So this means slope=4 and int = 8.

Answer: 4

Step-by-step explanation:

        This question is given to us in slope-intercept form. This is written as y = mx + b. The slope is the m variable, y = mx + b.

        Using the equation given, the slope is;

                 y = 4x + 8 ➜ m = 4

I will have 11 cookies remaining.

The expression will be; Y = 33 - X

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. A linear equation can have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on.

For the first batch

Total = 36 - 33 (collected by dad)

Total = 33

Second batch

Let remainder = Y

Y = 33 - X

where X = teachers part

To find the remainder, X = 2/3 x Total

X = 2/3 x 33

X = 22

Therefore;

Y = 33 - 22

Y = 11

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Answer:

53

Step-by-step explanation:

They're vertical angles so they equal the

Answer:

∠ VUX = 53°

Step-by-step explanation:

∠ VUX and ∠ TUS are vertically opposite angles and are congruent, so

∠ VUX = 53°

Answer:

-3.5,-3,-2[tex]\frac{1}{2}[/tex], -2,2.5

Step-by-step explanation:

For numbers that are negative, the larger the number is the lesser the value is. For numbers that are positive, the larger the number is the larger is value is. Positive numbers are always greater than negative numbers.

Answer:

-3.5 | -3 | -2[tex]\frac{1}{2}[/tex] | -2 | 2.5 |

Step-by-step explanation:

Negative number are smaller than positive numbers so 2.5 is the largest number. Negative numbers are kind of opposite of positive numbers. The larger the negative number is, the smaller it is. With positive numbers, the larger the number, the larger the value is.

The maximum number of boxes in each pack is 9, and:

To find the greatest number of boxes in each pack, we need to find the largest common factor between the given numbers.

We know that:

We can decompose these numbers as a product between their prime factors, we will get:

18 = 2*3*3

36 = 2*2*3*3

45 = 5*3*3

You can see that the largest common factor is 3*3 = 9

So the maximum number of boxes that each pack can have is 9 boxes.

In that case:

Garth bought 18/9 = 2 packs.

Rico bougth 36/9 = 4 packs.

Mia bought 45/9 = 5 packs.

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