A sports company wants to package a ball with a 1.5-inch radius in sets of two. They have two options: a cylinder or a square prism.


The company wants to use the package that has the least amount of wasted space. The company should choose

a.)the prism because it has approximately 11.6 in.3 less wasted space than the cylinder.
b.)the prism because it has approximately 14.1 in.3 less wasted space than the cylinder.
c.)the cylinder because it has approximately 11.6 in.3 less wasted space than the prism.
d.)the cylinder because it has approximately 14.1 in.3 less wasted space than the prism.

The correlation of two pairs of data values tells about the degree of movement(along or opposite) that can occur. The correct option is A, C, and D.

The correlation of two pairs of data values tells about the degree of movement(along or opposite) that can occur in one of the data values when another data value is increased or decreased respectively.

The relationships that would most likely be causal are:

A.) A positive correlation between depth under water and pressure.

This is a casual relationship since the water pressure increases with depth, and can be observed while swimming in a deep swimming pool.

C.) A positive correlation between a puppy’s age and weight.

This is a casual relationship because as the puppy grows, its weight as well as its size both increase.

E.) A negative correlation between temperature and snowboards sold

This is a casual relationship because as the temperature increases fewer people prefer going out snowboarding.

Hence, the correct option is A, C, and D.

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Answer:cos(S) =  

60

65

Step-by-step explanation:

Answer:

D.[tex]Cos S=\frac{60}{65}[/tex]

Step-by-step explanation:

We are given that in triangle RST, RS=65 and ST=60

We have to find the equation that could be used to find the value of angle S.

We know that

[tex]cos\theta=\frac{Base}{Hypotenuse}[/tex]

Base=ST=60 units

Hypotenuse=RS=65 units

[tex]\theta=S[/tex]

Substitute the values in the given formula

Then, we get

[tex]Cos S=\frac{60}{65}[/tex]

Hence, option D is true.

Answer:

  ? = 14

Step-by-step explanation:

If ∆EFG ~ ∆CBA, we have the proportion

  FG/FE = BA/BC . . . . . any pairs of corresponding sides will have the same ratio for similar triangles. (It is convenient to put the unknown in the numerator.)

  ?/18 = 21/27 . . . . . . filling in the given numbers

Multiplying by 18, we have ...

  ? = 18·21/27

  ? = 14

_____

If the triangles are not designated as being similar, the problem is unworkable.

Answer: so bc. a length not can being minus so this mean that the width of the rectangle is equal 9 in

Answer:

ASA

Step-by-step explanation:

One pair of corresponding angles (in the bottom left/right) are already marked for us, and we're also given a pair of corresponding sides (the 8cm ones on the left and right). The two triangles have one more angle in common too - the one they're overlapping on the top corner. So, we have:

- Two pairs of congruent corresponding angles, and

- A pair of congruent corresponding sides between them,

which is enough information to call the triangles congruent by Angle-Side-Angle (ASA).

Answer:

  3|x|

Step-by-step explanation:

√(x^2) = |x|, the positive root. Multiplying this by 3, you get ...

  3√(x²) = 3|x|

Answer:

23%

Step-by-step explanation:

156 / 678 * 100 = 23%

The correct answer is 23%

Final answer:

Joshua brought about 23% of his LEGOs to Emily's house, which is calculated by dividing 156 (the number of LEGOs he brought) by 678 (the total number he owns) and then multiplying by 100.

Explanation:

To find what percentage of LEGOs Joshua brought to Emily's house, you divide the number of LEGOs Joshua brought by the total number of LEGOs he owns and then multiply the result by 100.

The formula to find the percentage is:

(Number of items of interest ÷ Total number of items) × 100 = Percentage

So in this case, it would be:

(156 ÷ 678) × 100

First, you perform the division:

156 ÷ 678 = 0.23 (rounded to two decimal places)

Then multiply by 100 to find the percentage:

0.23 × 100 = 23%

Therefore, Joshua brought about 23% of his LEGOs to Emily's house.

The answer is D

Let x = -2

f(-2) = 8 - 4(-2)

f(-2) = 8 + 8

f(-2) = 16

D is the answer.

If f(-2)=16 which could be the equation for f(x) f(x)=8-4x will yield f(-2)=16

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

Given

Let x = -2

f(-2) = 8 - 4(-2)

f(-2) = 8 + 8

f(-2) = 16

therefore, f(x)=8-4x will yield f(-2)=16

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Answer:

[tex](x-3)^2+(y+4)^2=9[/tex]

Step-by-step explanation:

The equation of a circle with center at (h,k) and radius r units is found using:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

The given circle is centered at the (3,-4) and has radius 3 units,

The equation of this circle is obtained by substituting the given values.

This gives us:

[tex](x-3)^2+(y--4)^2=3^2[/tex]

We simplify to get:

[tex](x-3)^2+(y+4)^2=9[/tex]

Answer:

(x-3)2+(y-4)2=9

Step-by-step explanation:

Answer: C. 41

Step-by-step explanation:

The quadratic function is:

 [tex]f(x) = 6x^2-13[/tex]

Then, to find [tex]f(-3)[/tex] you need to substitute the input value [tex]x=-3[/tex] into the quadratic function, to obtain the corresponding output value.

Then, when [tex]x=-3[/tex] the  output value is:

[tex]f(x) = 6x^2-13[/tex]

[tex]f(-3) = 6(-3)^2-13[/tex]

[tex]f(-3) = 6(9)-13[/tex]

[tex]f(-3) = 41[/tex]

This matches with the option C.

Answer:

-4

Step-by-step explanation:

Please write f(x) as 6x^2 - 13; " ^ " indicates exponentiation.

With f(x) = 6x^2 - 13, we substitute -3 for x in both instances:

f(-3)       =(-3)^2 - 13 = 9 - 13  = -4

Answer:

im on the same question

the 23rd term would be 71. try using the website * m a t h w a y *and you can find answers like this.

hope i helped :)

Answer: Your answer is 71 and the other answerer is right m a t h w a y is really helpful with algebra and math questions.

Answer:488

Multiply 12.20 and 40

Answer:

20 students

Step-by-step explanation:

The percentage of students scoring a B or A = 38 + 25 = 63%

We need to evaluate 63% of the 32 students who did the test

(63/100)*32 = 20.16

Therefore, approximately 20 students earned a B or higher

Answer:

20

Step-by-step explanation:

The percentage of students gaining an A or B = 38 + 25 = 63%

Calculate 63% of the 32 students

63% = [tex]\frac{63}{100}[/tex] = 0.63, hence

0.63 × 32 ≈ 20

Answer:

Answer: The slope is 2. The y-intercept is 4 which means point (0, 4).

Step-by-step explanation:

First, find the slope of the line that passes through those two points using the slope formula.

[tex] slope = m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]

where the points are [tex] (x_1, y_1) [/tex] and [tex] (x_2, y_2) [/tex]

[tex] slope = m = \dfrac{18 - 4}{7 - 0} = \dfrac{14}{7} = 2 [/tex]

The slope is 2.

One of the given points is (0, 4). Since the y-intercept lies on the y-axis, the x-coordinate of the y-intercept is 0. Point (0, 4) is the actual y-intercept.

Answer: The slope is 2. The y-intercept is 4, or point (0, 4).

To find the slope, use the S=(y2 - y1)/(x2 - x1) formula

S=(18-4)/(7-0)

S=14/7

S=2

After finding the slope, us the intercept formula to find the intercept

m is the slope

y-y1=m(x-x1)

y-4=2(x-0)

y=2x+4

Answer:

option c

Step-by-step explanation:

The object reaches -200 degrees C at 15 hrs, coldest temperature it ever achieved

Answer:

The correct option is C.

Step-by-step explanation:

It is given that the temperature of the material in degrees Celsius, y, can be modeled by the following graph, where x represents the time, in hours.

From the given graph it is clear that  

1. The y-intercept is 40, so the initial temperature is 40 degree Celsius.

2.The vertex of the upward parabola is at (15,-200), so material's temperature reaches a minimum -200 degrees Celsius at 15 hours.

3. The material return to its initial temperature after 30 hours because the temperature is 40 degree Celsius at x=30.

Therefore the correct option is C.

Answer:

5 inch

Step-by-step explanation:

The frames are proportional, so we can set the ratios equal:

width / height = width / height

3 / h = 9 / 15

9h = 45

h = 5

Given the proportionality between two pictures one with width 3 inches and another with dimensions 9 inches by 15 inches, we can set up a ratio and solve for the unknown length, yielding the length of the picture frame as 5 inches.

The question is asking to find the length of a picture frame, given that its width is 3 inches and that it has the same proportions as a picture that is 9 inches wide and 15 inches long. The proportions can be used to set up a ratio, as follows:

To solve for x, cross-multiply: 3 inches * 15 inches = 9 inches * x.

Then, divide by 9 to solve for x: 45 inches/9 = 5 inches.

So, the length of the picture frame whose width is 3 inches would be 5 inches, if it shares the same proportions as the 9 inch wide by 15 inch long picture.

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Answer:

2x^2+x-4=0

x^2+\dfrac12x-2=0

x^2+\dfrac12x+\dfrac1{16}-\dfrac{33}{16}=0

\left(x+\dfrac14\right)^2=\dfrac{33}{16}

x+\dfrac14=\pm\dfrac{\sqrt{33}}4

x=\dfrac{-1\pm\sqrt{33}}4

Step-by-step explanation: lol tooooo much ∅∞

Answer:

1/2 and -2 are the first answers to the question

1/16 and 1/16 are the next answers  

1/4 and 33/16 are the last ones

and for the multiple choice answer which is last is A

Step-by-step explanation:

Answer:

the answer is C 0.75 to 1.0

Over the intervals 0.25 to 0.5, 0.5 to 0.75, and 0.75 to 1.0, the exponential and linear functions are approximately equal.

To determine over which interval the exponential and linear functions are approximately the same, we first need to define the functions. Let's denote the exponential function as [tex]\( f(x) = e^x \)[/tex] and the linear function as ( g(x) = mx + c ), where ( m ) is the slope and ( c ) is the y-intercept.

Given the intervals, we'll first need to calculate the values of the exponential function at the endpoints of each interval and then find the linear function that best approximates those values. We'll choose the linear function with the same value at the starting point of each interval and approximate the slope ( m ) based on the difference in the exponential function values at the endpoints of the interval.

Let's start with each interval:

1. Interval from 0.25 to 0.5:

  - Endpoint 1:[tex]\( f(0.25) = e^{0.25} \approx 1.284 \)[/tex]

  - Endpoint 2: [tex]\( f(0.5) = e^{0.5} \approx 1.649 \)[/tex]

  - Approximating a linear function starting at ( f(0.25) ):

  [tex]- \( m = \frac{f(0.5) - f(0.25)}{0.5 - 0.25} = \frac{1.649 - 1.284}{0.5 - 0.25} \approx 0.73 \)[/tex]

[tex]- \( c = f(0.25) \approx 1.284 \)[/tex]

    - So, the linear function is [tex]\( g(x) \approx 0.73x + 1.284 \)[/tex]

2. Interval from 0.5 to 0.75:

  - Endpoint 1:[tex]\( f(0.5) = e^{0.5} \approx 1.649 \)[/tex]

  - Endpoint 2: [tex]\( f(0.75) = e^{0.75} \approx 2.117 \)[/tex]

  - Approximating a linear function starting at ( f(0.5) ):

  [tex]- \( m = \frac{f(0.75) - f(0.5)}{0.75 - 0.5} = \frac{2.117 - 1.649}{0.75 - 0.5} \approx 0.934 \)[/tex]

 [tex]- \( c = f(0.5) \approx 1.649 \)[/tex]

    - So, the linear function is [tex]\( g(x) \approx 0.934x + 1.649 \)[/tex]

3. Interval from 0.75 to 1.0:

  - Endpoint 1: [tex]\( f(0.75) = e^{0.75} \approx 2.117 \)[/tex]

  - Endpoint 2: [tex]\( f(1.0) = e^{1.0} \approx 2.718 \)[/tex]

  - Approximating a linear function starting at ( f(0.75) ):

 [tex]- \( m = \frac{f(1.0) - f(0.75)}{1.0 - 0.75} = \frac{2.718 - 2.117}{1.0 - 0.75} \approx 1.202 \)[/tex]

 [tex]- \( c = f(0.75) \approx 2.117 \)[/tex]

    - So, the linear function is [tex]\( g(x) \approx 1.202x + 2.117 \)[/tex]

4. Interval from 1.25 to 1.5:

  - Endpoint 1:[tex]\( f(1.25) = e^{1.25} \approx 3.490 \)[/tex]

  - Endpoint 2: [tex]\( f(1.5) = e^{1.5} \approx 4.482 \)[/tex]

  - Approximating a linear function starting at ( f(1.25) ):

   [tex]- \( m = \frac{f(1.5) - f(1.25)}{1.5 - 1.25} = \frac{4.482 - 3.490}{1.5 - 1.25} \approx 3.946 \)[/tex]

    - [tex]\( c = f(1.25) \approx 3.490 \)[/tex]

    - So, the linear function is[tex]\( g(x) \approx 3.946x + 3.490 \)[/tex]

Now, we can compare each linear approximation to the exponential function within its respective interval:

1. For the interval from 0.25 to 0.5, the linear function [tex]( g(x) \approx 0.73x + 1.284 \)[/tex] is approximately equal to the exponential function [tex]\( f(x) = e^x \).[/tex]

2. For the interval from 0.5 to 0.75, the linear function[tex]\( g(x) \approx 0.934x + 1.649 \)[/tex] is approximately equal to the exponential function [tex]\( f(x) = e^x \).[/tex]

3. For the interval from 0.75 to 1.0, the linear function [tex]\( g(x) \approx 1.202x + 2.117 \)[/tex] is approximately equal to the exponential function [tex]\( f(x) = e^x \).[/tex]

4. For the interval from 1.25 to 1.5, the linear function [tex]\( g(x) \approx 3.946x + 3.490 \)[/tex] is not approximately equal to the exponential function [tex]\( f(x) = e^x \).[/tex]

So, the exponential and linear functions are approximately the same over the intervals from 0.25 to 0.5, 0.5 to 0.75, and 0.75 to 1.0.

Answer:

C  x=6

Step-by-step explanation:

sqrt(x+3) = x-3

Square each side

(sqrt(x+3))^2 = (x-3)^2

x+3 = (x-3)^2

x+3 = (x-3)(x-3)

FOIL

x+3 = x^2 -3x-3x+9

Combine like terms

x+3 = x^2 -6x+9

Subtract x from each side

x-x+3 = x^2 -6x-x +9

3 =  x^2 -7x +9

Subtract 3 from each side

3-3 =  x^2 -7x +9-3

0 = x^2 -7x+6

Factor

0 = (x-6)(x-1)

Using the zero product property

x-6=0   x-1 =0

x=6  x=1

Since we squared we need to check for extraneous solutions

x=1

sqrt(1+3) = 1-3

sqrt(4) = -2

2=-2

False

Extraneous

x=6

sqrt(6+3) = 6-3

sqrt(9) = 3

3=3

True   solutions

Answer: Option C.

Step-by-step explanation:

First, we need to square both sides of the equation:

[tex]\sqrt{x+3}=x-3\\\\(\sqrt{x+3})^2=(x-3)^2[/tex]

We know that:

[tex](a-b)^2=a^2-2ab+b^2[/tex]

Then, applying this, we get:

[tex]x+3=x^2-2(x)(3)+3^2\\\\x+3=x^2-6x+9[/tex]

Now we need to subtract "x" and 3 from both sides of the equation:

[tex]x+3-(x)-(3)=x^2-6x+9-(x)-(3)\\\\0=x^2-6x+9-x-3[/tex]

Adding like terms:

[tex]0=x^2-7x+6[/tex]

Factor the quadratic equation.  Find two numbers whose sum be -7 and whose product be 6. These numbers are: -1 and -6. Then:

[tex](x-1)(x-6)=0[/tex]

Then:

[tex]x_1=1\\x_2=6[/tex]

Checking the first solution is correct:

[tex]\sqrt{1+3}=1-3\\ 2=-2 \ (False)[/tex]

Checking the second solution is correct:

[tex]\sqrt{6+3}=6-3\\ 3=3 \ (True)[/tex]

Answer:

Part 1) [tex](10x+15y)^{2}=(6x+9y)^{2}+(8x+12y)^{2}[/tex]

Part 2) The answer in the procedure

Step-by-step explanation:

Part 1)

we know that

Applying the Pythagoras Theorem

[tex]c^{2}=a^{2}+b^{2}[/tex]

we have

[tex]c=(10x+15y)[/tex]

[tex]a=(6x+9y)[/tex]

[tex]b=(8x+12y)[/tex]

substitute the values

[tex](10x+15y)^{2}=(6x+9y)^{2}+(8x+12y)^{2}[/tex]

Part 2) Transform each side of the equation to determine if it is an identity

[tex](10x+15y)^{2}=(6x+9y)^{2}+(8x+12y)^{2}\\ \\100x^{2}+150xy+225y^{2}=36x^{2}+54xy+81y^{2}+64x^{2}+96xy+144y^{2}\\ \\100x^{2}+150xy+225y^{2}=100x^{2}+150xy+225y^{2}[/tex]

The left side is equal to the right side

therefore

Is an identity

Answer:

b. [tex]\displaystyle 225y^2 + 150xy + 100x^2 = 225y^2 + 150xy + 100x^2[/tex]

a. [tex]\displaystyle [8x + 12y]^2 + [6x + 9y]^2 = [10x + 15y]^2[/tex]

Step-by-step explanation:

b. [tex]\displaystyle 225y^2 + 150xy + 100x^2 = 225y^2 + 150xy + 100x^2[/tex]

a. [tex]\displaystyle [8x + 12y]^2 + [6x + 9y]^2 = [10x + 15y]^2[/tex]

The two expressions are identical on each side of the equivalence symbol, therefore they are an identity.

I am joyous to assist you anytime.

Answer:

  x = -7

Step-by-step explanation:

The vertex form of this equation tells us it is a downward-opening parabola with its vertex at (-7, -3). The line of symmetry is the vertical line through the vertex: x = -7.

___

Vertex form is ...

  y = a(x -h) +k

where a is the vertical expansion factor, and (h, k) is the vertex. When a < 0, the parabola opens downward. When a > 0, it opens upward. (When a=0, the "parabola" is a horizontal line at y=k.)

The equation of the axis of symmetry for [tex]f(x) = -4\cdot (x+7)^{2}-3[/tex] is [tex]x = -7[/tex].

The function given in statement represents a parabola whose axis of symmetry is parallel to the y-axis. The standard form of the function is described below:

[tex]f(x) -k = C\cdot (x-h)^{2}[/tex] (1)

Where:

The equation for the axis of symmetry is of the form [tex]x = h[/tex]. By direct comparison, we determine that the equation of the axis of symmetry for [tex]f(x) = -4\cdot (x+7)^{2}-3[/tex] is [tex]x = -7[/tex].

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Answer:

jina by .1 cm

Step-by-step explanation:

3/5 = .6

caleb = 23.6

jina = 23.7

Jina's model of the Empire State Building was taller by 0.1 centimeter compared to Caleb's model.

The question is comparing the heights of two models of the Empire State Building. Jina's model is 23.7 centimeters tall. Caleb's model is 23 3/5 centimeters tall, which in decimal form is equivalent to 23.6 centimeters tall. Therefore, Jina's model is taller. The height difference between Jina's model and Caleb's model is 23.7 - 23.6 = 0.1 centimeter. So, Jina's model is 0.1 centimeter taller than Caleb's model.

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Answer:

i) 35

ii) 0.95

iii) employees’ annual earnings are strongly related to their tenure

iv) Employee earnings increase with tenure.

Step-by-step explanation:

i) The regression line for this data set has a slope close to m = 35

To find the slope of the regression line we need to find two points that lie on the line or that are very close to the line.

We have the following two points;

(1, 175) and (2.5, 225)

slope = (change in y) / (change in x)

         = (225-175)/(2.5-1) = 33.33

This is close to 35.

ii) The correlation coefficient is close to 0.95

The coefficient of correlation is a measure of the degree of association between two variables. Correlation coefficient gives information on the strength and direction of a linear association.

The scatter-plot reveals that the annual earnings and tenures of the employees of Stan & Earl Corp are strongly positively associated hence the correlation coefficient is close to 0.95.

iii) Based on this information, we can conclude that employees’ annual earnings are strongly related to their tenure.

The correlation coefficient was found to be close to 0.95. A value greater than 0.7 shows a strong degree of association between two variables. Therefore, employees’ annual earnings are strongly related to their tenure

iv) Employee earnings increase with tenure.

The slope of the regression line of the data set was found to be close to 35. A positive slope implies that the response variable increases with increase in the explanatory variable.

Nevertheless, the correlation coefficient was also found to be positive which suggests a positive association between employee earnings and tenure.

Answer:

The regression line for this data set has a slope close to m = (35) , and the correlation coefficient is close to (0.95) .

Based on this information, we can conclude that employees’ annual earnings are (strongly related) to their tenure. Employee earnings (increase with) tenure.

Step-by-step explanation:

Answer:

y = 2.4

Step-by-step explanation:

Given y varies inversely with x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

To find k use the condition y = 8 when x = 3

k = yx = 8 × 3 = 24

y = [tex]\frac{24}{x}[/tex] ← equation of variation

When x = 10, then

y = [tex]\frac{24}{10}[/tex] = 2.4

The variation is an illustration of inverse variation, and the value of y when x = 10 is 2.4

The variation is an inverse variation.

An inverse variation is represented as:

k = xy

Rewrite as:

x₁y₁ = x₂y₂

When y = 8, x = 3; we have:

3 * 8 = x₂y₂

This gives

24 = x₂y₂

When x = 10; we have:

24 = 10 * y

Divide both sides by 10

y = 2.4

Hence, the value of y when x = 10 is 2.4

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Formula for degree to radian:

degree ×[tex]\frac{\pi }{180}[/tex]

so...

[tex]280* \frac{\pi }{180}[/tex]

Exact answer:

[tex]\frac{14\pi }{9}[/tex]

Rounded answer:

4.89

Hope this helped!

Answer:

Midpoint Formula is (x1+x2/2, y1+y2/2)

(-3+4/2, -5+4/2)

Midpoint is (1/2, -1/2)

Step-by-step explanation:

The length of the hypotenuse of a right triangle with legs of 5 cm and 12 cm is 13 cm.

The length of the hypotenuse of a right triangle can be found by using the Pythagorean theorem. The theorem states that the square of the hypotenuse is equal to the sum of the squares of the two legs.

In this case, we have a right triangle with legs of 5 cm and 12 cm. To find the length of the hypotenuse, we can use the formula c = √(a² + b²).

Substituting the given values, we get c = √(5² + 12²) = √(25 + 144) = √169 = 13 cm.

Answer:

1

Step-by-step explanation:

Count the amount of dots given. There are 20 dots in all. To find the middle value, set the numbers in a line first.

0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 4, 4, 4, 5

Find the middle value. Note that the two middle values are both 1. Find the mean of the two values.

1 + 1 = 2

2/2 = 1

1 is your median .

~

Answer:

1

Step-by-step explanation:

If you go in from left to right starting on the left side on the top of the dots (0) and start from the right side on the bottum and go up (5) and you slowly work your way up to the top, you get the answer 1.

Answer:

Radius of the ball is approximately 6.5 cm to the nearest tenth

Explanation:

The ball has the shape of a sphere

Surface area of a sphere can be calculated using the following rule:

Surface area of sphere = 4πr² square units

In the given problem, we have:

Surface area of the ball = 531 cm²

Substitute with the area in the above equation and solve for the radius as follows:

[tex]531 = 4\pi r^2\\ r^2=\frac{531}{4\pi } = 42.255 \\ \\ r=\sqrt{42.255}=6.5004 cm[/tex] which is approximately 6.5 cm to the nearest tenth

Hope this helps :)