This Stem-and-Leaf Plot represents test scores of students in a math class. If two test scores, 68 and 75, are added to the data, which statement will be true?

A. The median will change; the mode will stay the same.
B. The mode will change; the median will stay the same.
C. The median and the mode will both change.
D. The median and the mode will stay the same.

The height of the cylinder is 4 x units.

The area of the cylinder’s base is One-fourthπx2 square units .

What is the volume of cylinder?

We know the volume of a cylinder is given by the formula  π r2 h, where r is the radius of the cylinder and h is the height.

Formula for volume of the cylinder

V = r² π h

Volume of the cylinder= πx³

Diameter=x

Radius (r)=diameter/2

       r  =  x/2

     V = r² π h

   πx³=(x/2)² πh

πx³= (x²/4)πh

Divide both sides by π

x³ =(x²/4)h

Make h the subject of the formula

  h = x³ ÷ x²/4

     =x³ ×4 / x²

     =4x³ / x²

     =4 * x * x * x / x * x

  h=4x

Area of the base:

B = r² π

r=x/2

B=(x/2)² * π

 =(x²/4)π

=πx²/4

=1/4(πx²)

Therefore, The area of the cylinder’s base is One-fourthπx2 square units.

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The complete question is -

A cylinder with a base diameter of x units has a volume of πx3 cubic units. A cylinder with a base diameter of x units has a volume of pi x cubed cubic units. Which statements about the cylinder are true? Select two options. The radius of the cylinder is 2x units. The area of the cylinder’s base is One-fourthπx2 square units. The area of the cylinder’s base is One-halfπx2 square units. The height of the cylinder is 2x units. The height of the cylinder is 4x units.

Answer:

70

Step-by-step explanation:

the 30/100 of 100 is 30

So 100-30=70

Answer:

70kg

Step-by-step explanation:

30% of 100kg is

--> 100 x 30/100 which is 30kg.

If you want to decrease 100kg by 30%, you can take away 30kg from 100kg.

--> 100 - 30 = 70

So 70kg is the remainder.

52.94% of the viewers prefer videos on a mobile or laptop device

The given parameters are

Viewers that prefer videos on a mobile or laptop device = 18

Total number of viewers = 34

The percentage of voters in this category is then calculated as

Percentage = 18/34 * 100%

Evaluate the expression

Percentage = 52.94%

Hence, 52.94% of the viewers prefer videos on a mobile or laptop device

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The point F as described in the task content is at point; 0.6 on the number line.

Since it follows from.tge task content that; point D is at -3, and point E Is at 6, it follows that the length of segment, DE is; |-3-6| = 9.

Consequently, since the ratio of Df to FE ls 2:3

It follows that point F is at -3 + (2/5) × 9.

Point F is therefore at 0.6 on the number line.

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \: \angle1 \cong \angle2[/tex]

( by corresponding angle pair )

[tex]\qquad❖ \: \sf \: \angle2 \cong \angle3[/tex]

( given in the question )

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \: \angle1 \cong \angle3[/tex]

Answer:

626.7 [tex]cm^{2}[/tex]

Step-by-step explanation:

Consider the figure as a circle with radius 7.5 and a rectangle with width 30 and length 15.

CIRCLE

A = pi*r*r = pi*7.5*7.5 = 56.25pi =176.7

RECTANGLE

A = l*w = 15*30 = 450

176.7 + 450 = 626.7 [tex]cm^{2}[/tex]

Answer: 626.7cm^2

Step-by-step explanation:

30 * 15 = 450

area of circle = πr^2

r = 15/2 = 7.5

[tex]7.5^2=56.25*pi=176.7[/tex]

450+176.7 = 626.7

The correct statement comparing the theoretical and experimental probabilities is given as follows:

[tex]\frac{1}{4} < \frac{7}{25}[/tex].

A probability is given by the number of desired outcomes divided by the number of total outcomes.

The theoretical probability is taken before any experiment. Since the four sections are equal, the theoretical probability is:

T(H) = 1/4.

The experimental probability is taken considering previous experiments. Out of 100 tosses, 28 landed on H, hence:

E(H) = 28/100 = 7/25.

Hence the correct statement is:

[tex]\frac{1}{4} < \frac{7}{25}[/tex].

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Answer:

C. B=38.8, C=95.2, c=42.9

Step-by-step explanation:

Find B by using sine rule

sin 46/31=sin B/27

sin B= 27 sin 46/31

B=sin‐¹(0.627)

B=38.8

Find C

C= 180-(A+B)

C=180-(38.8+46)

C=95.2

Using sine rule, Find c

31/sin 46=c/sin 95.2

c=31 sin 95.2/sin 46

c=42.9

The length of ED is half the length of AB.

Reasons:

The given parameters are;

In ΔABC, point E is the midpoint of AC

The midpoint of BC is the point D

Segment ED = s

Segment CE = p

Segment EA = r

Segment CD = q

Segment DB = t

Segment ED = s

Segment AB = u

Required:

The expression that represents the value of [tex]s[/tex].

Solution:

CE = 0.5 × AC Definition of midpoint

CD = 0.5 × CB Definition of midpoint

Therefore, we have;

[tex]\frac{CE}{AC} =\frac{CD}{CB} =0.5[/tex]

Therefore, given that ∠C ≅ ∠C, by the reflexive property, we have;

ΔABC is similar to ΔCDE by Side-Angle-Side similarity

Which gives;

[tex]\frac{CE}{AC} = \frac{CD}{CB} = \frac{ED}{AB} =0.5=\frac{1}{2}[/tex]

ED = s and AB = u which gives;

[tex]\frac{ED}{AB}=\frac{s}{u} =0.5=\frac{1}{2}[/tex]

[tex]\frac{s}{u} =\frac{1}{2}[/tex]

Which gives:

[tex]s=\frac{1}{2} *u[/tex]

The expression that represents the value of s is; s = one-half u

Therefore, the length of ED is half the length of AB.

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The question you are looking for is here:

If point E is the midpoint of segment AC and point D is the midpoint of segment BC, which expression represents the value of s? triangle CAB, point E is on segment AC between points A and C and point D is on segment BC between points B and C, creating segment ED, CE equals p, EA equals r, CD equals q, DB equals t, ED equals s, and AB equals u s equals p over q s = one half s equals q over p s = 2u

The inverse function of [tex]A(b) = 12 \cdot \frac{b + 9}2[/tex] is b(a) = a/6 - 9

The function is given as:

[tex]A(b) = 12 \cdot \frac{b + 9}2[/tex]

Divide 12 by 2

[tex]A(b) = 6 \cdot (b + 9)[/tex]

Rewrite the function as

[tex]a = 6 \cdot (b + 9)[/tex]

Divide both sides by 6

a/6 = b + 9

Subtract 9 from both sides

b = a/6 - 9

Express as a function

b(a) = a/6 - 9

Hence, the inverse function of [tex]A(b) = 12 \cdot \frac{b + 9}2[/tex] is b(a) = a/6 - 9

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Answer:

-1,-3,-4 it is just subtracting the same amount.

Step-by-step explanation:

The expression that is not a rational expression is:

[tex]\frac{(x + 3)(2x - 1)}{x + 3}[/tex]

A rational expression is an expression that has a variable in the denominator.

For expression [tex]\frac{(x + 3)(2x - 1)}{x + 3}[/tex], x + 3 is a common term to the numerator and denominator, hence it is simplified to 2x - 1 and is not a rational expression.

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The option that is not a rational expression is [tex]\frac{3x + 4\sqrt{x} -7}{2x+2}[/tex]

Rational expression are fraction whose numerator and denominator are polynomials.

In other words, rational expression is the ratio of two polynomials.

Therefore, an example of a ration expression is as follows:

[tex]\frac{x^{2}+9 }{x + 1}[/tex]

Therefore, the option that is not a rational expression is as follows;

[tex]\frac{3x + 4\sqrt{x} -7}{2x+2}[/tex]

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Combining the like terms, the simplified polynomials are given as follows:

a) 4x² - 14x + 17

b) -5x² - 20x + 8

Polynomials are simplified combining the like terms, that is, adding these numbers with the same variable.

Item a:

4(x - 2)(x + 1) - 5(2x - 5)

Applying the distributive property:

4(x² - x - 2) - 10x + 25

4x² - 4x - 8 - 10x + 25

Combining the like terms:

4x² - 4x - 10x - 8 + 25

4x² - 14x + 17

Item b:

-5(x + 2)² + 28

-5(x² + 4x + 4) + 28

-5x² - 20x - 20 + 28

-5x² - 20x + 8

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The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation. Dilation preserves only the shape.

Polygon ABCD has vertex at A(1, 1), B(2, 3), C(5, 4), and D(4, 2).

Slope of CD = (2 - 4) / (4 - 5) = 2

Polygon ABCD is dilated by a scale factor of 8 with the origin resulting in the image A′B′C′D′.

Slope of C'D' = slope of CD (because preserves shape) = 2

The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2

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The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2

What is transformation?

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation. Dilation preserves only the shape.

Polygon ABCD has vertex at A(1, 1), B(2, 3), C(5, 4), and D(4, 2).

Slope of CD = (2 - 4) / (4 - 5) = 2

Polygon ABCD is dilated by a scale factor of 8 with the origin resulting in the image A′B′C′D′.

Slope of C'D' = slope of CD (because preserves shape) = 2

The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2

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Answer:

[tex]\sf Tan \ D = \dfrac{4}{3}[/tex]

Step-by-step explanation:

Trigonometry ratios:

       [tex]\sf \boxed{\bf \tan \ D =\dfrac{opposite \ side \ of \ \angle \ D}{adjacent \ side \ of \ \angle D}}[/tex]

                   [tex]\sf =\dfrac{BC}{DC}\\\\ =\dfrac{32}{24}\\\\=\dfrac{4}{3}[/tex]

Answer:

( x-3) ^2 + ( y-1) ^2 = 4

Step-by-step explanation:

The equation for a circle is given by

( x-h)^2 + ( y-k) ^2 = r^2  where (h,k) is the center and r is the radius

( x-3) ^2 + ( y-1) ^2 = 2^2

( x-3) ^2 + ( y-1) ^2 = 4

Percentage for lakeside is 38%

Percentage for Jungle is 26%

Percentage for Desert is 18%

Percentage for Coast is 12%

Percentage for Prairie is 6%

To determine the percentage, divide the given value by the total number and multiply by 100

Total  = 24000

Percentage for lakeside = [tex]\frac{9120}{24000}[/tex] × 100

% of lakeside = [tex]0. 38[/tex] × 100 = 38%

Percentage for Jungle = [tex]\frac{6240}{24000}[/tex] × 100

% of Jungle = [tex]0. 26[/tex] × 100 = 26%

Percentage for Desert = [tex]\frac{4320}{24000}[/tex] × 100

% of Desert = [tex]0. 18[/tex] × 100 = 18%

Percentage for Coast = [tex]\frac{2880}{24000}[/tex] × 100

% of coast = [tex]0. 12[/tex] × 100 = 12%

Percentage for Prairie = [tex]\frac{1440}{24000}[/tex] × 100

% of Prairie = [tex]0. 06[/tex] × 100 = 6%

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Answer:

  (c)  25/4

Step-by-step explanation:

A perfect square trinomial is obtained by "completing the square." The constant in a perfect square trinomial is the square of half the x-coefficient.

A "perfect square trinomial" is the square of a binomial.

  (x +a)² = x² +2ax +a²

Of note here is that the constant (a²) is the square of half of the x-term coefficient:

  ((2a)/2)² = a²

The given expression (x² +5x) has an x-term coefficient of 5. The square of half that is ...

  (5/2)² = 25/4

The constant that must be added to make x² +5x into a perfect square trinomial is 25/4.

  (x² +5x) +25/4 = x² +5x +25/4 = (x +5/2)²

The total amount of Chandra's investments after 8 years is $110.03

The formula for calculating the compound interest is expressed as;

A = P(1+r/n)^nt

where

P is the amount invested = $75

r is the rate. = 0.048

t is the time =8years

n = 12 (monthly)

Substitute

A = 75(1+0.048/12)^96
A = 75(1.467)
A = 110.03

Hence the total amount of Chandra's investments after 8 years is $110.03

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The NBA league exhibits more competitive balance.

The chance that each team in a league has of winning the title is referred to as competitive balance. The championship would be won by each team on a regular basis in an ideal competitive environment. In contrast, if there was no balance between the two types of competition, the same team would consistently prevail.

Competitive balance is often regarded as a desirable trait because too much predictability makes fans of the lesser franchises angry and fans of the defending champions complacent, which lowers interest in the sport as a whole.

The "Noll-Scully" measure is the competitive balancing metric that is most frequently used in sports. The winning percentage of each league team's standard deviation (SD) is used to compute it. The SD is then divided by what it would be if all teams had equal talent and the outcomes were entirely random.

For NBA team, competitive balance = 0.134/32*82 = 0.343

For EPL team, competitive balance = 0.158/20*38 = 0.30

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If the radius of sector is 12 centimeters and angle of 65 degrees then the arc's length is 13.6 cm.

Given a sector has a radius of 12 cm and an angle 65 degrees.

We have to calculate arc's length.

We know that arc's length is equal to Θr where Θ is in radians.

We have been given angle in degrees ,so we have to convert degrees in radians.

Angle=65*π/180=13π/36

length of arc =Θr

Putting the values in the formula above :

length =13π/36*12

=13*3.14/3

=40.82/3

=13.6

Hence if the radius of sphere is 12 cm and angle 65 degrees then the length of arc of sphere is 13.6 cm.

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Answer:

Step-by-step explanation:

Answer:

  (2)  A=4, B=0, C=9 . . . (4x = 9)

Step-by-step explanation:

A linear equation in standard form has mutually prime integer coefficients with a positive leading coefficient.

The values that would be the appropriate values for an equation to be in standard form (Ax + By = C) is A = 4, B = 0 and C = 9.

The linear equation is the equation which has the coefficient as the mutual prime numbers and the coefficient must be the positive leading coefficient.

From the choices,

Therefore, the values that would be the appropriate values for an equation to be in standard form as it lead to positive leading coefficient and mutual prime is A = 4, B = 0 and C = 9.

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A $2.00 base fare charge, and per-mile, and per-minute rates related as follows; 3•x + 7•y = 6.5 and 7•x + 14•y = 14, give the distance traveled in the third ride as 4.5 miles

The base fare = $2.00

Let x represent the per-mile rate, and let y represent the per-minute rate, we have;

The cost of Ryan's first taxi ride = $8.50

Distance traveled in the first ride = 3.0 miles

Time taken during the first ride = 7 minutes

Therefore;

2 + 3•x + 7•y = 8.5

Which gives;

3•x + 7•y = 8.5 - 2 = 6.5

Distance traveled in the second ride = 7.0 miles

Duration of the second ride = 14 minutes

The second ride cost = $16.00

Therefore;

2 + 7•x + 14•y = 16

Which gives;

7•x + 14•y = 16 - 2 = 14

Solving the above simultaneous equations by multiplying equation (1) by 2 then subtracting the result from equation (2) gives;

(7•x + 14•y) - 2 × (3•x + 7•y) = 14 - 2×6.5 = 1

x = 1

3•x + 7•y = 6.5

7•y = 6.5 - 3•x

7•y = 6.5 - 3×1 = 3.5

y = 3.5/7 = 1/2 = 0.5

Duration of the third taxi ride = 10 minutes

Cost of the third ride = $13.50

Therefore;

2 + 1×a + 10×y = $13.50

Where a is the distance traveled during the third ride, we have;

2 + 1×a + 10×0.5 = $13.50

2 + a + 5 = 13.5

a = 13.5 - 2 - 7 = 4.5

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Answer:

∠ABE = 33°

Step-by-step explanation:

        Angle bisector is a straight line that divides the angle into two congruent (equal) angles.

So, BE bisects the ∠ABD into two equal angles.

⇒∠ABE will be half of ∠ABD

∠ABD = ∠ABE + ∠BED

66°     = ∠ABE + ∠ABE

66      = 2∠ABE

∠ABE = 66/2

∠ABE = 33°

The factorization that could represent the number of water bottles and weight of each water bottle is 12(5x^2 + 4x + 2). Option B

The term factorization has to do with the process of obtaining common factors in an expression. It involves dividing each term in the expression with a factor that is common to all the terms in the expression.

The factorization that could represent the number of water bottles and weight of each water bottle is 12(5x^2 + 4x + 2).

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Missing parts;

Mara carried water bottles to the field to share with her team at halftime. The water bottles weighed a total of 60x2 + 48x + 24 ounces. Which factorization could represent the number of water bottles and weight of each water bottle? 6(10x2 + 8x + 2) 12(5x2 + 4x + 2) 6x(10x2 + 8x + 2) 12x(5x2 + 4x + 2)

20 years is the answer.

A= R(1+r)^ t

A-415    

R=230

r=3%

415=230 (1+3%)^ t

t=log1.03  315/230

t=19.89 (use calculator)

David will invest at least 20 years.

An investment is a dedication of an asset to achieve an increase in value over a period of time. Investing requires the sacrifice of current assets such as time, money and effort. In finance, the purpose of an investment is to generate a profit on the invested asset

The most common example of an investment type. Investment is generally what you want to use in the future with the aim of generating regular cash flow or increasing the value of something over time so that you can sell it at a higher price than you purchased.

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The missing digit for the American Express Traveler's Check identification number is option (C) 6 is the correct answer.

In this question,

A Check Digit is a decimal (or alphanumeric) digit added to a number for the purpose of detecting the sorts of errors humans typically make on data entry.

A check digit is a digit added to a string of numbers for error detection purposes. Normally, the check digit is computed from the other digits in the string. A check digit helps digital systems detect changes when data is transferred from transmitter to receiver.

The last digit of a bar code number is a calculated check digit. The check digit is calculated from all the other numbers in the bar code and helps to confirm the integrity of your bar code number.

The American Express Traveler's Check identification number is 783920*814.

In Airline tickets, there are several digits plus a check digit.

Divide the ID number by 7. The check digit is the remainder.

Sum of digits = 7+8+3+9+2+0+8+1+4

⇒ 42

Now divide the sum by 7, the remainder is

⇒ 42 mod 7 = 42 - (5×7)

⇒ 42 mod 7 = 6

Hence we can conclude that the missing digit for the American Express Traveler's Check identification number is option (C) 6 is the correct answer.

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